Astronomy

# About the Hohmann Transfer Orbit

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A Hohmann transfer orbit is a special and common type of spacecraft maneuver which is used to move the spacecraft between two orbits. It was also known as a Vetchinkin transfer orbit during the Cold War, after a Soviet mathematician at the time credited by the Communist bloc with the independent discovery of the same technique. Essentially, Hohmann transfer orbits rely on a Newtonian understanding of gravity and motion, adjusting a spacecraft's speed to either accelerate it into a higher orbit, or decelerate it into a lower orbit.

- How Orbits Work -

One of the first things that we learned as children about space travel was that astronauts in orbit have escaped Earth's gravity: they are weightless. In fact, however, this is not true. So long as they are still in orbit, spacecraft are still fully within the influence of Earth's gravity well - that is why they are in orbit, after all. The weightlessness that these astronauts experience is actually resulting from a sort of continuous free-fall caused by the mechanics of orbital travel.

An object in orbit travels in either a rough circle or an elliptical path (an oval) around the Earth. The path of this orbit can be calculated entirely as a function of the object's mass (note the difference between weight and mass when one moves away from the Earth's surface) and speed. An object travelling too slowly will simply be yanked into the Earth's atmosphere by the force of the planet's gravity, and either be burned up or crash to the surface. An object travelling too fast will escape Earth's gravity and head off into the solar system.

In between, however, are a range of speeds at which the Earth can hold the object from escaping, but cannot actually pull it to the ground. In this range, the object will "orbit" the Earth: gravity will pull it into a circular path in which it neither escapes nor crashes. The effect is precisely the same as spinning with a weight on the end of a string; however, in the case of orbital dynamics, the centripetal force which forces the object into a circular path is applied through gravity rather than a person pulling on the end of the string.

- Changing Orbits and the Hohmann Transfer Orbit -

Our satellites and spacecraft, like the Space Shuttle, often have to change their orbits, either to move into a new position and get new coverage (like the spacecraft or spy satellites), or to correct for gradual orbital changes.

The technique for transferring from one stable orbit to another is called the Hohmann transfer orbit. Essentially, the transfer orbit is the path the object will follow between its original orbit and its new orbit, while it is firing its thrusters to either gain or lose speed. In either case, there are two thrusts needed: the first to leave the original orbit, and the second to enter the new orbit.

If we want to move a satellite from a lower orbit to a higher orbit, for example, we must first increase the velocity of the satellite (i.e. accelerate it) so that it starts to pull away from its current orbit, escaping the Earth. Then, as it approaches the point of its new orbit, the thrusters are fired again to pull it back to the correct speed for orbiting at the new distance. The process works in reverse for moving objects into lower orbits: first the thrusters are fired to slow the object so it starts to fall back to Earth, and then they are fired again to adjust the satellite's speed and push it into the new orbit.

Hohmann transfer orbits can typically satellites between the standard orbital zones of the Earth (low orbit and geosychronous orbit) within several hours. Because the Moon is located within the Earth's gravity well, Hohmann transfer orbits are also used to send spacecraft to the Moon, including unmanned probes as well as the manned Apollo missions of the late 1960s and 1970s.

- Travelling in the Solar System -

The Hohmann orbit is also applied to interplanetary travel, where, instead of talking about orbiting the Earth, we instead are talking about orbiting the Sun. Because the Sun's gravity applies the same way the Earth's does - it is merely far more powerful - the same orbital dynamics apply to space travel at this scale. There is also, however, an additional complicating factor here: in most cases, we want these spacecraft to start orbiting another planet again at the end of their trip (e.g. Mars). A Hohmann transfer orbit can be used to send a spacecraft to Mars in about eight months.

In theory, Hohmann transfer orbits can be used to send objects anywhere in the solar system: all we need to do is calculate the appropriate trajectory, fire their thrusters, and send them on their way. In the outer solar system, however, differences are far greater: it is 50 million miles from the Earth to Mars, but just under 900 million miles between Saturn and Uranus. As a result, NASA usually turns to an orbital technique that uses much higher speeds when it wants to send probes to these regions: the gravitational slingshot. The slingshot paths for travel around the solar system have all been calculated and are collectively known as the Interplanetary Transport Network.

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