Hohmann Transfer Orbit

Hohmann Transfer orbit is an elliptical orbit in orbit mechanism used to transfer between two circular orbitals with different radii around a central body in the same plane. The plane in such a case is usually tangential to both. 

A low amount or a less amount of propellant can be used to travel by the Hohmann transfer orbit between the two circular orbits. The orbital manoeuvre was named after the German scientist Walter Hohmann. This Orbital manoeuvre uses two prograde engine impulses and helps move a particular spacecraft onto a transfer orbit. 

The Hohmann Transfer Orbit Definition and Uses

Hohmann transfer orbit is a fuel-efficient manoeuvre invented by the German scientist Hohmann which it is named after. It assists in transferring a spacecraft from one orbit to the other. Although it saves fuel, it takes more time than the other transfer orbits to do the transferring. This technology is made by the astronomers for successful orbit transferring. 

Separate launch windows need to wait for their opening to do the transferring. Without this, the transfer cannot take place. Thus, particular starting and destination points are required to transfer a spacecraft from one celestial body to another, which can only be made when the launch windows are open. We can take the example of earth and mass. 

If a satellite mission has to be launched from the earth to mars, the astronomers have to wait for 26 months, which is when the launch windows between earth and mars get opened. The Hohmann transfer orbit formula can also help calculate the travel time between the two celestial bodies. 

The Hohmann orbit transfer to mars is one of the examples which can be considered while discussing the uses of the Hohmann transfer orbit. 

Oberth effect

The Oberth effect is the effect that occurs when a spacecraft flies closer to a celestial body (at the perihelion in the case of the Sun). The spacecraft has to speed up to change its orbit.

The Oberth manoeuvre is that kind of manoeuvre in which the spacecraft falls due to gravitational force and makes use of its engine to accelerate while it’s falling in order to continue moving from one orbit to another. The additional speed imparted helps in the transfer and travelling of the spacecraft. 

The increased speed and efficiency are a result of the Oberth effect which brings about a greater change in the mechanical energy of the reaction engine at a more significant speed. The gravitational potential is the lowest at periapsis and thus makes the Oberth effect at that point stronger than anywhere else. 

The two types of Hohmann transfer

The phenomenon of reversibility of orbits enables the Hohmann transfer orbit to push the spacecraft from a lower orbit to a higher orbit as well as pull a spacecraft from a higher orbit to a lower orbit easily. 

• Type I Hohmann transfer – This type of transfer takes place when the orbit transverses less than 180° around the primary. 
• Type II Hohmann Transfer – This type of transfer takes place when the orbit transverses more than 180° around the primary. 

An ideal Hohmann transfer orbit is used to transfer between the two circular orbits in the same place and transverse exactly 180° around the primary. When we talk about the transfer orbits in real life, they may not be exactly 180° and can be more or less than that around the primary. 

Use in Calculations

The Hohmann transfer orbit formula can also be easily used to determine various values regarding the magnitudes of the physical quantities involved. In a two-body system, where a smaller body revolves around a larger body with a greater mass, as the earth revolves around the sun, the total energy of the smaller body is the cumulation of its kinetic energy and potential energy.

The orbital transfer can be performed with the help of Hohmann transfer orbit and the various quantities involved can be obtained with the help of Hohmann transfer orbit formula which goes like this-

∆ϑ=GMr1-2GMr1+r2- GMr1

Here, G is the gravitational constant – 6.67 x 10-11

M stands for the mass of the body in kg.

And r1 and r2 stand for the current and desired orbital status. 

The Hohmann transfer orbit formula for calculating delta-v at periapsis and apoapsis is –

∆ϑ Periapsis= /r1[2r2r1+r2-1]

∆ϑ Apoapsis= /r2[1-2r1r1+r2]

Example

The Hohmann orbit transfer to mars in 9 months was the first attempt by any nation (to send a spacecraft to mars orbit) and was performed successfully by India. This duration can easily be put into use while calculating the various quantities like the distance and speed. 

Conclusion

The Hohmann orbit transfer helps in the transferring of spacecraft from one circular orbit to the other circular orbit while moving in an elliptical one. This elliptical orbit is formed due to the midway acceleration which is needed to make it jump from a lower orbit to a higher orbit. 

The Hohmann manoeuvre helps in saving fuel but consumes more time. It is used for the sending of spacecraft from one celestial body to another. The Hohmann orbit transfer to mars is one of the successful examples of Hohmann orbit transfer.