Question

1. you calculate the force of gravity between two asteroids in space. what would happen to the gravitational force between them if you were to double the mass of one asteroid, and cut the mass of the second asteroid in half?

the force does not change
the force would double
the force would be halved
the force is quadrupled

Explanation:

Step1: Recall the gravitational force formula

The gravitational force formula is \(F = G\frac{m_1m_2}{r^2}\), where \(G\) is the gravitational constant, \(m_1\) and \(m_2\) are the masses of the two objects, and \(r\) is the distance between them.

Step2: Analyze the change in mass

Let the original masses be \(m_1\) and \(m_2\), so the original force \(F_1=G\frac{m_1m_2}{r^2}\). After changing, \(m_1' = 2m_1\) and \(m_2'=\frac{1}{2}m_2\). Then the new force \(F_2 = G\frac{(2m_1)(\frac{1}{2}m_2)}{r^2}\).

Step3: Simplify the new - force expression

Simplify \(F_2\): \(F_2=G\frac{m_1m_2}{r^2}\)

Answer:

The force does not change.