consider a pair of planets that find the distance between them is decreased by a factoer of 5. Show that the force between them becomes 25 times as strong?

Answer 1

Use Newton's law of gravitation.

g=(m_1)(m_2)(G)/(d^2)

m_1 = mass of first body
m_2 = mass of second body
G = gravitational constant (value is unimportant for this particular problem)
d = distance between bodies.

Answer 2

look what happens when you use (1/5)d in place of d
F2 = F1 /(1/5)^2 = F1/(1/25) = 25 F1

Answer 3

Law of Gravitation:
F = GM1M2/r^2

Let the first distance = (5r)
then,
F1 = GM1M2/(5r)^2
or
F1= GM1M2/25r^2

The second distance is 1/5 of 5r = r
and
Let F2 = GM1M2/r^2 (with distance = r)
What is the ratio of F2 to F1, or
F2/F1 = ? (divide the expression for F2 by the expression for F1)