Hohmann Transfer

#orbital_mechanics#physics

A two burn mechanism to raise the orbit or lower the orbit of a vehicle within gravitational influence. The orbits in reference here are circular orbits. Following phases are involved:

1. Departure Burn
2. Coast Phase — the vehicle is in elliptical trajectory in this case
3. Arrival Burn

Hohmann transfer is considered to be the most fuel efficient transfer process. To calculate the fuel spent, the difference in pre burn and post burn orbital velocities is calculated. This difference from both the burns is added up to identify total delta for orbital velocity.

This delta can be used in further calculations to identify fuel spent.

Hohmann transfers are based on principles on conservation of Kinetic and Potential Energy. For instance, if a satellite is orbiting in Low Earth Orbit (LEO), to not fall back to Earth, the satellite has to maintain higher velocities compared to orbits farther away from Earth.

Hence, LEO satellite having a high Kinetic Energy but Low Potential Energy will have a higher Potential and low Kinetic Energy when transferred to a higher orbit.

$K{E}_1+P{E}_1=K{E}_2+P{E}_2$

Cons:

1. Assumes circular orbit, which practically is not the case with any planets in the solar system. Might work in case of satellites orbiting around Earth.
2. Assumes the objects are in the same plane as Earth, in reality all other planets are upto 3 degrees offset. Mercury and Pluto are more than 3 degree offset.
3. Does not consider gravity influence from other objects within the trajectory. Example: An object travelling from Earth to Mars will have to bear to influence of Sun’s gravity along with other planets or objects within influence.
4. For the most fuel efficient journey, we have to wait for a narrow launch window, which is when the Earth, Sun, and the target object/planet are in opposition. Opposition means, the Sun and the target object/planet is diametrically opposite to Earth. Example: This reduces the Earth-Mars travel window to once every 26 months. PS: This also affects the other orbital maneuvers in general and not specific to Hohmann Transfers.