Question

Two satellites of equal mass are in circular orbit around a planet. Satellite b is twice as far away. Which feels a stronger gravitational force? (1 point)

Satellite A

Satellie B

Both are the same

Neither feels a gravitational force

Answer 1

The gravitational force between two objects is given by Newton's law of universal gravitation, which states that the force \( F \) is proportional to the product of their masses and inversely proportional to the square of the distance between their centers. The formula is:

\[
F = G \frac{m_1 \cdot m_2}{r^2}
\]

Where:
- \( G \) is the gravitational constant,
- \( m_1 \) and \( m_2 \) are the masses of the two objects,
- \( r \) is the distance between their centers.

In this case, both satellites have the same mass, say \( m \). Let's denote the distance of Satellite A from the planet as \( r \), and for Satellite B, it is \( 2r \).

Now, the gravitational force on Satellite A:

\[
F_A = G \frac{M \cdot m}{r^2}
\]

And the gravitational force on Satellite B:

\[
F_B = G \frac{M \cdot m}{(2r)^2} = G \frac{M \cdot m}{4r^2}
\]

Comparing the two forces:

- \( F_A \) is proportional to \( \frac{1}{r^2} \).
- \( F_B \) is proportional to \( \frac{1}{4r^2} \), which is one-fourth of \( F_A \).

Thus, Satellite A experiences a stronger gravitational force because it is closer to the planet.

**Answer: Satellite A**.