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<h2 class="hd hd-2 unit-title">Energy of an Orbit</h2>
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<h2>4.4.1 Energy of an Orbit</h2>
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Explain the difference in orbital energy between open and closed orbit" type="button" id="LD">MO 4.4</button></p>
<p>In addition to Kepler's Laws of Planetary Motion, the motion of objects in orbit is also related to the energy of the orbit. In the following video, Prof. Hoffman focuses on circular and elliptical orbits and explains why the energy of an orbit depends on the orbit's size.</p>
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<h2 class="hd hd-2 unit-title">Escape Velocity</h2>
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<h2>4.4.2 Escape Velocity</h2>
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<p><img style="display: block; margin: 20px auto 20px auto;" src="/assets/courseware/v1/656c4342297f0d605712b83231851836/asset-v1:MITx+16.00x+2T2019+type@asset+block/Newton_Cannon_400.png" alt="Illustration of Newton's mountaintop cannon" type="saveimage" target="[object Object]" /></p>
<p style="text-align: center;"><em><span style="font-family: 'Open Sans', Verdana, Arial, Helvetica, sans-serif;">Illustraton of Newton's mountaintop cannon (Image credit: <a href="http://commons.wikimedia.org/wiki/File:Newton_Cannon.svg">Brian Brondel</a> via Wikimedia Commons)</span></em></p>
<p>Although we briefly mentioned open orbits (such as parabolic and hyperbolic orbits) in <a href="/courses/course-v1:MITx+16.00x+2T2019/jump_to_id/c270d76bcdc140c6a845321f927369df" style="line-height: 1.6;">Subsection 4.3.2</a>, we have thus far focused our discussion on closed orbits. In the next video, Prof. Hoffman introduces the concept of the parabolic escape velocity, which was first theorized by Isaac Newton and illustrated using a hypothetical "mountaintop cannon." Such a cannon would fire objects at faster and faster speeds, resulting in larger and larger elliptical orbits until an eventual transition into a parabolic orbit. This transition from a closed orbit to an open orbit has significant implications for interplanetary exploration missions.</p>
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<h3 class="hd hd-2">Video: Escape Velocity</h3>
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<h2 class="hd hd-2 unit-title">Review of Concepts: Orbital Energy and Escape Velocity</h2>
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<h2>4.4.3 Review of Concepts: Orbital Energy and Escape Velocity</h2>
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Comparing Elliptical Orbits
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<p>The elliptical orbits shown below all have the same ________. Check all that apply.</p>
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Energy of Different Types of Orbits
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Mars Escape Velocity
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<p>What is the parabolic escape velocity from the surface of Mars? Give your answer in km/s with at least 2 decimal places. Use the following quantities in your calculations and pay close attention to unit conversions:
<ul><li>Radius of Mars: \(R = 3396 \,\text{km}\)</li><li>Mass of Mars: \(M = 6.419 \times 10^{23} \,\text{kg}\)</li><li>Universal gravitational constant: \(G = 6.674 \times 10^{-11}\, \text{m}^3/\text{kg}/\text{s}^2\)</li></ul></p>
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<span class="notification-message" aria-describedby="ad002d80eb6343269ee782522c2c272e-problem-title">None
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<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
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<div class="notification general notification-show-answer
is-hidden"
tabindex="-1">
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<span class="notification-message" aria-describedby="ad002d80eb6343269ee782522c2c272e-problem-title">Answers are displayed within the problem
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<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
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data-graded="True">
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<i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i>
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