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## Main Question or Discussion Point

Hello,

I'm trying to really understand orbits. I want to be able to calculate the velocity at any given point in an orbit.

Now, parametrically an ellipse can be:

x = a*cos(t)

y = b*sin(t)

If those are position, can I take the derivative to obtain velocity?

x' = -a*sin(t)

y' = b*cos(t)

For the overall velocity:

V = sqrt( (-a*sin(t))^2 + (b*cos(t))^2)

However, there is a pesky t in there, now I use:

x' = -a*sin(t)

Solve for t

-x'/a = sin(t)

asin(-x'/a) = t

And subsitute t back into overall equation? Does this make sense or am I just making stuff up?

I'm trying to really understand orbits. I want to be able to calculate the velocity at any given point in an orbit.

Now, parametrically an ellipse can be:

x = a*cos(t)

y = b*sin(t)

If those are position, can I take the derivative to obtain velocity?

x' = -a*sin(t)

y' = b*cos(t)

For the overall velocity:

V = sqrt( (-a*sin(t))^2 + (b*cos(t))^2)

However, there is a pesky t in there, now I use:

x' = -a*sin(t)

Solve for t

-x'/a = sin(t)

asin(-x'/a) = t

And subsitute t back into overall equation? Does this make sense or am I just making stuff up?