<div class="xblock xblock-public_view xblock-public_view-vertical" data-request-token="2a6ad6faed2111efb9010e0e3c45b88f" data-usage-id="block-v1:MITx+16.00x+2T2019+type@vertical+block@2bf978a850254f348a83df7ddef1598b" data-graded="True" data-has-score="False" data-runtime-version="1" data-block-type="vertical" data-init="VerticalStudentView" data-course-id="course-v1:MITx+16.00x+2T2019" data-runtime-class="LmsRuntime">
<h2 class="hd hd-2 unit-title">Orbital Rendezvous</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITx+16.00x+2T2019+type@html+block@4546354018124a2097b5f5d9dc4c90a8">
<div class="xblock xblock-public_view xblock-public_view-html xmodule_display xmodule_HtmlBlock" data-request-token="2a6ad6faed2111efb9010e0e3c45b88f" data-usage-id="block-v1:MITx+16.00x+2T2019+type@html+block@4546354018124a2097b5f5d9dc4c90a8" data-graded="True" data-has-score="False" data-runtime-version="1" data-block-type="html" data-init="XBlockToXModuleShim" data-course-id="course-v1:MITx+16.00x+2T2019" data-runtime-class="LmsRuntime">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "HTMLModule"}
</script>
<h2>4.6.1 Orbital Rendezvous</h2>
<p><button border-radius="2px" class="mo_button" onclick="window.location.href='/courses/course-v1:MITx+16.00x+3T2016/5e0e82a56b234a2aaf12ac0b3359c3c5#MO49';" style="cursor: pointer;" title="MO 4.9:
Describe the principles of orbital rendezvous and the distinction between ideal and actual rendezvous" type="button" id="LD">MO 4.9</button></p>
<p><img style="display: block; margin: 20px auto 20px auto;" src="/assets/courseware/v1/3fb3c460269e4fa9d3948f3125288678/asset-v1:MITx+16.00x+2T2019+type@asset+block/STS123_ISS_Rendezvous_600.jpg" alt="Space Shuttle Endeavour approaches the ISS for rendezvous and docking on STS-123" type="saveimage" target="[object Object]" /></p>
<p style="text-align: center;"><em><span style="font-family: 'Open Sans', Verdana, Arial, Helvetica, sans-serif;">Space Shuttle Endeavour approaches the International Space Station during STS-123 for rendezvous and docking operations (Image credit: NASA)</span></em></p>
<p>Orbital rendezvous is an important part of astronautics and human spaceflight. After all, it is what makes it possible for us to send astronauts to the International Space Station or service satellites such as the Hubble Space Telescope. As you will see in the following video, performing a successful orbital rendezvous requires impeccable timing and precise maneuvering.</p>
</div>
</div>
<div class="vert vert-1" data-id="block-v1:MITx+16.00x+2T2019+type@video+block@a7fd9074170d490487616b1efdddd0ec">
<div class="xblock xblock-public_view xblock-public_view-video xmodule_display xmodule_VideoBlock" data-request-token="2a6ad6faed2111efb9010e0e3c45b88f" data-usage-id="block-v1:MITx+16.00x+2T2019+type@video+block@a7fd9074170d490487616b1efdddd0ec" data-graded="True" data-has-score="False" data-runtime-version="1" data-block-type="video" data-init="XBlockToXModuleShim" data-course-id="course-v1:MITx+16.00x+2T2019" data-runtime-class="LmsRuntime">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Video"}
</script>
<h3 class="hd hd-2">Video: Orbital Rendezvous</h3>
<div
id="video_a7fd9074170d490487616b1efdddd0ec"
class="video closed"
data-metadata='{"saveStateUrl": "/courses/course-v1:MITx+16.00x+2T2019/xblock/block-v1:MITx+16.00x+2T2019+type@video+block@a7fd9074170d490487616b1efdddd0ec/handler/xmodule_handler/save_user_state", "completionEnabled": false, "ytTestTimeout": 1500, "autohideHtml5": false, "completionPercentage": 0.95, "poster": "https://mitx-edx-video-meta-storage.s3.amazonaws.com/media/video-images/b6f102411a8146438480a9727ae96354.jpeg?Signature=A6EY6zBe6kPuRv5y4K8L21xyBRU%3D&Expires=1739791519&x-amz-security-token=IQoJb3JpZ2luX2VjEEsaCXVzLWVhc3QtMSJHMEUCIFyjhW%2FkTd1XKzrd0VSnzk%2BLdIW%2B1JPZwAQaZ3Ttrif4AiEAjDQgoiaengqarlWyq2J%2BElq0nmcuYmA8UjiqM2mUGrEquQUIdBADGgw4NTkyMDU2Mzc0MTEiDDwVoicEUOiCUH5mRiqWBbsy%2BB8V%2BHRvzHAri14CTm5emp5zTv0nepFgbVDCbCR%2BorH5cbDx5M%2Buyqm5vIJNt%2BsDNtYF8AOndmynRiJEQbYxsUonzh0A6SqXCJkS0Ry46tIsdXGdB2P7%2BYCvaBfH2l2kycyap%2BPDlcxbI6nx8Zv%2F48AFCedMNo9HR9IaNFD1vdal%2FKMRuERuVbs%2FCYmPERh8Nu72nBp4Sfw937gNEsgjXSNpuqepuKB8m9MzJY6%2BfbHg82bpJWVFx6ISc0fXQmMOO4b0xaa5EnZc2x40I0GVyAqe4yKWT9alGkUbB1mk5jepQ8QljZDEodl62rn%2FpfuO6My1S1BJk%2BhshX8x8qHjunz0djreYQgnUIaiH8vVcHKXbJ0946sffXhl%2BUq10SykYFSRilPZXolqvaZ62LbkR7v6ysG1UZ820ZPMZgdzQrWizdeo1YA6wNZOFoyyoiAWdOxkk1Z0pkLSpkAmDEPRn2A8le5bJUWKqbet9AClBOh8FPMVV5f%2Fndi6NKhoC0gifuxVpvozYoPvRrkEJyKm%2FRIT7LIGs1jbiIx2EdPRlrUIGHeHp2UplzqIcLoPBKw5su%2BMFzzoufIsNxhyq2Ad%2B0P0h4VCgkR12jdZTC8YSWeDbWRuugSaiMuWXorSUewWH5AqWCnM0T5FAyVlfA973aT2rjGUrPZg2Vift8v0NllUqDUy3l5uKxsa7elCrMBoXcIS5R8TWLg9pnE%2F9KUaa6xmJLp3x%2B6rplV7fuovMLfzVo7NVJz1wlMpykorWOHmP9cQ3lNvgzFPYCY8Lt%2FM3o%2Fi7THGOk%2FyoNmL3YLO6XpXke5XtmZDFD6DB8LqcUGHtrMD7dg4Ivr3cFOb10NzRtHipZcWqtQOJKSh53XyyEifDT8mMMitzL0GOrEBo682HfP%2FpMDUQTsjqPmjTUQ47H%2Fyem0K73Ujrf4%2BTuDoyDcqNQxRRfhdSgGjC1sE27270EpxE4N%2Bs5abRxoIN5qqVW0CbtLVmKPeFYEMA1tb1Bjrf9yAAmL9bfWj5yAYnCfCM0kQsv4vwf72B%2Fiw6jcqnbsquXFjpLdhAKp2%2B2ibKmL7wkOicthGKPlhk8NykbGdkQ5rxen4GJeqUf2phGVvT1ZWZBjiz0iEtqks0EQN&AWSAccessKeyId=ASIA4QDFFSURVR2MSOVE", "ytApiUrl": "https://www.youtube.com/iframe_api", "sources": ["https://d2f1egay8yehza.cloudfront.net/MIT1600X/MIT1600XT115-V005300_DTH.mp4", "https://d2f1egay8yehza.cloudfront.net/MIT1600X/MIT1600XT115-V005300_DTH.webm", "https://d2f1egay8yehza.cloudfront.net/MIT1600XT115-V005300/MIT1600XT115-V005300.m3u8"], "transcriptLanguages": {"en": "English"}, "saveStateEnabled": false, "captionDataDir": null, "recordedYoutubeIsAvailable": true, "autoAdvance": false, "duration": 671.5, "publishCompletionUrl": "/courses/course-v1:MITx+16.00x+2T2019/xblock/block-v1:MITx+16.00x+2T2019+type@video+block@a7fd9074170d490487616b1efdddd0ec/handler/publish_completion", "transcriptTranslationUrl": "/courses/course-v1:MITx+16.00x+2T2019/xblock/block-v1:MITx+16.00x+2T2019+type@video+block@a7fd9074170d490487616b1efdddd0ec/handler/transcript/translation/__lang__", "prioritizeHls": false, "autoplay": false, "savedVideoPosition": 0.0, "streams": "1.00:hOpWxPiG6qs", "speed": null, "generalSpeed": 1.0, "ytMetadataEndpoint": "", "showCaptions": "true", "start": 0.0, "transcriptLanguage": "en", "lmsRootURL": "https://openlearninglibrary.mit.edu", "end": 0.0, "transcriptAvailableTranslationsUrl": "/courses/course-v1:MITx+16.00x+2T2019/xblock/block-v1:MITx+16.00x+2T2019+type@video+block@a7fd9074170d490487616b1efdddd0ec/handler/transcript/available_translations"}'
data-bumper-metadata='null'
data-autoadvance-enabled="False"
data-poster='null'
tabindex="-1"
>
<div class="focus_grabber first"></div>
<div class="tc-wrapper">
<div class="video-wrapper">
<span tabindex="0" class="spinner" aria-hidden="false" aria-label="Loading video player"></span>
<span tabindex="-1" class="btn-play fa fa-youtube-play fa-2x is-hidden" aria-hidden="true" aria-label="Play video"></span>
<div class="video-player-pre"></div>
<div class="video-player">
<div id="a7fd9074170d490487616b1efdddd0ec"></div>
<h4 class="hd hd-4 video-error is-hidden">No playable video sources found.</h4>
<h4 class="hd hd-4 video-hls-error is-hidden">
Your browser does not support this video format. Try using a different browser.
