Question

If the mass of planets Earth doubled, how would the force of gravity between Earth and the Sun change?

Answer 1

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

In the case of Earth and the Sun, if the mass of Earth (\( m_1 \)) doubles, we can denote the new mass of Earth as \( 2m_1 \). The mass of the Sun (\( m_2 \)) and the distance between the Earth and Sun (\( r \)) remain constant.

Substituting the new mass of Earth into the equation:

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

This shows that the new gravitational force \( F' \) is:

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

where \( F \) is the original gravitational force.

Thus, if the mass of Earth doubled, the gravitational force between Earth and the Sun would also double.