Physics - Circular Motion and Gravitation

Circular motion and Gravitation are interconnected in a few ways.

The main equation of gravitation is:

All objects have an attraction towards each other. Using this equation, you can find the force of attraction between any two objects. This is Newton's law of universal gravitation. It also follows the inverse square law, meaning that the force decreases with the square of the distance between two points. Additionally, the force of attraction is proportional to the masses.

Additionally you can use this equation to find the gravity of a specfic planet. This can be done by removing the need for a second object's mass and by using the distance from the center of the planet to the surface.

F = Force of Attraction between the two objects.

G = The gravitational constant - 6.67 x 10^-11

M1 = Mass of object 1

M2 = Mass of object 2

r = the distance between the two objects

Getting into cicrular motion, the equations are:

a (Centripetal acceleration) = v^2/r

Fc (Centripetal force) = mv^2/r

Centripetal force is the force that is acting on an object and pulling it forward
Centripetal acceleration is the acceleration of a body ina circular path.

You can set centripetal force and the law of gravitation equal to each other to figure out any unknown values with an orbit. For example you can find the speed of an object's orbit around another body. Additionally, using an orbit's speed you can find the orbit period.
t = 2πr/v
t is the time it takes to orbit around the entire body, 2πr is the distance it has to travel around, and v is the velocity of the object we found using Fc = Fg