</h4>
</div>
<div class="video-player-post"></div>
<div class="closed-captions"></div>
<div class="video-controls is-hidden">
<div>
<div class="vcr"><div class="vidtime">0:00 / 0:00</div></div>
<div class="secondary-controls"></div>
</div>
</div>
</div>
</div>
<div class="focus_grabber last"></div>
<h3 class="hd hd-4 downloads-heading sr" id="video-download-transcripts_a7fd9074170d490487616b1efdddd0ec">Downloads and transcripts</h3>
<div class="wrapper-downloads" role="region" aria-labelledby="video-download-transcripts_a7fd9074170d490487616b1efdddd0ec">
<div class="wrapper-download-video">
<h4 class="hd hd-5">Video</h4>
<a class="btn-link video-sources video-download-button" href="https://d2f1egay8yehza.cloudfront.net/MIT1600X/MIT1600XT115-V005300_DTH.mp4">
Download video file
</a>
</div>
<div class="wrapper-download-transcripts">
<h4 class="hd hd-5">Transcripts</h4>
<ul class="list-download-transcripts">
<li class="transcript-option">
<a class="btn btn-link" href="/courses/course-v1:MITx+16.00x+2T2019/xblock/block-v1:MITx+16.00x+2T2019+type@video+block@a7fd9074170d490487616b1efdddd0ec/handler/transcript/download" data-value="srt">Download SubRip (.srt) file</a>
</li>
<li class="transcript-option">
<a class="btn btn-link" href="/courses/course-v1:MITx+16.00x+2T2019/xblock/block-v1:MITx+16.00x+2T2019+type@video+block@a7fd9074170d490487616b1efdddd0ec/handler/transcript/download" data-value="txt">Download Text (.txt) file</a>
</li>
</ul>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
<div class="xblock xblock-public_view xblock-public_view-vertical" data-request-token="2a6ad6faed2111efb9010e0e3c45b88f" data-usage-id="block-v1:MITx+16.00x+2T2019+type@vertical+block@a2abbbfe58324dcb93bdce6c4fa81401" data-graded="True" data-has-score="False" data-runtime-version="1" data-block-type="vertical" data-init="VerticalStudentView" data-course-id="course-v1:MITx+16.00x+2T2019" data-runtime-class="LmsRuntime">
<h2 class="hd hd-2 unit-title">Interplanetary Travel</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITx+16.00x+2T2019+type@html+block@b36d117effcd4f7893e846a508589543">
<div class="xblock xblock-public_view xblock-public_view-html xmodule_display xmodule_HtmlBlock" data-request-token="2a6ad6faed2111efb9010e0e3c45b88f" data-usage-id="block-v1:MITx+16.00x+2T2019+type@html+block@b36d117effcd4f7893e846a508589543" data-graded="True" data-has-score="False" data-runtime-version="1" data-block-type="html" data-init="XBlockToXModuleShim" data-course-id="course-v1:MITx+16.00x+2T2019" data-runtime-class="LmsRuntime">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "HTMLModule"}
</script>
<h2>4.6.2 Interplanetary Travel</h2>
<p><button border-radius="2px" class="mo_button" onclick="window.location.href='/courses/course-v1:MITx+16.00x+3T2016/5e0e82a56b234a2aaf12ac0b3359c3c5#MO410';" style="cursor: pointer;" title="MO 4.10:
Define gravity assist and explain its importance for interplanetary travel" type="button" id="LD">MO 4.10</button></p>
<p style="padding-left: 120px;"><img src="/assets/courseware/v1/edfae63f7e67ea08b2813cb25e460579/asset-v1:MITx+16.00x+2T2019+type@asset+block/Jupiter-Red-Spot-Voyager-1-300.jpg" alt="Jupiter's Great Red Spot viewed by the Voyager 1 spacecraft in 1979" type="saveimage" target="[object Object]" height="253" width="300" /> <img src="/assets/courseware/v1/70d5e49d9b27a94aa4e363379c48ba20/asset-v1:MITx+16.00x+2T2019+type@asset+block/Neptune-Voyager-2-300.jpg" alt="Photo of Neptune taken by the Voyager 2 spacecraft in 1989" type="saveimage" target="[object Object]" height="253" width="253" /></p>
<p style="padding-left: 60px;"><em style="line-height: 25.6000003814697px; text-align: center;"><span>Left: Jupiter's Great Red Spot viewed by the Voyager 1 spacecraft in 1979 (Image credit: NASA/JPL)<br />Right: Photo of Neptune taken by the Voyager 2 spacecraft in 1989 (Image credit: NASA)</span></em></p>
<p>Putting together everything we have learned thus far, in this video we examine the implications of orbital mechanics for interplanetary travel. What makes it possible for robotic probes to travel to the outer reaches of our solar system and beyond? How can we take advantage of "gravity assists" to minimize the amount of onboard propellant required for these long-duration missions?</p>
</div>
</div>
<div class="vert vert-1" data-id="block-v1:MITx+16.00x+2T2019+type@video+block@7886bc89cb9c4602974d353dfb572185">
<div class="xblock xblock-public_view xblock-public_view-video xmodule_display xmodule_VideoBlock" data-request-token="2a6ad6faed2111efb9010e0e3c45b88f" data-usage-id="block-v1:MITx+16.00x+2T2019+type@video+block@7886bc89cb9c4602974d353dfb572185" data-graded="True" data-has-score="False" data-runtime-version="1" data-block-type="video" data-init="XBlockToXModuleShim" data-course-id="course-v1:MITx+16.00x+2T2019" data-runtime-class="LmsRuntime">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Video"}
</script>
<h3 class="hd hd-2">Video: Interplanetary Travel</h3>
<div
id="video_7886bc89cb9c4602974d353dfb572185"
class="video closed"
data-metadata='{"saveStateUrl": "/courses/course-v1:MITx+16.00x+2T2019/xblock/block-v1:MITx+16.00x+2T2019+type@video+block@7886bc89cb9c4602974d353dfb572185/handler/xmodule_handler/save_user_state", "completionEnabled": false, "ytTestTimeout": 1500, "autohideHtml5": false, "completionPercentage": 0.95, "poster": "https://mitx-edx-video-meta-storage.s3.amazonaws.com/media/video-images/239b0caa8bef40858ccb1cda0943de33.jpeg?Signature=PVdF5%2Bnnb42Qj2pF%2BWZg%2FOQEbYI%3D&Expires=1739791519&x-amz-security-token=IQoJb3JpZ2luX2VjEEsaCXVzLWVhc3QtMSJHMEUCIFyjhW%2FkTd1XKzrd0VSnzk%2BLdIW%2B1JPZwAQaZ3Ttrif4AiEAjDQgoiaengqarlWyq2J%2BElq0nmcuYmA8UjiqM2mUGrEquQUIdBADGgw4NTkyMDU2Mzc0MTEiDDwVoicEUOiCUH5mRiqWBbsy%2BB8V%2BHRvzHAri14CTm5emp5zTv0nepFgbVDCbCR%2BorH5cbDx5M%2Buyqm5vIJNt%2BsDNtYF8AOndmynRiJEQbYxsUonzh0A6SqXCJkS0Ry46tIsdXGdB2P7%2BYCvaBfH2l2kycyap%2BPDlcxbI6nx8Zv%2F48AFCedMNo9HR9IaNFD1vdal%2FKMRuERuVbs%2FCYmPERh8Nu72nBp4Sfw937gNEsgjXSNpuqepuKB8m9MzJY6%2BfbHg82bpJWVFx6ISc0fXQmMOO4b0xaa5EnZc2x40I0GVyAqe4yKWT9alGkUbB1mk5jepQ8QljZDEodl62rn%2FpfuO6My1S1BJk%2BhshX8x8qHjunz0djreYQgnUIaiH8vVcHKXbJ0946sffXhl%2BUq10SykYFSRilPZXolqvaZ62LbkR7v6ysG1UZ820ZPMZgdzQrWizdeo1YA6wNZOFoyyoiAWdOxkk1Z0pkLSpkAmDEPRn2A8le5bJUWKqbet9AClBOh8FPMVV5f%2Fndi6NKhoC0gifuxVpvozYoPvRrkEJyKm%2FRIT7LIGs1jbiIx2EdPRlrUIGHeHp2UplzqIcLoPBKw5su%2BMFzzoufIsNxhyq2Ad%2B0P0h4VCgkR12jdZTC8YSWeDbWRuugSaiMuWXorSUewWH5AqWCnM0T5FAyVlfA973aT2rjGUrPZg2Vift8v0NllUqDUy3l5uKxsa7elCrMBoXcIS5R8TWLg9pnE%2F9KUaa6xmJLp3x%2B6rplV7fuovMLfzVo7NVJz1wlMpykorWOHmP9cQ3lNvgzFPYCY8Lt%2FM3o%2Fi7THGOk%2FyoNmL3YLO6XpXke5XtmZDFD6DB8LqcUGHtrMD7dg4Ivr3cFOb10NzRtHipZcWqtQOJKSh53XyyEifDT8mMMitzL0GOrEBo682HfP%2FpMDUQTsjqPmjTUQ47H%2Fyem0K73Ujrf4%2BTuDoyDcqNQxRRfhdSgGjC1sE27270EpxE4N%2Bs5abRxoIN5qqVW0CbtLVmKPeFYEMA1tb1Bjrf9yAAmL9bfWj5yAYnCfCM0kQsv4vwf72B%2Fiw6jcqnbsquXFjpLdhAKp2%2B2ibKmL7wkOicthGKPlhk8NykbGdkQ5rxen4GJeqUf2phGVvT1ZWZBjiz0iEtqks0EQN&AWSAccessKeyId=ASIA4QDFFSURVR2MSOVE", "ytApiUrl": "https://www.youtube.com/iframe_api", "sources": ["https://d2f1egay8yehza.cloudfront.net/MIT1600X/MIT1600XT115-V005200_DTH.mp4", "https://d2f1egay8yehza.cloudfront.net/MIT1600X/MIT1600XT115-V005200_DTH.webm", "https://d2f1egay8yehza.cloudfront.net/MIT1600XT115-V005200/MIT1600XT115-V005200.m3u8"], "transcriptLanguages": {"en": "English"}, "saveStateEnabled": false, "captionDataDir": null, "recordedYoutubeIsAvailable": true, "autoAdvance": false, "duration": 464.96, "publishCompletionUrl": "/courses/course-v1:MITx+16.00x+2T2019/xblock/block-v1:MITx+16.00x+2T2019+type@video+block@7886bc89cb9c4602974d353dfb572185/handler/publish_completion", "transcriptTranslationUrl": "/courses/course-v1:MITx+16.00x+2T2019/xblock/block-v1:MITx+16.00x+2T2019+type@video+block@7886bc89cb9c4602974d353dfb572185/handler/transcript/translation/__lang__", "prioritizeHls": false, "autoplay": false, "savedVideoPosition": 0.0, "streams": "1.00:R9Scwl3Xao4", "speed": null, "generalSpeed": 1.0, "ytMetadataEndpoint": "", "showCaptions": "true", "start": 0.0, "transcriptLanguage": "en", "lmsRootURL": "https://openlearninglibrary.mit.edu", "end": 0.0, "transcriptAvailableTranslationsUrl": "/courses/course-v1:MITx+16.00x+2T2019/xblock/block-v1:MITx+16.00x+2T2019+type@video+block@7886bc89cb9c4602974d353dfb572185/handler/transcript/available_translations"}'
