# Hohmann Transfer Orbit (Simple)

## Homework Statement

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

## Homework Equations

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

## 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

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

gneill
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.

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