Introduction to Aerospace Engineering: Astronautics and Human Spaceflight

<div class="xblock xblock-public_view xblock-public_view-vertical" data-runtime-version="1" data-course-id="course-v1:MITx+16.00x+2T2019" data-graded="False" data-block-type="vertical" data-has-score="False" data-usage-id="block-v1:MITx+16.00x+2T2019+type@vertical+block@b32b16e2f5a24367a9e6926e6345fefa" data-init="VerticalStudentView" data-runtime-class="LmsRuntime" data-request-token="83bc804e280911f0a7990e09798aea1b"> <h2 class="hd hd-2 unit-title">Changing Orbital Altitude</h2> <div class="vert-mod"> <div class="vert vert-0" data-id="block-v1:MITx+16.00x+2T2019+type@html+block@0a337d293754495e9ec4d737a17b0c65"> <div class="xblock xblock-public_view xblock-public_view-html xmodule_display xmodule_HtmlBlock" data-runtime-version="1" data-course-id="course-v1:MITx+16.00x+2T2019" data-graded="False" data-block-type="html" data-has-score="False" data-usage-id="block-v1:MITx+16.00x+2T2019+type@html+block@0a337d293754495e9ec4d737a17b0c65" data-init="XBlockToXModuleShim" data-runtime-class="LmsRuntime" data-request-token="83bc804e280911f0a7990e09798aea1b"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "HTMLModule"} </script> <h2>4.5.1 Changing Orbital Altitude</h2> <p><button border-radius="2px" class="mo_button" onclick="window.location.href='/courses/course-v1:MITx+16.00x+3T2016/5e0e82a56b234a2aaf12ac0b3359c3c5#MO46';" style="cursor: pointer;" title="MO 4.6: Describe how a Hohmann Transfer can be used to change the altitude of an orbiting spacecraft" type="button" id="LD">MO 4.6</button></p> <p>Now that we have seen how the energy of an orbit is related to its size and shape, in the next video Prof. Hoffman explains how that relationship can be used to change a spacecraft's orbital altitude, whether to reach a destination further away or to return to Earth at mission's end.</p>  <p></p> </div> </div> <div class="vert vert-1" data-id="block-v1:MITx+16.00x+2T2019+type@video+block@fc5fd8710b474248aab515b4f121ce25"> <div 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<div class="xblock xblock-public_view xblock-public_view-vertical" data-runtime-version="1" data-course-id="course-v1:MITx+16.00x+2T2019" data-graded="False" data-block-type="vertical" data-has-score="False" data-usage-id="block-v1:MITx+16.00x+2T2019+type@vertical+block@98d32de776e24cf9b00d87b9a6dbf57d" data-init="VerticalStudentView" data-runtime-class="LmsRuntime" data-request-token="83bc804e280911f0a7990e09798aea1b"> <h2 class="hd hd-2 unit-title">The Hohmann Transfer</h2> <div class="vert-mod"> <div class="vert vert-0" data-id="block-v1:MITx+16.00x+2T2019+type@html+block@d4b9458f2fea46a389fba510cd9e2abc"> <div class="xblock xblock-public_view xblock-public_view-html xmodule_display xmodule_HtmlBlock" data-runtime-version="1" data-course-id="course-v1:MITx+16.00x+2T2019" data-graded="False" data-block-type="html" data-has-score="False" data-usage-id="block-v1:MITx+16.00x+2T2019+type@html+block@d4b9458f2fea46a389fba510cd9e2abc" data-init="XBlockToXModuleShim" data-runtime-class="LmsRuntime" data-request-token="83bc804e280911f0a7990e09798aea1b"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "HTMLModule"} </script> <h2>4.5.2 The Hohmann Transfer</h2> <p><button border-radius="2px" class="mo_button" onclick="window.location.href='/courses/course-v1:MITx+16.00x+3T2016/5e0e82a56b234a2aaf12ac0b3359c3c5#MO46';" style="cursor: pointer;" title="MO 4.6: Describe how a Hohmann Transfer can be used to change the altitude of an orbiting spacecraft " type="button" id="LD">MO 4.6</button></p> <p style="padding-left: 180px;"><img src="/assets/courseware/v1/7cf318b63d7f541affcc5fd300d713c0/asset-v1:MITx+16.00x+2T2019+type@asset+block/Hohmann_Transfer_Larger.gif" alt="Illustration of using the Hohmann Transfer to