data-bumper-metadata='null'
data-autoadvance-enabled="False"
data-poster='null'
tabindex="-1"
>
<div class="focus_grabber first"></div>
<div class="tc-wrapper">
<div class="video-wrapper">
<span tabindex="0" class="spinner" aria-hidden="false" aria-label="Loading video player"></span>
<span tabindex="-1" class="btn-play fa fa-youtube-play fa-2x is-hidden" aria-hidden="true" aria-label="Play video"></span>
<div class="video-player-pre"></div>
<div class="video-player">
<div id="7886bc89cb9c4602974d353dfb572185"></div>
<h4 class="hd hd-4 video-error is-hidden">No playable video sources found.</h4>
<h4 class="hd hd-4 video-hls-error is-hidden">
Your browser does not support this video format. Try using a different browser.
</h4>
</div>
<div class="video-player-post"></div>
<div class="closed-captions"></div>
<div class="video-controls is-hidden">
<div>
<div class="vcr"><div class="vidtime">0:00 / 0:00</div></div>
<div class="secondary-controls"></div>
</div>
</div>
</div>
</div>
<div class="focus_grabber last"></div>
<h3 class="hd hd-4 downloads-heading sr" id="video-download-transcripts_7886bc89cb9c4602974d353dfb572185">Downloads and transcripts</h3>
<div class="wrapper-downloads" role="region" aria-labelledby="video-download-transcripts_7886bc89cb9c4602974d353dfb572185">
<div class="wrapper-download-video">
<h4 class="hd hd-5">Video</h4>
<a class="btn-link video-sources video-download-button" href="https://d2f1egay8yehza.cloudfront.net/MIT1600X/MIT1600XT115-V005200_DTH.mp4">
Download video file
</a>
</div>
<div class="wrapper-download-transcripts">
<h4 class="hd hd-5">Transcripts</h4>
<ul class="list-download-transcripts">
<li class="transcript-option">
<a class="btn btn-link" href="/courses/course-v1:MITx+16.00x+2T2019/xblock/block-v1:MITx+16.00x+2T2019+type@video+block@7886bc89cb9c4602974d353dfb572185/handler/transcript/download" data-value="srt">Download SubRip (.srt) file</a>
</li>
<li class="transcript-option">
<a class="btn btn-link" href="/courses/course-v1:MITx+16.00x+2T2019/xblock/block-v1:MITx+16.00x+2T2019+type@video+block@7886bc89cb9c4602974d353dfb572185/handler/transcript/download" data-value="txt">Download Text (.txt) file</a>
</li>
</ul>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
<div class="xblock xblock-public_view xblock-public_view-vertical" data-request-token="2a6ad6faed2111efb9010e0e3c45b88f" data-usage-id="block-v1:MITx+16.00x+2T2019+type@vertical+block@741c196a210a4f0fb5600591ad20eba2" data-graded="True" data-has-score="False" data-runtime-version="1" data-block-type="vertical" data-init="VerticalStudentView" data-course-id="course-v1:MITx+16.00x+2T2019" data-runtime-class="LmsRuntime">
<h2 class="hd hd-2 unit-title">Review of Concepts: Orbital Inclination and Rendezvous</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITx+16.00x+2T2019+type@html+block@a22424ea25724091933af1c6e7aae926">
<div class="xblock xblock-public_view xblock-public_view-html xmodule_display xmodule_HtmlBlock" data-request-token="2a6ad6faed2111efb9010e0e3c45b88f" data-usage-id="block-v1:MITx+16.00x+2T2019+type@html+block@a22424ea25724091933af1c6e7aae926" data-graded="True" data-has-score="False" data-runtime-version="1" data-block-type="html" data-init="XBlockToXModuleShim" data-course-id="course-v1:MITx+16.00x+2T2019" data-runtime-class="LmsRuntime">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "HTMLModule"}
</script>
<h2>4.6.3 Review of Concepts: Orbital Inclination and Rendezvous</h2>
<p><button border-radius="2px" class="mo_button" onclick="window.location.href='/courses/course-v1:MITx+16.00x+3T2016/5e0e82a56b234a2aaf12ac0b3359c3c5#MO47';" style="cursor: pointer;" title="MO 4.7:
Explain why it is difficult to change the inclination of a spacecraft’s orbit" type="button" id="LD">MO 4.7</button> <button border-radius="2px" class="mo_button" onclick="window.location.href='/courses/course-v1:MITx+16.00x+3T2016/5e0e82a56b234a2aaf12ac0b3359c3c5#MO48';" style="cursor: pointer;" title="MO 4.8:
Explain how the latitude of a launch site affects orbital inclination and the amount of payload that can be put into orbit " type="button" id="LD">MO 4.8</button> <button border-radius="2px" class="mo_button" onclick="window.location.href='/courses/course-v1:MITx+16.00x+3T2016/5e0e82a56b234a2aaf12ac0b3359c3c5#MO49';" style="cursor: pointer;" title="MO 4.9:
Describe the principles of orbital rendezvous and the distinction between ideal and actual rendezvous" type="button" id="LD">MO 4.9</button><!------></p>
<p>This is a long, multi-part question that integrates many of the concepts introduced in this unit. Make sure to complete one part before moving on to the next. <strong> Assume circular orbits</strong> for all calculations and use the following values for \(R\), \(M\), and \(G\).</p>
<ul>
<li><span style="font-size: 1em; line-height: 1.6em;">Radius of the Earth: \(R = 6371\, \text{km}\)</span></li>
<li><span style="font-size: 1em; line-height: 1.6;">Mass of the Earth: \(M = 5.972 \times 10^{24}\,\text{kg}\)</span><span style="font-size: 1em; line-height: 1.6;"> </span></li>
<li><span style="font-size: 1em; line-height: 1.6em;">Universal gravitational constant: </span>\(G = 6.674 \times 10^{-11}\, \text{m}^3/\text{kg}/\text{s}^2\) </li>
</ul>
<p class="MsoNormal"><o:p> </o:p> </p>
</div>
</div>
<div class="vert vert-1" data-id="block-v1:MITx+16.00x+2T2019+type@problem+block@fcf3ae77067f447a9b5b91186e172372">
<div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-request-token="2a6ad6faed2111efb9010e0e3c45b88f" data-usage-id="block-v1:MITx+16.00x+2T2019+type@problem+block@fcf3ae77067f447a9b5b91186e172372" data-graded="True" data-has-score="True" data-runtime-version="1" data-block-type="problem" data-init="XBlockToXModuleShim" data-course-id="course-v1:MITx+16.00x+2T2019" data-runtime-class="LmsRuntime">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Problem"}
</script>
<div id="problem_fcf3ae77067f447a9b5b91186e172372" class="problems-wrapper" role="group"
aria-labelledby="fcf3ae77067f447a9b5b91186e172372-problem-title"
data-problem-id="block-v1:MITx+16.00x+2T2019+type@problem+block@fcf3ae77067f447a9b5b91186e172372" data-url="/courses/course-v1:MITx+16.00x+2T2019/xblock/block-v1:MITx+16.00x+2T2019+type@problem+block@fcf3ae77067f447a9b5b91186e172372/handler/xmodule_handler"
data-problem-score="0.0"
data-problem-total-possible="3.0"
data-attempts-used="0"
data-content="
<h3 class="hd hd-3 problem-header" id="fcf3ae77067f447a9b5b91186e172372-problem-title" aria-describedby="block-v1:MITx+16.00x+2T2019+type@problem+block@fcf3ae77067f447a9b5b91186e172372-problem-progress" tabindex="-1">
Part 1: Launching into Orbit
</h3>
<div class="problem-progress" id="block-v1:MITx+16.00x+2T2019+type@problem+block@fcf3ae77067f447a9b5b91186e172372-problem-progress"></div>
<div class="problem">
<div>
<p>You are on a mission to rendezvous with the International Space Station (ISS), which is in orbit 400 km above the surface of the Earth, with an orbital inclination of 51 degrees. You are launching your spacecraft from Cape Canaveral, which is at a latitude of 28.5 degrees.</p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div class="choicegroup capa_inputtype" id="inputtype_fcf3ae77067f447a9b5b91186e172372_2_1">
