QuestionMay 6, 2025

In a far-off galaxy, an astronomer observes a moon orbiting a planet. The moon stays in orbit because of the planet's gravity. Which scenario would increase the gravity of the planet? decreasing the distance between the moon and the planet increasing the distance between the moon and planet increasing the planet's inertia increasing the moon's inertia

In a far-off galaxy, an astronomer observes a moon orbiting a planet. The moon stays in orbit because of the planet's gravity. Which scenario would increase the gravity of the planet? decreasing the distance between the moon and the planet increasing the distance between the moon and planet increasing the planet's inertia increasing the moon's inertia
In a far-off galaxy, an astronomer observes a moon orbiting a planet. The moon stays in orbit because of the planet's gravity. Which scenario would increase the gravity of the planet? decreasing the distance between the moon and the planet increasing the distance between the moon and planet increasing the planet's inertia increasing the moon's inertia

Solution
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Answer

Increasing the planet's inertia Explanation 1. Identify the formula for gravitational force Gravitational force is given by **F = G \frac{m_1 m_2}{r^2}**, where G is the gravitational constant, m_1 and m_2 are the masses of the two objects, and r is the distance between them. 2. Analyze the effect of each scenario - Decreasing the distance (r): Increases gravity because F \propto \frac{1}{r^2}. - Increasing the distance (r): Decreases gravity because F \propto \frac{1}{r^2}. - Increasing the planet's inertia (mass): Increases gravity because F \propto m_1. - Increasing the moon's inertia (mass): Also increases gravity because F \propto m_2. 3. Select the correct scenario The question asks specifically about increasing the *planet's* gravity. This corresponds to increasing the planet's mass (inertia).

Explanation

1. Identify the formula for gravitational force<br /> Gravitational force is given by **$F = G \frac{m_1 m_2}{r^2}$**, where $G$ is the gravitational constant, $m_1$ and $m_2$ are the masses of the two objects, and $r$ is the distance between them.<br /><br />2. Analyze the effect of each scenario<br /> - Decreasing the distance ($r$): Increases gravity because $F \propto \frac{1}{r^2}$.<br /> - Increasing the distance ($r$): Decreases gravity because $F \propto \frac{1}{r^2}$.<br /> - Increasing the planet's inertia (mass): Increases gravity because $F \propto m_1$.<br /> - Increasing the moon's inertia (mass): Also increases gravity because $F \propto m_2$.<br /><br />3. Select the correct scenario<br /> The question asks specifically about increasing the *planet's* gravity. This corresponds to increasing the planet's mass (inertia).
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