increase orbital altitude" type="saveimage" target="[object Object]" /> <img src="/assets/courseware/v1/e0caf19623da8e8008173130aa8035f9/asset-v1:MITx+16.00x+2T2019+type@asset+block/Hohmann_Transfer_Smaller.gif" alt="Illustration of using the Hohmann Transfer to decrease orbital altitude" type="saveimage" target="[object Object]" /></p> <p style="text-align: center;"><em><span style="font-family: 'Open Sans', Verdana, Arial, Helvetica, sans-serif;">Illustrated examples of using the Hohmann Transfer to change orbital altitude in order to reach Mars (left) or Venus (right) (Image credit: <a href="http://www2.jpl.nasa.gov/basics/bsf4-1.php">NASA/JPL</a>)</span></em></p> <p>In the previous video, we learned that an instantaneous change in velocity can change a spacecraft's orbit from a circular orbit to an elliptical one. However, this maneuver alone is not sufficient to change orbital altitude, since the spacecraft will eventually return to the initial point where the change in velocity occurred. Instead, we have to go one step further to "circularize" the elliptical orbit by performing a Hohmann Transfer. As Prof. Hoffman explains in the following video, the Hohmann Transfer uses two velocity changes at different locations to move a spacecraft between two circular orbits of varying sizes.</p>  </div> </div> <div class="vert vert-1" data-id="block-v1:MITx+16.00x+2T2019+type@video+block@db035ba7ea2c4dbb84222fc22be5b0bc"> <div class="xblock xblock-public_view xblock-public_view-video xmodule_display xmodule_VideoBlock" data-runtime-version="1" data-course-id="course-v1:MITx+16.00x+2T2019" data-graded="False" data-block-type="video" data-has-score="False" data-usage-id="block-v1:MITx+16.00x+2T2019+type@video+block@db035ba7ea2c4dbb84222fc22be5b0bc" data-init="XBlockToXModuleShim" data-runtime-class="LmsRuntime" data-request-token="83bc804e280911f0a7990e09798aea1b"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Video"} </script> <h3 class="hd hd-2">Video: Changing Orbital Altitude, Part 2 of 2</h3> <div id="video_db035ba7ea2c4dbb84222fc22be5b0bc" 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<div class="xblock xblock-public_view xblock-public_view-vertical" data-runtime-version="1" data-course-id="course-v1:MITx+16.00x+2T2019" data-graded="False" data-block-type="vertical" data-has-score="False" data-usage-id="block-v1:MITx+16.00x+2T2019+type@vertical+block@d1e95e61641d459eb1ce47ae928508c6" data-init="VerticalStudentView" data-runtime-class="LmsRuntime" data-request-token="83bc804e280911f0a7990e09798aea1b"> <h2 class="hd hd-2 unit-title">Changing Orbital Inclination</h2> <div class="vert-mod"> <div class="vert vert-0" data-id="block-v1:MITx+16.00x+2T2019+type@html+block@441bfa1944454d5c9e6b6ce37f7995a2"> <div class="xblock xblock-public_view xblock-public_view-html xmodule_display xmodule_HtmlBlock" data-runtime-version="1" data-course-id="course-v1:MITx+16.00x+2T2019" data-graded="False" data-block-type="html" data-has-score="False" data-usage-id="block-v1:MITx+16.00x+2T2019+type@html+block@441bfa1944454d5c9e6b6ce37f7995a2" data-init="XBlockToXModuleShim" data-runtime-class="LmsRuntime" data-request-token="83bc804e280911f0a7990e09798aea1b"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "HTMLModule"} </script> <h2>4.5.3 Changing Orbital Inclination</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></p> <p>In addition to changing the size and shape of an orbit, it is also often desirable to change the orientation of an orbit in space while preserving the same size and shape. To do this, we turn our discussion to the topic of orbital inclination. In the next video, Prof. Hoffman lists the six parameters that can be used to exactly describe an orbit and the position of an object within it, and explains why it takes a (perhaps surprisingly) large amount of energy in order to change an orbit's inclination.