<fieldset aria-describedby="status_fcf3ae77067f447a9b5b91186e172372_2_1">
<legend id="fcf3ae77067f447a9b5b91186e172372_2_1-legend" class="response-fieldset-legend field-group-hd">The best time to launch is:</legend>
<div class="field">
<input type="radio" name="input_fcf3ae77067f447a9b5b91186e172372_2_1" id="input_fcf3ae77067f447a9b5b91186e172372_2_1_choice_0" class="field-input input-radio" value="choice_0"/><label id="fcf3ae77067f447a9b5b91186e172372_2_1-choice_0-label" for="input_fcf3ae77067f447a9b5b91186e172372_2_1_choice_0" class="response-label field-label label-inline" aria-describedby="status_fcf3ae77067f447a9b5b91186e172372_2_1"> Just after sunrise when thermal conditions are optimal
</label>
</div>
<div class="field">
<input type="radio" name="input_fcf3ae77067f447a9b5b91186e172372_2_1" id="input_fcf3ae77067f447a9b5b91186e172372_2_1_choice_1" class="field-input input-radio" value="choice_1"/><label id="fcf3ae77067f447a9b5b91186e172372_2_1-choice_1-label" for="input_fcf3ae77067f447a9b5b91186e172372_2_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_fcf3ae77067f447a9b5b91186e172372_2_1"> When the rotation of the Earth brings the launch site into the plane of the ISS orbit
</label>
</div>
<div class="field">
<input type="radio" name="input_fcf3ae77067f447a9b5b91186e172372_2_1" id="input_fcf3ae77067f447a9b5b91186e172372_2_1_choice_2" class="field-input input-radio" value="choice_2"/><label id="fcf3ae77067f447a9b5b91186e172372_2_1-choice_2-label" for="input_fcf3ae77067f447a9b5b91186e172372_2_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_fcf3ae77067f447a9b5b91186e172372_2_1"> Anytime that is convenient for the crew
</label>
</div>
<span id="answer_fcf3ae77067f447a9b5b91186e172372_2_1"/>
</fieldset>
<div class="indicator-container">
<span class="status unanswered" id="status_fcf3ae77067f447a9b5b91186e172372_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</div>
</div></div>
<div class="solution-span">
<span id="solution_fcf3ae77067f447a9b5b91186e172372_solution_1"/>
</div><div class="wrapper-problem-response" tabindex="-1" aria-label="Question 2" role="group"><div id="formulaequationinput_fcf3ae77067f447a9b5b91186e172372_3_1" class="inputtype formulaequationinput">
<div class="unanswered">
<label class="problem-group-label" for="input_fcf3ae77067f447a9b5b91186e172372_3_1" id="label_fcf3ae77067f447a9b5b91186e172372_3_1">If you launch due east from Cape Canaveral, what will be the inclination of your orbit in degrees?</label>
<input type="text" name="input_fcf3ae77067f447a9b5b91186e172372_3_1" id="input_fcf3ae77067f447a9b5b91186e172372_3_1" data-input-id="fcf3ae77067f447a9b5b91186e172372_3_1" value="" aria-describedby="status_fcf3ae77067f447a9b5b91186e172372_3_1" size="20"/>
<span class="trailing_text" id="trailing_text_fcf3ae77067f447a9b5b91186e172372_3_1"/>
<span class="status unanswered" id="status_fcf3ae77067f447a9b5b91186e172372_3_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_fcf3ae77067f447a9b5b91186e172372_3_1" class="answer"/>
<div id="input_fcf3ae77067f447a9b5b91186e172372_3_1_preview" class="equation">
\(\)
<img src="/static/images/spinner.bc34f953403f.gif" class="loading" alt="Loading"/>
</div>
</div>
<div class="script_placeholder" data-src="/static/js/capa/src/formula_equation_preview.b1967ab28c31.js"/>
</div></div>
<div class="solution-span">
<span id="solution_fcf3ae77067f447a9b5b91186e172372_solution_2"/>
</div><div class="wrapper-problem-response" tabindex="-1" aria-label="Question 3" role="group"><div id="formulaequationinput_fcf3ae77067f447a9b5b91186e172372_4_1" class="inputtype formulaequationinput">
<div class="unanswered">
<label class="problem-group-label" for="input_fcf3ae77067f447a9b5b91186e172372_4_1" id="label_fcf3ae77067f447a9b5b91186e172372_4_1">How much of a velocity boost will you get from the Earth&#8217;s rotation? Give you answer in km/s with at least 2 decimal places. Hint: First compute the velocity boost at the equator based on the Earth's circumference and rotational period.</label>
<input type="text" name="input_fcf3ae77067f447a9b5b91186e172372_4_1" id="input_fcf3ae77067f447a9b5b91186e172372_4_1" data-input-id="fcf3ae77067f447a9b5b91186e172372_4_1" value="" aria-describedby="status_fcf3ae77067f447a9b5b91186e172372_4_1" size="20"/>
<span class="trailing_text" id="trailing_text_fcf3ae77067f447a9b5b91186e172372_4_1"/>
<span class="status unanswered" id="status_fcf3ae77067f447a9b5b91186e172372_4_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_fcf3ae77067f447a9b5b91186e172372_4_1" class="answer"/>
<div id="input_fcf3ae77067f447a9b5b91186e172372_4_1_preview" class="equation">
\(\)
<img src="/static/images/spinner.bc34f953403f.gif" class="loading" alt="Loading"/>
</div>
</div>
<div class="script_placeholder" data-src="/static/js/capa/src/formula_equation_preview.b1967ab28c31.js"/>
</div></div>
<div class="solution-span">
<span id="solution_fcf3ae77067f447a9b5b91186e172372_solution_3"/>
</div></div>
<div class="action">
<input type="hidden" name="problem_id" value="Part 1: Launching into Orbit" />
<div class="submit-attempt-container">
<button type="button" class="submit btn-brand" data-submitting="Submitting" data-value="Submit" data-should-enable-submit-button="True" aria-describedby="submission_feedback_fcf3ae77067f447a9b5b91186e172372" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_fcf3ae77067f447a9b5b91186e172372">
<span class="sr">Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.</span>
</div>
</div>
<div class="problem-action-buttons-wrapper">
</div>
</div>
<div class="notification warning notification-gentle-alert
is-hidden"
tabindex="-1">
<span class="icon fa fa-exclamation-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="fcf3ae77067f447a9b5b91186e172372-problem-title">
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification warning notification-save
is-hidden"
tabindex="-1">
<span class="icon fa fa-save" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="fcf3ae77067f447a9b5b91186e172372-problem-title">None
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification general notification-show-answer
is-hidden"
tabindex="-1">
<span class="icon fa fa-info-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="fcf3ae77067f447a9b5b91186e172372-problem-title">Answers are displayed within the problem
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
</div>
"
data-graded="True">
<p class="loading-spinner">
<i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i>
<span class="sr">Loading…</span>
</p>
</div>
</div>
</div>
<div class="vert vert-2" data-id="block-v1:MITx+16.00x+2T2019+type@problem+block@8278d1080f5249828f0ba5a1ba93b032">
<div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-request-token="2a6ad6faed2111efb9010e0e3c45b88f" data-usage-id="block-v1:MITx+16.00x+2T2019+type@problem+block@8278d1080f5249828f0ba5a1ba93b032" data-graded="True" data-has-score="True" data-runtime-version="1" data-block-type="problem" data-init="XBlockToXModuleShim" data-course-id="course-v1:MITx+16.00x+2T2019" data-runtime-class="LmsRuntime">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Problem"}
</script>
<div id="problem_8278d1080f5249828f0ba5a1ba93b032" class="problems-wrapper" role="group"
aria-labelledby="8278d1080f5249828f0ba5a1ba93b032-problem-title"
data-problem-id="block-v1:MITx+16.00x+2T2019+type@problem+block@8278d1080f5249828f0ba5a1ba93b032" data-url="/courses/course-v1:MITx+16.00x+2T2019/xblock/block-v1:MITx+16.00x+2T2019+type@problem+block@8278d1080f5249828f0ba5a1ba93b032/handler/xmodule_handler"
data-problem-score="0.0"
data-problem-total-possible="3.0"
data-attempts-used="0"
data-content="
