Finding speed ratio at perigee and apogee for Explorer VIII satellite

[BbyBlue24]

The Explorer VIII satellite, placed into orbit November 3, 1960, to investigate the ionosphere, had the following orbit parameters: perigee, 459 km; apogee, 2289 km (both distances above the Earth's surface); period, 112.7 min. Find the ratio vp/va of the speed at perigee to that at apogee.

 

[enigma]

Welcome to Physicsforums, BbyBlue.

First off, questions like this should be submitted to the homework help section.

Second, before you can expect an answer, you should at least post what you have tried to get an answer.

It doesn't benefit you to have someone do your homework for you.

 

[BbyBlue24]

FYI: This isn't a homework problem, I am doing random problems throughout the book to prepare for an exam tomorrow.

I have played around with equations of conservation of angular momentum and equations such as v=(2πr)/T and v=√(GMe/r)=√(GMe/Re+h). I tried using Vp=(Ra/Rp)Va, but I have gotten nowhere. Thanks!

 

[Pyrrhus]

Well, by using conservation of angular momentum for the satellite

$$r_{perigee} v_{perigee} = r_{apogee} v_{apogee}$$

we rearrange this to:

$$\frac{v_{perigee}}{v_{apogee}} = \frac{r_{apogee}}{r_{perigee}}$$

you don't need the period.

 

[BbyBlue24]

I have; Vp/Va = Ra/Rp = 2289/459 = 4.99 km

 

[Pyrrhus]

The problem states distances above the surface, you need to add the Earth radius to each of those radius.

 

[BbyBlue24]

I got it, thanks! I think that's all I have tonight, thank you very much!

 

[Pyrrhus]

good luck on your test.