</p>  </div> </div> <div class="vert vert-1" data-id="block-v1:MITx+16.00x+2T2019+type@video+block@2d3adc4e17c7423a93320e2a2ea15fee"> <div class="xblock xblock-public_view xblock-public_view-video xmodule_display xmodule_VideoBlock" data-runtime-version="1" data-course-id="course-v1:MITx+16.00x+2T2019" data-graded="False" data-block-type="video" data-has-score="False" data-usage-id="block-v1:MITx+16.00x+2T2019+type@video+block@2d3adc4e17c7423a93320e2a2ea15fee" data-init="XBlockToXModuleShim" data-runtime-class="LmsRuntime" data-request-token="83bc804e280911f0a7990e09798aea1b"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Video"} </script> <h3 class="hd hd-2">Video: Changing Orbital Inclination, Part 1 of 2</h3> <div id="video_2d3adc4e17c7423a93320e2a2ea15fee" class="video closed" data-metadata='{"autoplay": false, "speed": null, "duration": 454.72, "generalSpeed": 1.0, "lmsRootURL": "https://openlearninglibrary.mit.edu", "ytTestTimeout": 1500, "showCaptions": "true", "savedVideoPosition": 0.0, "completionEnabled": false, "ytMetadataEndpoint": "", "sources": ["https://d2f1egay8yehza.cloudfront.net/MIT1600X/MIT1600XT115-V005000_DTH.mp4", "https://d2f1egay8yehza.cloudfront.net/MIT1600X/MIT1600XT115-V005000_DTH.webm", "https://d2f1egay8yehza.cloudfront.net/MIT1600XT115-V005000/MIT1600XT115-V005000.m3u8"], "autohideHtml5": false, "autoAdvance": false, "transcriptAvailableTranslationsUrl": "/courses/course-v1:MITx+16.00x+2T2019/xblock/block-v1:MITx+16.00x+2T2019+type@video+block@2d3adc4e17c7423a93320e2a2ea15fee/handler/transcript/available_translations", "end": 0.0, "saveStateUrl": 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<div class="xblock xblock-public_view xblock-public_view-vertical" data-runtime-version="1" data-course-id="course-v1:MITx+16.00x+2T2019" data-graded="False" data-block-type="vertical" data-has-score="False" data-usage-id="block-v1:MITx+16.00x+2T2019+type@vertical+block@bd549733997f4676ad213883450d1c9d" data-init="VerticalStudentView" data-runtime-class="LmsRuntime" data-request-token="83bc804e280911f0a7990e09798aea1b"> <h2 class="hd hd-2 unit-title">The Influence of Launch Location</h2> <div class="vert-mod"> <div class="vert vert-0" data-id="block-v1:MITx+16.00x+2T2019+type@html+block@e8cd637487524a51b2b9d33674cc5413"> <div class="xblock xblock-public_view xblock-public_view-html xmodule_display xmodule_HtmlBlock" data-runtime-version="1" data-course-id="course-v1:MITx+16.00x+2T2019" data-graded="False" data-block-type="html" data-has-score="False" data-usage-id="block-v1:MITx+16.00x+2T2019+type@html+block@e8cd637487524a51b2b9d33674cc5413" data-init="XBlockToXModuleShim" data-runtime-class="LmsRuntime" data-request-token="83bc804e280911f0a7990e09798aea1b"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "HTMLModule"} </script> <h2>4.5.4 The Influence of Launch Location</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></p> <p><span style="line-height: 25.6000003814697px;">Now that we understand why it is extraordinarily difficult to </span><span style="line-height: 25.6000003814697px;">change orbital inclination, we discuss the implications of this challenge for launching spacecraft into orbit.  As we will see, not all launch sites are created equal.  In the next video, Prof. Hoffman addresses how the location of a launch site influences </span><span style="line-height: 25.6000003814697px;">the $\Delta V$ required to achieve orbit, as well as the change in inclination needed to reach geostationary orbit.</span></p> <p></p> <p></p>  </div> </div> <div class="vert vert-1" data-id="block-v1:MITx+16.00x+2T2019+type@video+block@51ccffa5f70a4216a4c40f979b1bc22e"> <div class="xblock xblock-public_view xblock-public_view-video xmodule_display xmodule_VideoBlock" data-runtime-version="1" data-course-id="course-v1:MITx+16.00x+2T2019" data-graded="False" data-block-type="video" data-has-score="False" data-usage-id="block-v1:MITx+16.00x+2T2019+type@video+block@51ccffa5f70a4216a4c40f979b1bc22e" 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The Influence of Launch Location