<h3 class="hd hd-3 problem-header" id="8278d1080f5249828f0ba5a1ba93b032-problem-title" aria-describedby="block-v1:MITx+16.00x+2T2019+type@problem+block@8278d1080f5249828f0ba5a1ba93b032-problem-progress" tabindex="-1">
Part 2: Changing Orbital Inclination
</h3>
<div class="problem-progress" id="block-v1:MITx+16.00x+2T2019+type@problem+block@8278d1080f5249828f0ba5a1ba93b032-problem-progress"></div>
<div class="problem">
<div>
<p>Assume that you launch due east from Cape Canaveral and reach the orbital altitude of the ISS (400 km). </p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div id="formulaequationinput_8278d1080f5249828f0ba5a1ba93b032_2_1" class="inputtype formulaequationinput">
<div class="unanswered">
<label class="problem-group-label" for="input_8278d1080f5249828f0ba5a1ba93b032_2_1" id="label_8278d1080f5249828f0ba5a1ba93b032_2_1">What is the velocity of your spacecraft in this orbit? Give your answer in km/s with at least 2 decimal places.</label>
<input type="text" name="input_8278d1080f5249828f0ba5a1ba93b032_2_1" id="input_8278d1080f5249828f0ba5a1ba93b032_2_1" data-input-id="8278d1080f5249828f0ba5a1ba93b032_2_1" value="" aria-describedby="status_8278d1080f5249828f0ba5a1ba93b032_2_1" size="20"/>
<span class="trailing_text" id="trailing_text_8278d1080f5249828f0ba5a1ba93b032_2_1"/>
<span class="status unanswered" id="status_8278d1080f5249828f0ba5a1ba93b032_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_8278d1080f5249828f0ba5a1ba93b032_2_1" class="answer"/>
<div id="input_8278d1080f5249828f0ba5a1ba93b032_2_1_preview" class="equation">
\(\)
<img src="/static/images/spinner.bc34f953403f.gif" class="loading" alt="Loading"/>
</div>
</div>
<div class="script_placeholder" data-src="/static/js/capa/src/formula_equation_preview.b1967ab28c31.js"/>
</div></div>
<div class="solution-span">
<span id="solution_8278d1080f5249828f0ba5a1ba93b032_solution_1"/>
</div><p>How large a burn is required to change your initial inclination to that of the ISS? Give your answer in km/s with at least 2 decimal places. Hint: You may wish to review the expression for \(\Delta V\) given in <a href="/courses/course-v1:MITx+16.00x+2T2019/jump_to_id/d1e95e61641d459eb1ce47ae928508c6">Subsection 4.5.3</a>.</p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 2" role="group"><div id="formulaequationinput_8278d1080f5249828f0ba5a1ba93b032_3_1" class="inputtype formulaequationinput">
<div class="unanswered">
<input type="text" name="input_8278d1080f5249828f0ba5a1ba93b032_3_1" id="input_8278d1080f5249828f0ba5a1ba93b032_3_1" data-input-id="8278d1080f5249828f0ba5a1ba93b032_3_1" value="" aria-describedby="status_8278d1080f5249828f0ba5a1ba93b032_3_1" size="20"/>
<span class="trailing_text" id="trailing_text_8278d1080f5249828f0ba5a1ba93b032_3_1"/>
<span class="status unanswered" id="status_8278d1080f5249828f0ba5a1ba93b032_3_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_8278d1080f5249828f0ba5a1ba93b032_3_1" class="answer"/>
<div id="input_8278d1080f5249828f0ba5a1ba93b032_3_1_preview" class="equation">
\(\)
<img src="/static/images/spinner.bc34f953403f.gif" class="loading" alt="Loading"/>
</div>
</div>
<div class="script_placeholder" data-src="/static/js/capa/src/formula_equation_preview.b1967ab28c31.js"/>
</div></div>
<div class="solution-span">
<span id="solution_8278d1080f5249828f0ba5a1ba93b032_solution_2"/>
</div><div class="wrapper-problem-response" tabindex="-1" aria-label="Question 3" role="group"><div class="choicegroup capa_inputtype" id="inputtype_8278d1080f5249828f0ba5a1ba93b032_4_1">
<fieldset aria-describedby="status_8278d1080f5249828f0ba5a1ba93b032_4_1">
<legend id="8278d1080f5249828f0ba5a1ba93b032_4_1-legend" class="response-fieldset-legend field-group-hd">In what direction should you perform the burn with respect to your orbital velocity?</legend>
<div class="field">
<input type="radio" name="input_8278d1080f5249828f0ba5a1ba93b032_4_1" id="input_8278d1080f5249828f0ba5a1ba93b032_4_1_choice_0" class="field-input input-radio" value="choice_0"/><label id="8278d1080f5249828f0ba5a1ba93b032_4_1-choice_0-label" for="input_8278d1080f5249828f0ba5a1ba93b032_4_1_choice_0" class="response-label field-label label-inline" aria-describedby="status_8278d1080f5249828f0ba5a1ba93b032_4_1"> In line with the spacecraft's direction of motion
</label>
</div>
<div class="field">
<input type="radio" name="input_8278d1080f5249828f0ba5a1ba93b032_4_1" id="input_8278d1080f5249828f0ba5a1ba93b032_4_1_choice_1" class="field-input input-radio" value="choice_1"/><label id="8278d1080f5249828f0ba5a1ba93b032_4_1-choice_1-label" for="input_8278d1080f5249828f0ba5a1ba93b032_4_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_8278d1080f5249828f0ba5a1ba93b032_4_1"> Perpendicular to the spacecraft's direction of motion
</label>
</div>
<div class="field">
<input type="radio" name="input_8278d1080f5249828f0ba5a1ba93b032_4_1" id="input_8278d1080f5249828f0ba5a1ba93b032_4_1_choice_2" class="field-input input-radio" value="choice_2"/><label id="8278d1080f5249828f0ba5a1ba93b032_4_1-choice_2-label" for="input_8278d1080f5249828f0ba5a1ba93b032_4_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_8278d1080f5249828f0ba5a1ba93b032_4_1"> Radially outward away from the Earth
</label>
</div>
<span id="answer_8278d1080f5249828f0ba5a1ba93b032_4_1"/>
</fieldset>
<div class="indicator-container">
<span class="status unanswered" id="status_8278d1080f5249828f0ba5a1ba93b032_4_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</div>
</div></div>
<div class="solution-span">
<span id="solution_8278d1080f5249828f0ba5a1ba93b032_solution_3"/>
</div></div>
<div class="action">
<input type="hidden" name="problem_id" value="Part 2: Changing Orbital Inclination" />
<div class="submit-attempt-container">
<button type="button" class="submit btn-brand" data-submitting="Submitting" data-value="Submit" data-should-enable-submit-button="True" aria-describedby="submission_feedback_8278d1080f5249828f0ba5a1ba93b032" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_8278d1080f5249828f0ba5a1ba93b032">
<span class="sr">Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.</span>
</div>
</div>
<div class="problem-action-buttons-wrapper">
</div>
</div>
<div class="notification warning notification-gentle-alert
is-hidden"
tabindex="-1">
<span class="icon fa fa-exclamation-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="8278d1080f5249828f0ba5a1ba93b032-problem-title">
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification warning notification-save
is-hidden"
tabindex="-1">
<span class="icon fa fa-save" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="8278d1080f5249828f0ba5a1ba93b032-problem-title">None
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification general notification-show-answer
is-hidden"
tabindex="-1">
<span class="icon fa fa-info-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="8278d1080f5249828f0ba5a1ba93b032-problem-title">Answers are displayed within the problem
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
</div>
"
data-graded="True">
<p class="loading-spinner">
<i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i>
<span class="sr">Loading…</span>
</p>
</div>
</div>
</div>
<div class="vert vert-3" data-id="block-v1:MITx+16.00x+2T2019+type@problem+block@d1f0ad0bb4a74bc283bf4d8033c57464">
<div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-request-token="2a6ad6faed2111efb9010e0e3c45b88f" data-usage-id="block-v1:MITx+16.00x+2T2019+type@problem+block@d1f0ad0bb4a74bc283bf4d8033c57464" data-graded="True" data-has-score="True" data-runtime-version="1" data-block-type="problem" data-init="XBlockToXModuleShim" data-course-id="course-v1:MITx+16.00x+2T2019" data-runtime-class="LmsRuntime">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Problem"}
</script>
<div id="problem_d1f0ad0bb4a74bc283bf4d8033c57464" class="problems-wrapper" role="group"
