If the mass of planet Earth doubled, how would the force of gravity between Earth and the Sun change?(1 point)

Responses

The force of gravity would not change
The force of gravity would not change

The force of gravity would decrease by half
The force of gravity would decrease by half

The force of gravity would double
The force of gravity would double

The force of gravity would increase four times
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 \( F \) is proportional to the product of the masses of the two objects and inversely proportional to the square of the distance between their centers:

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

Where:

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

If the mass of the Earth (let's call it \( m_1 \)) doubles, then:

  • New mass of Earth = \( 2m_1 \)
  • Mass of the Sun remains \( m_2 \)

The new gravitational force \( F' \) would be:

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

This means that the force of gravity would double if the mass of Earth doubled.

Therefore, the correct response is:

The force of gravity would double.