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<title>Adventure 15 Activity 1 – Student</title>
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<h1>🧩 Adventure 15 – Activity 1</h1>
<p class="small"><b>The Sun Controls the Solar System</b></p>
<p>
In this activity, you will calculate one powerful quantity, <b>GM<sub>sun</sub></b>, and then use it
to compute orbital speed, orbit size, and orbital period for Mercury, Earth, and Neptune.
Enter only numerical answers in the boxes below.
</p>
</div>
<div class="card">
<h2>🔹 Part I — Compute GM of the Sun</h2>
<p>Newton’s gravitational constant:</p>
<div class="formula">G = (6.67e-11) N m² / kg²</div>
<p>N=Newton unit of Force=ma kg(m/s²)</p>
<p>Mass of the Sun:</p>
<div class="formula">M_sun = (2.0e30) kg</div>
<p><b>Task:</b> Compute <span class="formula">GM_sun = G × M_sun</span></p>
<p>GM<sub>sun</sub> = <input class="answer" id="gm" /> m³/s²</p>
</div>
<div class="card">
<h2>📊 Table 1 — Orbital Velocity and Period for 3 Planets</h2>
<p class="small">No decimals unless the number is less than 1.</p>
<table>
<tr>
<th>Planet</th>
<th>Distance from Sun r (m)</th>
<th>Orbital Velocity v (m/s)</th>
<th>Orbit Size 2πr (m)</th>
<th>Period T (s)</th>
<th>Period (years)</th>
</tr>
<tr><td>Mercury</td><td>(5.79e10)</td><td><input class="answer" id="mer_v" /></td><td><input class="answer" id="mer_c" /></td><td><input class="answer" id="mer_t" /></td><td><input class="answer" id="mer_y" /></td></tr>
<tr><td>Earth</td><td>(1.496e11)</td><td><input class="answer" id="ear_v" /></td><td><input class="answer" id="ear_c" /></td><td><input class="answer" id="ear_t" /></td><td><input class="answer" id="ear_y" /></td></tr>
<tr><td>Neptune</td><td>(4.495e12)</td><td><input class="answer" id="nep_v" /></td><td><input class="answer" id="nep_c" /></td><td><input class="answer" id="nep_t" /></td><td><input class="answer" id="nep_y" /></td></tr>
</table>
<h3>Useful Formulas</h3>
<div class="formula">v = sqrt(GM / r)</div><br>
<div class="formula">Orbit size = 2πr</div><br>
<div class="formula">T = (2πr) / v</div><br>
<div class="formula">years = seconds / 31557600</div>
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<script>
const answers = {
gm: 1.334e20,
mer_v: 47995,
mer_c: 3.638e11,
mer_t: 7.58e6,
mer_y: 0.24,
ear_v: 29855,
ear_c: 9.40e11,
ear_t: 3.15e7,
ear_y: 1.00,
nep_v: 5448,
nep_c: 2.824e13,
nep_t: 5.18e9,
nep_y: 164.1
};
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ear_c: '9.40e11',
ear_t: '3.15e7',
ear_y: '1.00',
nep_v: '5448',
nep_c: '2.824e13',
nep_t: '5.18e9',
nep_y: '164.1'
};
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