aria-labelledby="d1f0ad0bb4a74bc283bf4d8033c57464-problem-title"
data-problem-id="block-v1:MITx+16.00x+2T2019+type@problem+block@d1f0ad0bb4a74bc283bf4d8033c57464" data-url="/courses/course-v1:MITx+16.00x+2T2019/xblock/block-v1:MITx+16.00x+2T2019+type@problem+block@d1f0ad0bb4a74bc283bf4d8033c57464/handler/xmodule_handler"
data-problem-score="0.0"
data-problem-total-possible="3.0"
data-attempts-used="0"
data-content="
<h3 class="hd hd-3 problem-header" id="d1f0ad0bb4a74bc283bf4d8033c57464-problem-title" aria-describedby="block-v1:MITx+16.00x+2T2019+type@problem+block@d1f0ad0bb4a74bc283bf4d8033c57464-problem-progress" tabindex="-1">
Part 3: Launching into 51 Degree Inclination
</h3>
<div class="problem-progress" id="block-v1:MITx+16.00x+2T2019+type@problem+block@d1f0ad0bb4a74bc283bf4d8033c57464-problem-progress"></div>
<div class="problem">
<div>
<p>Now assume that instead of launching due east, you launch at a northerly launch azimuth so that you fly directly into a 51 degree inclination orbit.</p>
<p><b>Important Note!</b> Use the provided answers from the previous problems, not the solutions you calculated, if needed when solving these. Otherwise, rounding errors may provide you an incorrect solution.</p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div id="formulaequationinput_d1f0ad0bb4a74bc283bf4d8033c57464_2_1" class="inputtype formulaequationinput">
<div class="unanswered">
<label class="problem-group-label" for="input_d1f0ad0bb4a74bc283bf4d8033c57464_2_1" id="label_d1f0ad0bb4a74bc283bf4d8033c57464_2_1">How much of a velocity boost do you get from the rotation of the Earth? Give your answer in km/s with at least 2 decimal places.</label>
<input type="text" name="input_d1f0ad0bb4a74bc283bf4d8033c57464_2_1" id="input_d1f0ad0bb4a74bc283bf4d8033c57464_2_1" data-input-id="d1f0ad0bb4a74bc283bf4d8033c57464_2_1" value="" aria-describedby="status_d1f0ad0bb4a74bc283bf4d8033c57464_2_1" size="20"/>
<span class="trailing_text" id="trailing_text_d1f0ad0bb4a74bc283bf4d8033c57464_2_1"/>
<span class="status unanswered" id="status_d1f0ad0bb4a74bc283bf4d8033c57464_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_d1f0ad0bb4a74bc283bf4d8033c57464_2_1" class="answer"/>
<div id="input_d1f0ad0bb4a74bc283bf4d8033c57464_2_1_preview" class="equation">
\(\)
<img src="/static/images/spinner.bc34f953403f.gif" class="loading" alt="Loading"/>
</div>
</div>
<div class="script_placeholder" data-src="/static/js/capa/src/formula_equation_preview.b1967ab28c31.js"/>
</div></div>
<div class="solution-span">
<span id="solution_d1f0ad0bb4a74bc283bf4d8033c57464_solution_1"/>
</div><div class="wrapper-problem-response" tabindex="-1" aria-label="Question 2" role="group"><div id="formulaequationinput_d1f0ad0bb4a74bc283bf4d8033c57464_3_1" class="inputtype formulaequationinput">
<div class="unanswered">
<label class="problem-group-label" for="input_d1f0ad0bb4a74bc283bf4d8033c57464_3_1" id="label_d1f0ad0bb4a74bc283bf4d8033c57464_3_1">How much less velocity boost did you get from launching directly into a 51 degree inclination orbit compared to launching due east? Give your answer in km/s with at least 2 decimal places.</label>
<input type="text" name="input_d1f0ad0bb4a74bc283bf4d8033c57464_3_1" id="input_d1f0ad0bb4a74bc283bf4d8033c57464_3_1" data-input-id="d1f0ad0bb4a74bc283bf4d8033c57464_3_1" value="" aria-describedby="status_d1f0ad0bb4a74bc283bf4d8033c57464_3_1" size="20"/>
<span class="trailing_text" id="trailing_text_d1f0ad0bb4a74bc283bf4d8033c57464_3_1"/>
<span class="status unanswered" id="status_d1f0ad0bb4a74bc283bf4d8033c57464_3_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_d1f0ad0bb4a74bc283bf4d8033c57464_3_1" class="answer"/>
<div id="input_d1f0ad0bb4a74bc283bf4d8033c57464_3_1_preview" class="equation">
\(\)
<img src="/static/images/spinner.bc34f953403f.gif" class="loading" alt="Loading"/>
</div>
</div>
<div class="script_placeholder" data-src="/static/js/capa/src/formula_equation_preview.b1967ab28c31.js"/>
</div></div>
<div class="solution-span">
<span id="solution_d1f0ad0bb4a74bc283bf4d8033c57464_solution_2"/>
</div><div class="wrapper-problem-response" tabindex="-1" aria-label="Question 3" role="group"><div class="choicegroup capa_inputtype" id="inputtype_d1f0ad0bb4a74bc283bf4d8033c57464_4_1">
<fieldset aria-describedby="status_d1f0ad0bb4a74bc283bf4d8033c57464_4_1">
<legend id="d1f0ad0bb4a74bc283bf4d8033c57464_4_1-legend" class="response-fieldset-legend field-group-hd">Of the two launch options we've considered, which option is more efficient (requires less total \(\Delta V\))?</legend>
<div class="field">
<input type="radio" name="input_d1f0ad0bb4a74bc283bf4d8033c57464_4_1" id="input_d1f0ad0bb4a74bc283bf4d8033c57464_4_1_choice_0" class="field-input input-radio" value="choice_0"/><label id="d1f0ad0bb4a74bc283bf4d8033c57464_4_1-choice_0-label" for="input_d1f0ad0bb4a74bc283bf4d8033c57464_4_1_choice_0" class="response-label field-label label-inline" aria-describedby="status_d1f0ad0bb4a74bc283bf4d8033c57464_4_1"> Launch due east from Cape Canaveral, then perform a burn to change inclination once in orbit
</label>
</div>
<div class="field">
<input type="radio" name="input_d1f0ad0bb4a74bc283bf4d8033c57464_4_1" id="input_d1f0ad0bb4a74bc283bf4d8033c57464_4_1_choice_1" class="field-input input-radio" value="choice_1"/><label id="d1f0ad0bb4a74bc283bf4d8033c57464_4_1-choice_1-label" for="input_d1f0ad0bb4a74bc283bf4d8033c57464_4_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_d1f0ad0bb4a74bc283bf4d8033c57464_4_1"> Launch at a northerly launch azimuth and fly directly into a 51 degree inclination orbit
</label>
</div>
<span id="answer_d1f0ad0bb4a74bc283bf4d8033c57464_4_1"/>
</fieldset>
<div class="indicator-container">
<span class="status unanswered" id="status_d1f0ad0bb4a74bc283bf4d8033c57464_4_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</div>
</div></div>
<div class="solution-span">
<span id="solution_d1f0ad0bb4a74bc283bf4d8033c57464_solution_3"/>
</div></div>
<div class="action">
<input type="hidden" name="problem_id" value="Part 3: Launching into 51 Degree Inclination" />
<div class="submit-attempt-container">
<button type="button" class="submit btn-brand" data-submitting="Submitting" data-value="Submit" data-should-enable-submit-button="True" aria-describedby="submission_feedback_d1f0ad0bb4a74bc283bf4d8033c57464" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_d1f0ad0bb4a74bc283bf4d8033c57464">
<span class="sr">Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.</span>
</div>
</div>
<div class="problem-action-buttons-wrapper">
</div>
</div>
<div class="notification warning notification-gentle-alert
is-hidden"
tabindex="-1">
<span class="icon fa fa-exclamation-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="d1f0ad0bb4a74bc283bf4d8033c57464-problem-title">
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification warning notification-save
is-hidden"
tabindex="-1">
<span class="icon fa fa-save" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="d1f0ad0bb4a74bc283bf4d8033c57464-problem-title">None
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification general notification-show-answer
is-hidden"
tabindex="-1">
<span class="icon fa fa-info-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="d1f0ad0bb4a74bc283bf4d8033c57464-problem-title">Answers are displayed within the problem
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
</div>
"
data-graded="True">
<p class="loading-spinner">
<i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i>
<span class="sr">Loading…</span>
</p>
</div>
</div>
</div>
<div class="vert vert-4" data-id="block-v1:MITx+16.00x+2T2019+type@problem+block@767a9941e2a149fdb869bdb1633a1a98">