4.5.4 The Influence of Launch Location

Now that we understand why it is extraordinarily difficult to change orbital inclination, we discuss the implications of this challenge for launching spacecraft into orbit. As we will see, not all launch sites are created equal. In the next video, Prof. Hoffman addresses how the location of a launch site influences the $\Delta V$ required to achieve orbit, as well as the change in inclination needed to reach geostationary orbit.

Video: Changing Orbital Inclination, Part 2 of 2

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Why did I choose 30 degrees?
Well, here we get into an interesting question
of where do we want our satellites ultimately
to end up?
Well, it turns out that a lot of satellites we
want to put in geostationary orbit, which
is 42,000 kilometers above the center of the Earth
in the equatorial plane.
So that as the Earth rotates and the satellites
are going at the same rotational rate as the Earth,
they appear to be motionless above one point on the Earth.
But we launch from various places around the world.
For instance, in the US, a lot of our flights
go out of Cape Canaveral.
In Russia, they go out of Kazakhstan, Baikonur.
The Europeans have a launch site in Kourou in French Guiana.
Let's take a look now at what happens
when we launch out of Florida.
I'm going to take my orbit and I'm
going to put it right over Florida here.
And of course, the plane of the orbit
has to go through the center of the Earth.
So that means that in this case, the northernmost point
of our orbit-- this is assuming we fly directly to the east
once we launch out of Florida.
The northernmost point is going to be
at the latitude of Cape Canaveral, which is
about 28 and 1/2 degrees north.
And the other side of the orbit is
going to be 28 degrees south.
Now I have a little bit of freedom when I launch.
I don't have to launch due east.
I could launch a little bit to the north, in which case
for instance, if I want to fly to a high inclination
near polar orbit, I'll fly to the north out of the Cape
and I'll go into a much higher inclination orbit.
What happens now if I want to get to a lower inclination
orbit?
Well, let's go back to an easterly trajectory.
Now let's launch further to the south.
Does that get me into a lower inclination orbit?
No, not at all, because look what happens
on the other side of the orbit.
Its going to a higher northerly attitude.
So no matter what I do, I could rotate,
but the pivot point goes right around our launch site.
And the net result is that by launching due east,
I go into an orbital inclination which
is inclined to the Equator at an angle equal to the latitude
of my launch site, 28 and 1/2 degrees for Cape Canaveral.
Any other launch azimuth to the north or south,
and I go into a higher inclination orbit,
and it doesn't matter whether I go to the north or the south.
A lot of satellites that we launch ultimately
are destined to become telecommunication satellites
at geostationary orbits, which means
that they have to be over the equator
because the Earth is rotating.
And out at 42,000 kilometers from the center of the Earth,
the satellites will be in a circular orbit
with the same period as the Earth's rotation,
and so they will appear to be stationary.
But you have to get from a 28 degree orbit
to a 0 degree inclination orbit, and as we saw,
that's incredibly expensive if we do it near the Earth
where our orbital velocity is 7.9 kilometers per second.
