Bi-elliptic transfer

A space ship can move to a new path.

It uses engines to change its speed. This is a special way to move.

First, the ship fires its engine. This sends it on a long path. Then, it fires the engine again. This moves it to a second path.

Finally, it fires the engine one more time. This helps it stay in a new circle. This way uses less fuel.

But it takes a much longer time. It is a smart way to fly.

Spacecraft often need to move from one orbit to another. An orbit is the path a ship takes around a planet. Most ships use a Hohmann transfer. This is a simple way to move between paths. But there is another way called a bi-elliptic transfer.

This way uses two different oval paths. The first step is a burn. A burn is when the ship fires its engine to change speed. This first burn sends the ship into a long, oval path. The ship travels far away from the planet. At the furthest point, the ship fires its engine a second time. This second burn moves the ship into a new oval path.

Finally, the ship reaches its target. It fires the engine a third time. This third burn helps the ship stay in a steady circle. This method can save fuel. We measure fuel use as delta-v. If the new orbit is very large, this way uses less delta-v than a Hohmann transfer. However, it takes much more time to finish the trip.

Spacecraft often need to change their paths around a planet. This change is called an orbital maneuver. Most missions use a method called a Hohmann transfer. However, there is another way called a bi-elliptic transfer.

This method uses two different oval-shaped paths to reach a destination. It can be very useful for certain trips. It might even save fuel when moving to a very distant orbit. Scientists measure this fuel use as delta-v.

This maneuver works in three specific steps. First, the ship performs a prograde burn. This means the engines fire to speed up the craft. This burn puts the ship on its first oval path. The ship travels far away from the planet to a high point. At this high point, the ship performs a second burn. This second burn changes the path so the ship begins to fall back toward the target orbit.

Finally, the ship reaches the target distance. It performs a third burn to settle into a steady circle. This last step is a retrograde burn, which slows the ship down.

The idea for this special path was first published in 1934. A person named Ary Sternfeld shared this idea. It provides a different choice for engineers. While it uses more engine burns, it can be more efficient. A Hohmann transfer only uses two burns. The bi-elliptic transfer uses three burns instead. This extra step is what allows the ship to save energy. It is a more general way to move between orbits.

Whether this method is better depends on the distance. If the final orbit is much larger than the first, it helps. Specifically, the ratio must be 11.94 or greater. If the final orbit is more than 15.58 times larger, any bi-elliptic transfer is better. For example, a ship moving from a low Earth orbit to a far orbit can save fuel this way. In one example, the bi-elliptic way saved 16.19 meters per second of delta-v. This was a small but real saving. However, it took much longer to finish the trip.

There is a trade-off between speed and fuel. The bi-elliptic transfer takes a much longer time to complete. A Hohmann transfer is much faster. For a specific trip, a Hohmann transfer might take only 15 hours. The bi-elliptic version could take 17 days or even 4.5 years! This happens because the ship travels to a very far point first. Even so, the method is very versatile. It helps when ships need to change their tilt or use a planet's air to slow down.

In aerospace engineering, a bi-elliptic transfer is a specialized orbital maneuver. It is used to move a spacecraft from one circular orbit to another. While most missions use a simpler two-step method called a Hohmann transfer, the bi-elliptic transfer can be more efficient in specific cases. It achieves this by using two separate half-elliptical orbits instead of one. This method is measured by its total delta-v, which is the total change in velocity required for the trip.

The mechanism of a bi-elliptic transfer involves three distinct engine burns. First, the spacecraft performs a prograde burn to increase its velocity. This burn places the craft into its first elliptical transfer orbit. The spacecraft travels far away from the central body toward a distant point called the apoapsis.

Once the spacecraft reaches this distant apoapsis, a second prograde burn is performed. This second burn raises the periapsis, which is the closest point of the orbit, to match the radius of the final target orbit. This action places the spacecraft onto a second elliptical trajectory. Finally, when the spacecraft reaches the target radius, it performs a third burn. This is a retrograde burn, which acts against the direction of travel to slow the craft down. This final step circularizes the trajectory into the desired target orbit.

The concept of the bi-elliptical trajectory was first published by Ary Sternfeld in 1934. This maneuver is considered a more general class of orbital transfers. In fact, a Hohmann transfer is actually a special case of the bi-elliptic transfer. If the intermediate apoapsis distance is equal to the final orbit radius, the maneuver effectively becomes a Hohmann transfer.

Whether this maneuver is better than a Hohmann transfer depends on the ratio of the final orbit radius to the initial orbit radius. If this ratio is less than 11.94, the Hohmann transfer is always more efficient. However, if the final orbit is more than 15.58 times larger than the initial orbit, any bi-elliptic transfer will require less delta-v. In the range between 11.94 and 15.58, the best choice depends on the chosen apoapsis distance.

There is a significant trade-off between fuel efficiency and travel time. The bi-elliptic transfer takes much longer than a Hohmann transfer because of the long path to the distant apoapsis. For example, a transfer from a low Earth orbit to a distant target might take only 15 hours and 34 minutes using a Hohmann transfer. A bi-elliptic transfer for the same trip could take 17 days if the apoapsis is 1.3 times the distance to the Moon. In an extreme case, an apoapsis 30 times the distance to the Moon could result in a 4.5-year journey.

Despite the long travel times, bi-elliptic transfers are very versatile. At the distant apoapsis, the spacecraft is traveling at a very low orbital velocity. This makes it inexpensive to perform other maneuvers, such as changing the orbital plane. It also allows for efficient periapsis changes. Engineers can also use this to drop the periapsis into a planet's atmosphere for aerobraking. This uses atmospheric drag to help circularize the orbit, which can save even more delta-v.