The Mystery of Satellite Speed: Solving an Elliptical Orbit

[hellothere123]

Homework Statement

A satellite is in an elliptical orbit at altitudes ranging from 230 to 890 km. At the high point it's moving at 7.23 km/s. How fast is it moving at the low point?

I would think i would have to use some sort of energy conservation equations. but i really don't know where to begin or how to set this up. any help would be greatly appreciated!. i would like to learn how to do this.

 

[Sumanyu]

I don't see why it wouldn't be 7.23 km/s at the low point...

 

[LowlyPion]

Homework Statement

A satellite is in an elliptical orbit at altitudes ranging from 230 to 890 km. At the high point it's moving at 7.23 km/s. How fast is it moving at the low point?

I would think i would have to use some sort of energy conservation equations. but i really don't know where to begin or how to set this up. any help would be greatly appreciated!. i would like to learn how to do this.

What does Kepler's Laws tell you about sweeping equal areas in equal times?

 

[hellothere123]

kepler's law says they sweep out equal area in equal times. but i do not know how much area they are sweeping and how long it takes to sweep the equal area.

 

[LowlyPion]

kepler's law says they sweep out equal area in equal times. but i do not know how much area they are sweeping and how long it takes to sweep the equal area.

Consider the velocity at aphelion and perihelion. At these 2 points they are moving ⊥ to the radius. Now you know that V = Δx/Δt For any small fixed Δt then you have a Δx and the radial distance.

Looking at the area of the triangle formed by this Δx and can't you say with some certainty that the areas will be equal, by Kepler's Law? A = 1/2*b*h.
So ...

1/2*Δx1*r1 = 1/2*Δx2*Δr2

Simplifying and dividing by Δt can't you say then that

V1*r1 = V2*r2?

 

[hellothere123]

well i did some crazy stuff and got it to work :P
but i tried with the v1r1 = v2r2, doesn't give me the right answer. i did 1/2 mv^2 + mgh where i found g at that height and it magically gave me the answer. so, did i get lucky? or did i do it right?

 

[LowlyPion]

well i did some crazy stuff and got it to work :P
but i tried with the v1r1 = v2r2, doesn't give me the right answer. i did 1/2 mv^2 + mgh where i found g at that height and it magically gave me the answer. so, did i get lucky? or did i do it right?

Don't forget that r1 = R_e + Altitude1 and r2 = R_e + Altitude2. Where R_e is the radius of earth.

 

[hellothere123]

ahh you are right. i did not account for that. thanks for all the help!