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)ResponsesThe force of gravity would decrease The force of gravity would decrease The force of gravity would doubleThe force of gravity would doubleThe force of gravity would increase four timesThe force of gravity would increase four timesThe force of gravity  would not change

1 answer

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 (\( m_1 \) becomes \( \frac{m_1}{2} \)), while the mass of the Sun and the distance \( r \) remains unchanged:

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

Thus, the force of gravity would decrease.

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