Question

If the mass of a planet is cut in half, how would the force of gravity between that planet and the Sun change? (The force of gravity’s would increase four times; The force of gravity would decrease; The force of gravity would double; The force of gravity would not change)

Answer 1

The force of gravity between two objects is described by Newton's Law of Universal Gravitation, which states:

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

where:
- \( F \) is the force of gravity,
- \( G \) is the gravitational constant,
- \( m_1 \) and \( m_2 \) are the masses of the two objects (in this case, the planet and the Sun),
- \( r \) is the distance between the centers of the two objects.

If the mass of the planet is cut in half, let's denote the original mass of the planet as \( m_1 \) and the new mass as \( \frac{m_1}{2} \).

The new force of gravity can be expressed as:

\[
F' = G \frac{\left(\frac{m_1}{2}\right) m_2}{r^2}
\]

We can see that the new force \( F' \) would be:

\[
F' = \frac{1}{2} G \frac{m_1 m_2}{r^2} = \frac{1}{2} F
\]

Thus, when the mass of the planet is cut in half, the force of gravity between that planet and the Sun would decrease.

Therefore, the correct answer is: **The force of gravity would decrease.**