<div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-request-token="2a6ad6faed2111efb9010e0e3c45b88f" data-usage-id="block-v1:MITx+16.00x+2T2019+type@problem+block@767a9941e2a149fdb869bdb1633a1a98" data-graded="True" data-has-score="True" data-runtime-version="1" data-block-type="problem" data-init="XBlockToXModuleShim" data-course-id="course-v1:MITx+16.00x+2T2019" data-runtime-class="LmsRuntime">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Problem"}
</script>
<div id="problem_767a9941e2a149fdb869bdb1633a1a98" class="problems-wrapper" role="group"
aria-labelledby="767a9941e2a149fdb869bdb1633a1a98-problem-title"
data-problem-id="block-v1:MITx+16.00x+2T2019+type@problem+block@767a9941e2a149fdb869bdb1633a1a98" data-url="/courses/course-v1:MITx+16.00x+2T2019/xblock/block-v1:MITx+16.00x+2T2019+type@problem+block@767a9941e2a149fdb869bdb1633a1a98/handler/xmodule_handler"
data-problem-score="0.0"
data-problem-total-possible="3.0"
data-attempts-used="0"
data-content="
<h3 class="hd hd-3 problem-header" id="767a9941e2a149fdb869bdb1633a1a98-problem-title" aria-describedby="block-v1:MITx+16.00x+2T2019+type@problem+block@767a9941e2a149fdb869bdb1633a1a98-problem-progress" tabindex="-1">
Part 4: Preparing for Orbital Rendezvous
</h3>
<div class="problem-progress" id="block-v1:MITx+16.00x+2T2019+type@problem+block@767a9941e2a149fdb869bdb1633a1a98-problem-progress"></div>
<div class="problem">
<div>
<p>Assume that you launch shortly after the ISS passes overhead, so that you get into orbit trailing the ISS by 10 minutes. </p>
<p><b>Important Note!</b> Use the provided answers from the previous problems, not the solutions you calculated, if needed when solving these. Otherwise, rounding errors may provide you an incorrect solution.</p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div class="choicegroup capa_inputtype" id="inputtype_767a9941e2a149fdb869bdb1633a1a98_2_1">
<fieldset aria-describedby="status_767a9941e2a149fdb869bdb1633a1a98_2_1">
<legend id="767a9941e2a149fdb869bdb1633a1a98_2_1-legend" class="response-fieldset-legend field-group-hd">In order to catch up with the ISS, you go into an orbit with an altitude that differs from that of the ISS by 20 km. Should you go into a higher or a lower orbit than the ISS in order to catch up?</legend>
<div class="field">
<input type="radio" name="input_767a9941e2a149fdb869bdb1633a1a98_2_1" id="input_767a9941e2a149fdb869bdb1633a1a98_2_1_choice_0" class="field-input input-radio" value="choice_0"/><label id="767a9941e2a149fdb869bdb1633a1a98_2_1-choice_0-label" for="input_767a9941e2a149fdb869bdb1633a1a98_2_1_choice_0" class="response-label field-label label-inline" aria-describedby="status_767a9941e2a149fdb869bdb1633a1a98_2_1"> Higher orbit
</label>
</div>
<div class="field">
<input type="radio" name="input_767a9941e2a149fdb869bdb1633a1a98_2_1" id="input_767a9941e2a149fdb869bdb1633a1a98_2_1_choice_1" class="field-input input-radio" value="choice_1"/><label id="767a9941e2a149fdb869bdb1633a1a98_2_1-choice_1-label" for="input_767a9941e2a149fdb869bdb1633a1a98_2_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_767a9941e2a149fdb869bdb1633a1a98_2_1"> Lower orbit
</label>
</div>
<span id="answer_767a9941e2a149fdb869bdb1633a1a98_2_1"/>
</fieldset>
<div class="indicator-container">
<span class="status unanswered" id="status_767a9941e2a149fdb869bdb1633a1a98_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</div>
</div></div>
<div class="solution-span">
<span id="solution_767a9941e2a149fdb869bdb1633a1a98_solution_1"/>
</div><div class="wrapper-problem-response" tabindex="-1" aria-label="Question 2" role="group"><div id="formulaequationinput_767a9941e2a149fdb869bdb1633a1a98_3_1" class="inputtype formulaequationinput">
<div class="unanswered">
<label class="problem-group-label" for="input_767a9941e2a149fdb869bdb1633a1a98_3_1" id="label_767a9941e2a149fdb869bdb1633a1a98_3_1">What is the orbital period of the ISS, rounded to the nearest second?</label>
<input type="text" name="input_767a9941e2a149fdb869bdb1633a1a98_3_1" id="input_767a9941e2a149fdb869bdb1633a1a98_3_1" data-input-id="767a9941e2a149fdb869bdb1633a1a98_3_1" value="" aria-describedby="status_767a9941e2a149fdb869bdb1633a1a98_3_1" size="20"/>
<span class="trailing_text" id="trailing_text_767a9941e2a149fdb869bdb1633a1a98_3_1"/>
<span class="status unanswered" id="status_767a9941e2a149fdb869bdb1633a1a98_3_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_767a9941e2a149fdb869bdb1633a1a98_3_1" class="answer"/>
<div id="input_767a9941e2a149fdb869bdb1633a1a98_3_1_preview" class="equation">
\(\)
<img src="/static/images/spinner.bc34f953403f.gif" class="loading" alt="Loading"/>
</div>
</div>
<div class="script_placeholder" data-src="/static/js/capa/src/formula_equation_preview.b1967ab28c31.js"/>
</div></div>
<div class="solution-span">
<span id="solution_767a9941e2a149fdb869bdb1633a1a98_solution_2"/>
</div><div class="wrapper-problem-response" tabindex="-1" aria-label="Question 3" role="group"><div id="formulaequationinput_767a9941e2a149fdb869bdb1633a1a98_4_1" class="inputtype formulaequationinput">
<div class="unanswered">
<label class="problem-group-label" for="input_767a9941e2a149fdb869bdb1633a1a98_4_1" id="label_767a9941e2a149fdb869bdb1633a1a98_4_1">What is the orbital period of your spacecraft, rounded to the nearest second?</label>
<input type="text" name="input_767a9941e2a149fdb869bdb1633a1a98_4_1" id="input_767a9941e2a149fdb869bdb1633a1a98_4_1" data-input-id="767a9941e2a149fdb869bdb1633a1a98_4_1" value="" aria-describedby="status_767a9941e2a149fdb869bdb1633a1a98_4_1" size="20"/>
<span class="trailing_text" id="trailing_text_767a9941e2a149fdb869bdb1633a1a98_4_1"/>
<span class="status unanswered" id="status_767a9941e2a149fdb869bdb1633a1a98_4_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_767a9941e2a149fdb869bdb1633a1a98_4_1" class="answer"/>
<div id="input_767a9941e2a149fdb869bdb1633a1a98_4_1_preview" class="equation">
\(\)
<img src="/static/images/spinner.bc34f953403f.gif" class="loading" alt="Loading"/>
</div>
</div>
<div class="script_placeholder" data-src="/static/js/capa/src/formula_equation_preview.b1967ab28c31.js"/>
</div></div>
<div class="solution-span">
<span id="solution_767a9941e2a149fdb869bdb1633a1a98_solution_3"/>
</div></div>
<div class="action">
<input type="hidden" name="problem_id" value="Part 4: Preparing for Orbital Rendezvous" />
<div class="submit-attempt-container">
<button type="button" class="submit btn-brand" data-submitting="Submitting" data-value="Submit" data-should-enable-submit-button="True" aria-describedby="submission_feedback_767a9941e2a149fdb869bdb1633a1a98" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_767a9941e2a149fdb869bdb1633a1a98">
<span class="sr">Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.</span>
</div>
</div>
<div class="problem-action-buttons-wrapper">
</div>
</div>
<div class="notification warning notification-gentle-alert
is-hidden"
tabindex="-1">
<span class="icon fa fa-exclamation-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="767a9941e2a149fdb869bdb1633a1a98-problem-title">
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification warning notification-save
is-hidden"
tabindex="-1">
<span class="icon fa fa-save" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="767a9941e2a149fdb869bdb1633a1a98-problem-title">None
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification general notification-show-answer
is-hidden"
tabindex="-1">
<span class="icon fa fa-info-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="767a9941e2a149fdb869bdb1633a1a98-problem-title">Answers are displayed within the problem
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
</div>
"
data-graded="True">
<p class="loading-spinner">
<i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i>
<span class="sr">Loading…</span>
</p>