So here's how we do it.
We actually go into what we call a geostationary transfer
orbit using a Hohmann Transfer, which we now understand.
We do a burn and we go out to apogee.
And now of course using Kepler's second law,
we know that the velocity out at apogee
is a lot smaller than the velocity at perigee.
And so instead of having to change
the 7.9 kilometers per second, it's a much lower burn.
And so if you want to change your inclination
and you're in an elliptical orbit, for goodness sakes,
change it when you're far away near apogee
and you're moving as slowly as possible.
Now that was the situation for Cape Canaveral at 28 degrees.
The European launch center at Kourou in French Guiana
is only 6 degrees north of the Equator.
And so when they are launching geostationary satellites
for telecommunications purposes, they only
have to change their inclination by 6 degrees
whereas from Cape Canaveral we have to change it
by 28 and 1/2 degrees.
And the poor Russians launching from Kazakhstan-- they've
got 51 degrees that they have to change if they want
to go to geostationary orbit.
So a couple of takeaway points.
First of all, getting into geosynchronous orbit
takes different amounts of propellant because
of the inclination change that you
have to make for different latitudes of launch sites.
Also, remember geostationary orbit
is the orbit that is economically useful right
above the equator.
Geosynchronous just means 24 hour period.
Geostationary-- inclination of zero right above the equator.
The second critical point: for a given latitude of a launch
site, the minimum orbital inclination
that you can fly into directly is
equal to the latitude of a launch site.
And the third point is if you want
to get to geostationary orbit, you
have to change your orbital inclination.
And the higher the latitude of your launch site, the more
inclination change you're going to have to make.
Now there's one other factor where launch sites have
a difference in their ability to get to orbit,
and that's because the Earth is rotating.
Every 24 hours we spin around, and if you calculate
the velocity at the equator of the Earth, it's about half
a kilometer a second.
Compared to the roughly 8 kilometers a second
that you need in orbit to have orbital velocity,
that's a reasonable fraction and that makes a difference.
And if you take off right from the Equator,
you can count that extra half a kilometer
per second you get from the Earth.
I mean, that's as good as burning rocket fuel.
In fact, it's a lot less expensive.
The problem is you go to more northerly latitudes
is that the eastward component of the Earth's rotation
decreases as the cosine of your latitude.
So by the time you get up to Cape Canaveral,
that half a kilometer per second you get at the Equator
has gone down to 4/10.
And by the time you get up to the 51 degrees
up in Kazakhstan, it's gone down to about 3/10
of a kilometer per second.
So this extra 100 or 200 meters per second,
that makes quite a difference in terms
of the amount of propellant you have to burn.
Of course, if you're going into a polar orbit
and you want to launch to the north,
then you don't really care about the rotation of the Earth.
But for an eastward trajectory where
you're flying into a typical orbit or an orbit
from which you're going to transfer
to geostationary orbit, you do get a boost
from the Earth's rotation.
And the closer you order the equator,
the bigger that boost is.
So we've seen quite a bit, and just a brief review
of where we've gotten to here.
We looked at simple circular orbits,
and we derived some relationships
in speed, period, which we found actually duplicated
some of Kepler's laws.
Which applied of course not just to the simple circular orbits
where we did the math, but to elliptical orbits in general.
And we saw the very important relationship
that the energy of the orbit varies
with the semi-major axis, and a larger orbit
has a larger energy.
We looked at what's involved in changing orbits,
using Hohmann Transfer to change the size of the orbit
to go from one nearly circular orbit to either a larger
or a smaller orbit.
And we looked at the implication of orbital inclination.
What it takes to change the inclination.
Why it's so difficult to change the inclination once
you are already in orbit.
And therefore, the importance of the launch site
in getting to orbits of general inclinations.
And the fact that the closer you are to the equator--
if you want to end up in an equatorial orbit,
which is what we want for geostationary satellites--
that you definitely have advantages.
Both because of not having to change the orbital inclination
so much, and because you get more of a boost
from the rotation of the Earth.
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