physics universal gravitation

Question

The planet Krypton has a mass of 4.1 × 1023 kg and radius of 4.4 × 106 m. What is the acceleration of an object in free fall near the surface of Krypton? The gravitational constant is 6.6726 × 10−11 N · m2 /kg2 . Answer in units of m/s 2 .

Answer 1

The law of universal gravitation gives a force, and we need acceleration. By re-arranging F=ma, we see that the acceleration of an object is the force acting on it, divided by it's mass. So, we can divide both sides of the law of universal gravitation to find acceleration:

a = (G*M)/r²

where M is the mass of the planet, and r is it's radius.

a = (6.6726e-11 * 4.1e23)/((4.4e6)²).

After some simplification, this works out to

a = (6.6726 * 4.1e12)/(4.4²e12) = 6.6726 * 4.1/(4.4²)

This gives an answer somewhere between 1 and 2, and the answer will naturally be in m/s² since we were working with meters, kg, and newtons. Finally, the answer should be rounded to two significant figues.