</div>
</div>
</div>
<div class="vert vert-5" data-id="block-v1:MITx+16.00x+2T2019+type@problem+block@f60e7b46f75e4206b7e557a332d78434">
<div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-request-token="2a6ad6faed2111efb9010e0e3c45b88f" data-usage-id="block-v1:MITx+16.00x+2T2019+type@problem+block@f60e7b46f75e4206b7e557a332d78434" data-graded="True" data-has-score="True" data-runtime-version="1" data-block-type="problem" data-init="XBlockToXModuleShim" data-course-id="course-v1:MITx+16.00x+2T2019" data-runtime-class="LmsRuntime">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Problem"}
</script>
<div id="problem_f60e7b46f75e4206b7e557a332d78434" class="problems-wrapper" role="group"
aria-labelledby="f60e7b46f75e4206b7e557a332d78434-problem-title"
data-problem-id="block-v1:MITx+16.00x+2T2019+type@problem+block@f60e7b46f75e4206b7e557a332d78434" data-url="/courses/course-v1:MITx+16.00x+2T2019/xblock/block-v1:MITx+16.00x+2T2019+type@problem+block@f60e7b46f75e4206b7e557a332d78434/handler/xmodule_handler"
data-problem-score="0.0"
data-problem-total-possible="3.0"
data-attempts-used="0"
data-content="
<h3 class="hd hd-3 problem-header" id="f60e7b46f75e4206b7e557a332d78434-problem-title" aria-describedby="block-v1:MITx+16.00x+2T2019+type@problem+block@f60e7b46f75e4206b7e557a332d78434-problem-progress" tabindex="-1">
Part 5: Performing Orbital Rendezvous
</h3>
<div class="problem-progress" id="block-v1:MITx+16.00x+2T2019+type@problem+block@f60e7b46f75e4206b7e557a332d78434-problem-progress"></div>
<div class="problem">
<div>
<p>Using the information from Part 4, how far behind the ISS is your spacecraft? Round your answer to the nearest kilometer. Hint: Use the spacecraft's orbital velocity and the fact that it is trailing the ISS by 10 minutes to calculate your answer.</p>
<p><b>Important Note!</b> Use the provided answers from the previous problems, not the solutions you calculated, if needed when solving these. Otherwise, rounding errors may provide you an incorrect solution.</p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div id="formulaequationinput_f60e7b46f75e4206b7e557a332d78434_2_1" class="inputtype formulaequationinput">
<div class="unanswered">
<input type="text" name="input_f60e7b46f75e4206b7e557a332d78434_2_1" id="input_f60e7b46f75e4206b7e557a332d78434_2_1" data-input-id="f60e7b46f75e4206b7e557a332d78434_2_1" value="" aria-describedby="status_f60e7b46f75e4206b7e557a332d78434_2_1" size="20"/>
<span class="trailing_text" id="trailing_text_f60e7b46f75e4206b7e557a332d78434_2_1"/>
<span class="status unanswered" id="status_f60e7b46f75e4206b7e557a332d78434_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_f60e7b46f75e4206b7e557a332d78434_2_1" class="answer"/>
<div id="input_f60e7b46f75e4206b7e557a332d78434_2_1_preview" class="equation">
\(\)
<img src="/static/images/spinner.bc34f953403f.gif" class="loading" alt="Loading"/>
</div>
</div>
<div class="script_placeholder" data-src="/static/js/capa/src/formula_equation_preview.b1967ab28c31.js"/>
</div></div>
<div class="solution-span">
<span id="solution_f60e7b46f75e4206b7e557a332d78434_solution_1"/>
</div><div class="wrapper-problem-response" tabindex="-1" aria-label="Question 2" role="group"><div id="formulaequationinput_f60e7b46f75e4206b7e557a332d78434_3_1" class="inputtype formulaequationinput">
<div class="unanswered">
<label class="problem-group-label" for="input_f60e7b46f75e4206b7e557a332d78434_3_1" id="label_f60e7b46f75e4206b7e557a332d78434_3_1">How much closer do you get to the ISS for every orbit of your spacecraft? Give your answer in km with at least 2 decimal places. Hint: Think about the spacecraft's orbital velocity, as well as the difference between the orbital periods of the ISS and the spacecraft.</label>
<input type="text" name="input_f60e7b46f75e4206b7e557a332d78434_3_1" id="input_f60e7b46f75e4206b7e557a332d78434_3_1" data-input-id="f60e7b46f75e4206b7e557a332d78434_3_1" value="" aria-describedby="status_f60e7b46f75e4206b7e557a332d78434_3_1" size="20"/>
<span class="trailing_text" id="trailing_text_f60e7b46f75e4206b7e557a332d78434_3_1"/>
<span class="status unanswered" id="status_f60e7b46f75e4206b7e557a332d78434_3_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_f60e7b46f75e4206b7e557a332d78434_3_1" class="answer"/>
<div id="input_f60e7b46f75e4206b7e557a332d78434_3_1_preview" class="equation">
\(\)
<img src="/static/images/spinner.bc34f953403f.gif" class="loading" alt="Loading"/>
</div>
</div>
<div class="script_placeholder" data-src="/static/js/capa/src/formula_equation_preview.b1967ab28c31.js"/>
</div></div>
<div class="solution-span">
<span id="solution_f60e7b46f75e4206b7e557a332d78434_solution_2"/>
</div><div class="wrapper-problem-response" tabindex="-1" aria-label="Question 3" role="group"><div id="formulaequationinput_f60e7b46f75e4206b7e557a332d78434_4_1" class="inputtype formulaequationinput">
<div class="unanswered">
<label class="problem-group-label" for="input_f60e7b46f75e4206b7e557a332d78434_4_1" id="label_f60e7b46f75e4206b7e557a332d78434_4_1">How many orbits will it take for your spacecraft to catch up with the ISS (i.e., to be along the same radius vector)? Round your answer to the nearest integer.</label>
<input type="text" name="input_f60e7b46f75e4206b7e557a332d78434_4_1" id="input_f60e7b46f75e4206b7e557a332d78434_4_1" data-input-id="f60e7b46f75e4206b7e557a332d78434_4_1" value="" aria-describedby="status_f60e7b46f75e4206b7e557a332d78434_4_1" size="20"/>
<span class="trailing_text" id="trailing_text_f60e7b46f75e4206b7e557a332d78434_4_1"/>
<span class="status unanswered" id="status_f60e7b46f75e4206b7e557a332d78434_4_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_f60e7b46f75e4206b7e557a332d78434_4_1" class="answer"/>
<div id="input_f60e7b46f75e4206b7e557a332d78434_4_1_preview" class="equation">
\(\)
<img src="/static/images/spinner.bc34f953403f.gif" class="loading" alt="Loading"/>
</div>
</div>
<div class="script_placeholder" data-src="/static/js/capa/src/formula_equation_preview.b1967ab28c31.js"/>
</div></div>
<div class="solution-span">
<span id="solution_f60e7b46f75e4206b7e557a332d78434_solution_3"/>
</div></div>
<div class="action">
<input type="hidden" name="problem_id" value="Part 5: Performing Orbital Rendezvous" />
<div class="submit-attempt-container">
<button type="button" class="submit btn-brand" data-submitting="Submitting" data-value="Submit" data-should-enable-submit-button="True" aria-describedby="submission_feedback_f60e7b46f75e4206b7e557a332d78434" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_f60e7b46f75e4206b7e557a332d78434">
<span class="sr">Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.</span>
</div>
</div>
<div class="problem-action-buttons-wrapper">
</div>
</div>
<div class="notification warning notification-gentle-alert
is-hidden"
tabindex="-1">
<span class="icon fa fa-exclamation-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="f60e7b46f75e4206b7e557a332d78434-problem-title">
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification warning notification-save
is-hidden"
tabindex="-1">
<span class="icon fa fa-save" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="f60e7b46f75e4206b7e557a332d78434-problem-title">None
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification general notification-show-answer
is-hidden"
tabindex="-1">
<span class="icon fa fa-info-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="f60e7b46f75e4206b7e557a332d78434-problem-title">Answers are displayed within the problem
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
</div>
"
data-graded="True">
<p class="loading-spinner">
<i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i>
<span class="sr">Loading…</span>
</p>
</div>
</div>
</div>
</div>
</div>
© All Rights Reserved