What is the orbital velocity at pericenter and apocenter

[dairycat]

One way of lifting a satellite into geosynchronorous orbit is to use the space shuttle to lift it into a circular, low-earth orbit(h=300km) and then use a booster rocket to place the satellite on a hohmann transfer orbit up to a circular geosynchronous orbit. what is the orbital velocity of the satellite while it is still in low-earth orbit? what is the orbital velocity at pericenter, of the appropriate hohmann transfer orbit? what is the orbital velocity at apocenter of the hohmann transfer orbit? how long does it take the satellite to travel from the low-earth orbit to the geosynchronous orbit?

Homework Equations

v=sqrt(g*m/r)
i think Vp=sqrt(U(2/r-1/a)
Va=sqrt(U(2/r-1/a)

The Attempt at a Solution

i found the orbital velocity of low-earth orbit using v=sqrt(g*m/r) = 7.67km/s
i don't know how to find the rest. a little help please?

 

[gneill]

Hi Dairycat, welcome to PF.

First you'll want to determine the parameters of the required Hohmann transfer orbit; it's starting radius, it's ending radius, then it's semimajor axis (a). You'll need the orbital radius of a geosynchronous satellite. Once you have that you can apply the formulas that you've stated.

By the way, it's traditional to refer to Newton's gravitational constant as G (capital G), since small g is "reserved" for the acceleration due to gravity near the Earth's surface. The mass of the large body that something of negligible mass orbits, like the Earth in this problem, is also usually granted capital letter status. Thus $\mu = GM$, where here M would be the mass of the Earth.