Question

If the mass of a planet is cut in half, how would the force of gravity between that planet and the Sun change?(1 point) Responses The force of gravity would double The force of gravity would double The force of gravity would decrease The force of gravity would decrease The force of gravity would increase four times The force of gravity would increase four times The force of gravity would not change

Answer 1

The force of gravity between two objects is given by Newton's law of universal gravitation, which states that the gravitational force \( F \) is directly proportional to the product of the masses of the two objects (\( m_1 \) and \( m_2 \)) and inversely proportional to the square of the distance \( r \) between their centers:

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

Where \( G \) is the gravitational constant.

If the mass of the planet (\( m_1 \)) is cut in half, the new mass becomes \( \frac{m_1}{2} \). Substituting this into the equation, the new gravitational force \( F' \) becomes:

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

This shows that the force of gravity would decrease by half.

So, the correct response would be: **The force of gravity would decrease.**