# Hohmann Transfer Orbit (Simple)

• bmb2009
In summary, the conversation discusses a problem involving calculating the velocity at pericenter for a satellite being sent from a Low Earth Orbit to a geosynchronous orbit. The formula used for velocity is questioned and an alternative formula is suggested for easier use.
bmb2009

## 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

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:
1 person

## 1. What is a Hohmann Transfer Orbit?

A Hohmann Transfer Orbit is a type of orbital maneuver used by spacecraft to transfer from one circular orbit to another.

## 2. How does a Hohmann Transfer Orbit work?

A Hohmann Transfer Orbit works by taking advantage of the natural orbital mechanics of a planet. The spacecraft first enters an elliptical orbit around the planet, with the point of closest approach being at the same altitude as the destination orbit. The spacecraft then performs a burn at the farthest point of the elliptical orbit, known as the transfer orbit, to raise the point of closest approach to the same altitude as the destination orbit. Another burn is then performed at the new point of closest approach to circularize the orbit.

## 3. What are the advantages of using a Hohmann Transfer Orbit?

A Hohmann Transfer Orbit is the most efficient way to transfer between two circular orbits, as it requires the least amount of energy. It also allows for a smooth and predictable trajectory, making it easier to plan and execute.

## 4. How long does a Hohmann Transfer Orbit take?

The duration of a Hohmann Transfer Orbit depends on the distance and relative velocities of the two orbits. As a general rule, the longer the distance between the two orbits, the longer the transfer orbit will take. However, with careful planning and precise burns, the duration can be minimized.

## 5. Are there any limitations to using a Hohmann Transfer Orbit?

While a Hohmann Transfer Orbit is the most efficient way to transfer between two circular orbits, it is not always feasible. For example, if the destination orbit has a significantly different inclination than the current orbit, a Hohmann Transfer Orbit may not be possible without additional maneuvers. Additionally, it may not be the best option for time-sensitive missions, as it can take weeks or months to complete the transfer.

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