difference between g as acceleration in space and centripetal acceleration in space?

Question

g= GM/r^2, ac= v^2/r. do they both give acceleration? What is the difference between these two?

Answer 1

The first one, 'g', is a specific acceleration caused by the force of gravity. This is the acceleration that objects experience when they fall in the air due to Earth's gravitational attraction.

If you multiply this 'g' by the mass undergoing this acceleration, you find the weight - the force of gravity applied to it.

F_g = mg = GMm/R²

However, a_c is the centripetal acceleration that causes objects to move in circular orbits. This acceleration is an effect that can be created by different types of forces (friction on the ramp, tension on a swinging string, normal contact force on a roller coaster, electrostatic force between charges). a_c occurs when circular motions happen, and it is a model acceleration to explain the circular motion that occurs with the centripetal force (center-calling force).

For example, between the Earth and the Moon, there is the force of gravity. F = G(M_Earth m_Moon)/R²

Since the motion is 'circular' this force can be written as a circular/centripetal force as well.

G(M_Earth m_Moon)/R² = M_moonV_moon/R²