# Perigee Apogee Ratio

A satellite, placed into the Earth's orbit to investigate the ionosphere, had the following orbit parameters: perigee, 475 km; apogee, 2265 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.

I was told by someone that this ratio is equal to the inverse ratio of the distances. But the period is thrown in so I have no idea where to start on this one. I know this follows an elliptical shape but I still can't think of where to begin.

Can anyone give a first couple of steps to get me started?
Thanks

Google Keplers laws of motion. He found that equal orbital areas are swept in equal time, and developed the math to explain it. Which still hols up well, unless looking at Mercury, but thats a later chapter.

ive done reasearch and i have notes but i cant seem to apply it properly, only post plz if u can give me a concrete path to take or equation to use

Ok, if the research didn't help, try the following, assume that in both cases, that the orbit is circular where v^2/r=g. What results do you get for v in both cases?

Ok, if the research didn't help, try the following, assume that in both cases, that the orbit is circular where v^2/r=g. What results do you get for v in both cases?

v = sqrt(gr)

but then the ratio would be equal to sqrt(r1)/sqrt(r2) since g cancels,
is this right?

Post some numbers.

Vp/Va = sqrt(2265)/sqrt(475)
= 2.184

but sum1 told me before that
Vp/Va = 2265/475 (inverse ratio)

but i dont kno why the period is not a factor

because g is not constant. You need to correct for that first.

because g is not constant. You need to correct for that first.

o ya oops i forgot

i kno ur not supposed to give ppl direct answers on this, but im super frustrated with this question so could sumbody please give me a big boost,
like just explain wut need to be equated together cuz all the hints make me more confused and with planetary motion there are too many equations and its rough enough trying to simplify them
i dont mind working hard for this question but i just need a good foundation to work with

ok ive seen the equations for kepplers laws, i just dont know where to get the velocity out of it
i know there is the equation with the squared equal to the cubed
but i have no clue where to get the velocity into the picture,
also do i need to find the eccentricity first

sum1 please tell me the first few steps to follow in roder to solve this