# Hohmann Transfer Orbit (Simple)

1. Oct 8, 2013

### bmb2009

1. The problem statement, all variables and given/known data
I've been stuck on this problem forever, any help is greatly appreciated. A satellite is in a LEO at h=300km and it is sent to a geosynchronous orbit at 4.224x10^4 km. Calculate velocity at pericenter i.e v_pe

2. Relevant equations

v_pe = (2πa_to)/p_to[2a_to/a_leo -1 ]^(1/2)

3. The attempt at a solution

I ran the numbers several times slowly in all the right units etc and still get a ridiculous number... i.e. a boost velocity of 10^6 power...

do I have the right equation for v_pe?

i used a_to = a_gs + a_leo / 2 where a_gs is the given quantity and a_leo = radius of earth + h

2. Oct 8, 2013

### bmb2009

and p^2=a^3 with a in au for period of the transfer orbit

3. Oct 8, 2013

### Staff: Mentor

If I may suggest, perhaps an easier to use formula for the velocity of a body on orbit is given by:
$$v(r) = \sqrt{\mu \left(\frac{2}{r} - \frac{1}{a} \right)}$$
where $\mu$ is the gravitational parameter of the central body (GM for the Earth in this case).

You know the perigee radius and a for the transfer orbit... so no mucking about with AU and periods.

Last edited: Oct 9, 2013