Hi there!
The equation for gravitational force is:
[tex]F_g = \frac{Gm_1m_2}{r^2}[/tex]
We can plug in the given values to calculate Gm₁m₂:
[tex]2 * 10^{20} = \frac{Gm_1m_2}{(3.84*10^8)^2} \\\\Gm_1m_2 = 2.949 * 10^{37}[/tex]
Now, we can calculate the new force with the other radius:
[tex]Fg = \frac{2.949*10^{37}}{(1.92*10^8)^2} = \large\boxed{8 * 10^{20} N}[/tex]
**You could also look at the ratio between the two distances:
3.84 * 10⁸ : 1.92 * 10⁸
2 : 1
The new radius is 1/2 the size, so with the inverse square relationship of gravitational force:
1/2² = 1/4
The reciprocal of 1/4 is 4, so:
4(2.0 * 10²⁰) = 8.0 * 10²⁰ N
