What would happen to the force between Earth and the sun if the mass of the sun tripled?(1 point)

Responses

The force would stay the same
The force would stay the same

The force would be tripled
The force would be tripled

The force would decrease

1 answer

The force between the Earth and the Sun is described by Newton's law of universal gravitation, which states that the gravitational force \( F \) between two masses is given by the formula:

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

where:

  • \( G \) is the gravitational constant,
  • \( m_1 \) is the mass of the first object (the Sun),
  • \( m_2 \) is the mass of the second object (the Earth), and
  • \( r \) is the distance between the centers of the two masses.

If the mass of the Sun triples (let’s denote the new mass as \( 3m_1 \)), the force becomes:

\[ F' = G \frac{(3m_1) m_2}{r^2} = 3 \left( G \frac{m_1 m_2}{r^2} \right) = 3F \]

This shows that the force would be tripled.

So the correct response is:

The force would be tripled.