Question

The force of gravity, F, exerted between two objects is equal to the product of the gravitational constant, G, the mass of the first object, m1, and the mass of the second object, m2, divided by the square of the distance between their centers,
d. This is often used to determine the gravitational attraction between two massive bodies, such as planets, in space.
a. Write the formula for F described in the situation above.

Answer 1

The formula that you have accurately described in words
is written as

          F  =  G  m₁m₂/R²

This is Newton's law of universal gravitation.  It gives the exact force
between any two masses in the universe, whether they're two planets,
a black hole and a comet, or a blade of grass in Canada and a hair on
the tail of a camel in Qatar.

That's not all this formula tells.  If you know enough geometry and calculus,
and you know how to use them to give the formula a good massage,  then
Newton's equation for gravity shows why there are orbits, why the orbits of
planets are shaped as they are, why all objects on the same planet fall to the
ground at the same speed, how to put up a satellite that can be used for TV,
and why comets, moons, TV satellites, and planets take the time that they take
to orbit whatever body they're orbiting.