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 not change The force of gravity would not change The force of gravity would increase four times

1 answer

The force of gravity between two objects is described by Newton's law of universal gravitation, which states that the gravitational force \( F \) between two masses \( m_1 \) and \( m_2 \) separated by a distance \( r \) is given by the formula:

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

where \( G \) is the gravitational constant.

If the mass of the planet is cut in half, the new gravitational force can be expressed as:

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

This shows that the gravitational force would decrease to half of its original value.

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