# Calculus in the velocity and acceleration of satellites.

## Homework Statement

I am working on a project dealing with the velocity and acceleration of satellites based on their distance from Earth. I was recommended to include some calculus in this project. Originally I thought I could just take the derivative of the orbital speed equation to find acceleration, given the mass of the Earth and the gravitational constant would be constants in the situation. When I tested this hypothesis with the accepted acceleration equation the answers came out different. I am fairly sure this is because the remaining variable is R (the radius of the orbit) as opposed to time, but perhaps I am making a different mistake. So at this point I am in search for a way to make calculus relevant in this situation.

v = SQRT(G*M/R)
a = G*M/R^2

## The Attempt at a Solution

I also have been looking for a way to calculate the distance of objects like the ISS from Earth based on observations/ measurements I can take myself (from Earth), but I assume any solution to this would be related to trigonometry or geometry.

Homework Helper
Gold Member
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take the derivative of the orbital speed equation to find acceleration
Remember that velocity and acceleration are vectors. Differentiating a speed (a scalar) does not give acceleration.

VinnyO
Kaura
Remember that acceleration is change in velocity with respect to change in time

Mentor
Moved to Calculus & Beyond section

Remember that velocity and acceleration are vectors. Differentiating a speed (a scalar) does not give acceleration.
Remember that velocity and acceleration are vectors. Differentiating a speed (a scalar) does not give acceleration.