Question

A probe orbiting Venus exerts a gravitational force of 2.58 × 10^3 N on Venus. Venus has a mass of 4.87 × 10^24 kg. The mass of the probe is 655 kilograms.To three significant digits, the probe is 9.08 × 10^6 m from the center of Venus.

Answer 1

So this is the info that's given to us:
m1 = 4.87 x 10^24 kg
m2 = 4.87 x 10^24kg
F = 2.58 x 10^3 N

Now we can use this equation to solve: $f_g= \frac{Gm_1m_2}{r^2}$

You may be asking what g is. Well, it is equal to 6.67x10^-11 m3 /kg s2. G is gravitational constant. So :

$2.58 x 10^3 = \frac{6.67x10^{-11} * 4.87 x 10^{24} * 655}{r^{2}}$ 

As you can see we only have one variable, so we solve for r! 

$r = 9.08 x 10^6 km$

I hope this helps you out. I remember when I was first learning Newton's law of universal gravitation and I had some trouble. But with some practice, I got better. =)