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<h2 class="hd hd-2 unit-title">Topics and Reading List</h2>
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<p> As you go through the lesson, you will find this list of reading from the textbook complementary to the videos and exercises, and on many occasions these readings will contain relevant material to the presentation:</p><ul><li> Force Laws: <a href="/courses/course-v1:MITx+8.01.1x+3T2018/pdfbook/0/chapter/8/2"><i class="it">chapter 8, section 1</i></a></li><li> Free Body Diagrams: <a href="/courses/course-v1:MITx+8.01.1x+3T2018/pdfbook/0/chapter/8/16"><i class="it">chapter 8, section 4</i></a></li></ul>
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<h2 class="hd hd-2 unit-title">L5v1: Universal Law of Gravitation</h2>
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<h3 class="hd hd-2">L5v1: Universal Law of Gravitation</h3>
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<h2 class="hd hd-2 unit-title">L5WE1/L5v2: Worked Example: Gravity Superpositon</h2>
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L5WE1: Gravity Superposition (Worked Example)
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<p>
The center of two spherical planets of masses [mathjaxinline]m_1[/mathjaxinline] and [mathjaxinline]m_2[/mathjaxinline] are separated by a distance [mathjaxinline]d[/mathjaxinline]. Consider the origin of the coordinate system to be at the center of planet 1. At what location [mathjaxinline]x[/mathjaxinline] measured from the center of planet 1 will a third planet of mass [mathjaxinline]m[/mathjaxinline] experience zero gravitational force? Assume [mathjaxinline]m_1 \ne m_2[/mathjaxinline]. </p>
<p>
Express your answer in terms of the gravitational constant [mathjaxinline]G[/mathjaxinline], m_1 for [mathjaxinline]m_1[/mathjaxinline], m_2 for [mathjaxinline]m_2[/mathjaxinline] and [mathjaxinline]d[/mathjaxinline] as needed. <p style="display:inline">[mathjaxinline]x =[/mathjaxinline] </p> <div class="inline" tabindex="-1" aria-label="Question 1" role="group"><div id="inputtype_ls_ls02_ls02_12_2_1" class="text-input-dynamath capa_inputtype inline textline">
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<h3 class="hd hd-2">L5v2: Worked Example: Gravity - Superpositon</h3>
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<h2 class="hd hd-2 unit-title">L5Q1: Gravity Superposition</h2>
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L5Q1: Gravity Superposition
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Three balls of masses [mathjaxinline]M[/mathjaxinline], [mathjaxinline]2M[/mathjaxinline], and [mathjaxinline]5M[/mathjaxinline] are arranged as shown in the figure. What is [mathjaxinline]\vec{F}_{total}[/mathjaxinline], the total gravitational force on the middle ball, ball 2, due to balls 1 and 3? Express your answer in terms of the gravitational constant [mathjaxinline]G[/mathjaxinline], [mathjaxinline]M[/mathjaxinline], [mathjaxinline]d[/mathjaxinline] and hati for [mathjaxinline]\hat{i}[/mathjaxinline]. <p style="display:inline">[mathjaxinline]\vec{F}_{total} =[/mathjaxinline] </p> <div class="inline" tabindex="-1" aria-label="Question 1" role="group"><div id="inputtype_ls_ls02_ls02_07_2_1" class="text-input-dynamath capa_inputtype inline textline">
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<h2 class="hd hd-2 unit-title">L5v3: Gravity at the surface of the Earth: The value of g.</h2>
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<h2 class="hd hd-2 unit-title">L5Q2: Gravity at the surface of the Jupiter</h2>
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L5Q2: Gravity at the surface of Jupiter
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Consider an object of mass [mathjaxinline]m = 2.7[/mathjaxinline] kg that is falling near the surface of Jupiter. If the planet's mass is [mathjaxinline]M = 1.9\times 10^{27}[/mathjaxinline] kg and its radius is [mathjaxinline]R = 7.0 \times 10^7[/mathjaxinline] m, what is the magnitude of the acceleration of this falling object? Neglect air resistance. </p>
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<p style="display:inline">[mathjaxinline]a =[/mathjaxinline]</p>
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<span class="trailing_text" id="trailing_text_ls_ls02_ls02_08_2_1">[mathjaxinline]\mathrm{(m/s^2)}[/mathjaxinline]</span>
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<h2 class="hd hd-2 unit-title">L5Q3: Comparing Universal Gravity and the Uniform Gravity Approximation</h2>
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L5Q3: Comparing Universal Gravity and the Uniform Gravity Approximation
</h3>
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<p>Let's explore the uniformity of the gravitional force near the surface of the earth.
Compare the magnitude of the gravitational interaction force between the earth and a person of
mass \(m=80 \,\text{kg}\). </p>
<p>Useful data for your convenience:</p>
<table>
<tr>
<th>Mass of Earth:</th>
<td>\(M_E = 5.97 \times 10^{24} \,\text{kg} \)</td>
</tr>
<tr>
<th>Radius of Earth:</th>
<td>\(R_E = 6.37 \times 10^6 \,\text{m} \)</td>
</tr>
<tr>
<th>Universal Gravitation Constant:</th>
<td>\(G = 6.67 \times 10^{-11} \,\text{N}\cdot\text{m}^2/\text{kg}^2\)</td>
</tr>
</table>
<p><b>(Part a.)</b> Use the universal law of gravitation to calculate the force due to gravity on
the person at sea level:</p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><p style="display:inline">\(F_g=\) </p>
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<span class="trailing_text" id="trailing_text_lore_ls02_19225_5a987cf5fe604e9fbf2b948302c67ad7_2_1">N</span>
<span class="status unanswered" id="status_lore_ls02_19225_5a987cf5fe604e9fbf2b948302c67ad7_2_1" data-tooltip="Not yet answered.">
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<p><b>(Part b.)</b> Use the universal law of gravitation to calculate the force due to gravity on
the person when that person is in a plane at a height \(h=12000 \,\text{m}\) above sea level:</p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 2" role="group"><p style="display:inline">\(F_g=\) </p>
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<input type="text" name="input_lore_ls02_19225_5a987cf5fe604e9fbf2b948302c67ad7_3_1" id="input_lore_ls02_19225_5a987cf5fe604e9fbf2b948302c67ad7_3_1" aria-describedby="trailing_text_lore_ls02_19225_5a987cf5fe604e9fbf2b948302c67ad7_3_1 status_lore_ls02_19225_5a987cf5fe604e9fbf2b948302c67ad7_3_1" value=""/>
<span class="trailing_text" id="trailing_text_lore_ls02_19225_5a987cf5fe604e9fbf2b948302c67ad7_3_1">N</span>
<span class="status unanswered" id="status_lore_ls02_19225_5a987cf5fe604e9fbf2b948302c67ad7_3_1" data-tooltip="Not yet answered.">
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<p><b>(Part c.)</b> Calculate the force due to gravity on the person
using the gravitational approximation, with \(g=9.8 \,\text{m/s}^2\):</p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 3" role="group"><p style="display:inline">\(F_g=\) </p>
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<span class="trailing_text" id="trailing_text_lore_ls02_19225_5a987cf5fe604e9fbf2b948302c67ad7_4_1">N</span>
<span class="status unanswered" id="status_lore_ls02_19225_5a987cf5fe604e9fbf2b948302c67ad7_4_1" data-tooltip="Not yet answered.">
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<p>
<em>Comment: Observe that all three forces have roughly the same value, justifying our use of \(mg\)
to calculate the gravitational force exerted by the Earth on everyday objects.</em>
</p>
<p>
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