Question

When Earth and the Moon are separated by a
distance of 3.84 × 10^8 meters, the magnitude of
the gravitational force of attraction between
them is 2.0 × 10^20 newtons. What would be the
magnitude of this gravitational force of attraction
if Earth and the Moon were separated by a
distance of 1.92 × 10^8 meters?
(1) 5.0 × 10^19 N (3) 4.0 × 10^20 N
(2) 2.0 × 10^20 N (4) 8.0 × 10^20 N

Answer 1

     Using the Universal Gratitation Law, we have:

$F= \frac{MmG}{d^2} \\ MmG=2*10^{20}*(3.84*10^8)^2 \\ MmG=29.4912*10^36$
 
     Again applying the formula in the new situation, comes:

$F= \frac{MmG}{d^2} \\ F= \frac{29.4912*10^36}{(1.92*10^8)^2} \\ \boxed {F=8*10^{20}}$

Number 4

If you notice any mistake in my english, please let me know, because i am not native.

Answer 2

The strength of the gravitational forces between two masses is
inversely proportional to the square of the distance between them.

So if you change the distance to

               (1.92 x 10⁸) / (3.84 x 10⁸)  =  1/2

of what it is now, then you would change the force to

                     1 / (1/2)²  =  4

of what it is now.

   (4) x (2 x 10²⁰)  =  8.0 x 10²⁰ newtons .