- #1
relativitydude
- 70
- 0
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?