Bi Elliptic Transfer

Information about Bi Elliptic Transfer

In astronautics and aerospace engineering, the Bi-elliptic transfer is an orbital maneuver that moves a spacecraft from one orbit to another and may, in certain situations, require less delta-v than a Hohmann transfer.

The bi-elliptic transfer consists of two half elliptic orbits. From the initial orbit, a delta-v is applied boosting the spacecraft into the first transfer orbit with an apoapsis at some point $\text{[math]}$ away from the central body. At this point, a second delta-v is applied sending the spacecraft into the second elliptical orbit with periapsis at the radius of the final desired orbit where a third delta-v is performed injecting the spacecraft into the desired orbit.

While it requires one more burn than a Hohmann transfer and generally requires a greater period of time, the bi-elliptic transfer may require a lower amount of total delta-v than a Hohmann transfer in situations where the ratio of final to the initial semi-major axis is greater than 11.94 ^[1].

Calculation

Utilizing the vis viva equation where,

$\text{[math]}$

where:

$\text{[math]}$ is the speed of an orbiting body
$\text{[math]}$ is the standard gravitational parameter of the primary body
$\text{[math]}$ is the distance of the orbiting body from the primary
$\text{[math]}$ is the semi-major axis of the body's orbit

The magnitude of the first delta-v at the initial circular orbit with radius $\text{[math]}$ is:

$\text{[math]}$

At $\text{[math]}$ the delta-v is:

$\text{[math]}$

The final delta-v at the final circular orbit with radius $\text{[math]}$ :

$\text{[math]}$

Where $\text{[math]}$ and $\text{[math]}$ are the semimajor axes of the two elliptical transfer orbits and are given by:

$\text{[math]}$

Example

For example, to transfer from circular low earth orbit with $\text{[math]}$ km to a new circular orbit with $\text{[math]}$ km using Hohmann transfer orbit requires delta-v of 2824.34+1308.38=4132.72 m/s. However if spaceship first accelerates 3060.31 m/s, thus getting in elliptic orbit with apogee at $\text{[math]}$ km, then in apogee accelerates another 608.679 m/s, which places it in new orbit with perigee at $\text{[math]}$ , and, finally, in perigee slows down by 447.554 m/s, placing itself in final circular orbit, then total delta-v will be only 4116.54, which is a whopping 16.18 m/s less.

References

1. ^ Vallado, David Anthony: Fundamentals of Astrodynamics and Applications, page 317. Springer, 2001. ISBN 0792369033

• • [ e] Orbits
Orbit types	Box orbit • Circular orbit • Ecliptic orbit • Elliptic orbit • Highly Elliptical Orbit • Graveyard orbit • Hyperbolic trajectory • Inclined orbit • Osculating orbit • Parabolic trajectory • Capture orbit • Escape orbit • Semi-synchronous orbit • Subsynchronous orbit • Synchronous orbit • Parking orbit
Earth-centered orbits	Geosynchronous orbit • Geostationary orbit • Sun-synchronous orbit • Low Earth orbit • Medium Earth Orbit • Molniya orbit • Near equatorial orbit • Orbit of the Moon • Polar orbit • Tundra orbit
Other orbits	Areosynchronous orbit • Areostationary orbit • Halo orbit • Lissajous orbit • Lunar orbit • Heliocentric orbit • Heliosynchronous orbit
Orbital elements	Inclination ( $\text{[math]}$ ) • Longitude of the ascending node ( $\text{[math]}$ ) • Eccentricity ( $\text{[math]}$ ) • Argument of periapsis ( $\text{[math]}$ ) • Semi-major axis ( $\text{[math]}$ ) • Mean anomaly at epoch ( $\text{[math]}$ )
Other orbital parameters	True anomaly ( $\text{[math]}$ ) • Semi-minor axis ( $\text{[math]}$ ) • Linear eccentricity ( $\text{[math]}$ ) • Eccentric anomaly ( $\text{[math]}$ ) • Mean longitude ( $\text{[math]}$ ) • True longitude ( $\text{[math]}$ ) • Orbital period ( $\text{[math]}$ )
Orbital maneuvers	Bi-elliptic transfer • Geostationary transfer orbit • Gravitational slingshot • Hohmann transfer orbit • Orbital inclination change • Orbit phasing • Space rendezvous
Other orbital mechanics topics	Apsis • Celestial coordinate system • Delta-v budget • Epoch • Ephemeris • Equatorial coordinate system • Gravity turn • Ground track • Interplanetary Transport Network • Kepler's laws of planetary motion • Lagrangian point • List of orbits • n-body problem • Orbit equation • Orbital state vectors • Perturbation • Retrograde and direct motion • Specific orbital energy • Specific relative angular momentum • The Oberth effect

Astronautics, or Astronautical Engineering, is the branch of engineering that deals with machines designed to exit or work entirely beyond the Earth's atmosphere. In other words, it is the science and technology of space flight.
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Aerospace engineering is the branch of engineering that concerns aircraft, spacecraft, and related topics. Aerospace Engineering was originally known as aeronautical engineering and dealt solely with aircraft.
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An orbital maneuver is a change from one orbit to another, accomplished by applying thrust. In deep space it is called deep-space maneuver (DSM).

Impulsive maneuvers

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spacecraft is a vehicle or device designed for spaceflight. On a sub-orbital spaceflight, a spacecraft enters outer space but then returns to the planetary surface (such as Earth) without making a complete orbit.
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ORBit is a CORBA compliant Object Request Broker (ORB). The current version is called ORBit2 and is compliant with CORBA version 2.4. It is developed under the GPL license and is used as middleware for the GNOME project.
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In general physics, delta-v is simply the change in velocity.

Depending on the situation, delta-v can be referred to as a spatial vector () or scalar (). In both cases it is equal to the acceleration (vector or scalar) integrated over time:

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In astronautics and aerospace engineering, the Hohmann transfer orbit is an orbital maneuver that, under standard assumption, moves a spacecraft from one circular orbit to another using two engine impulses.
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elliptic orbit can be computed from the Vis-viva equation as:

where:

is standard gravitational parameter,
is radial distance of orbiting body from central body,
is length of semi-major axis.

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semi-major axis (also semimajor axis) is used to describe the dimensions of ellipses and hyperbolae.

Ellipse

The major axis of an ellipse is its longest diameter, a line that runs through the centre and both foci, its ends being at the widest points of the shape.
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In astrodynamics the specific orbital energy (or vis-viva energy) of an orbiting body traveling through space under standard assumptions is the sum of its potential energy () and kinetic energy () per unit mass.
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In astrodynamics, the standard gravitational parameter of a celestial body is the product of the gravitational constant and the mass :

The units of the standard gravitational parameter are km³s^-2

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semi-major axis (also semimajor axis) is used to describe the dimensions of ellipses and hyperbolae.

Ellipse

For other senses of this word, see magnitude.

The magnitude of a mathematical object is its size: a property by which it can be larger or smaller than other objects of the same kind; in technical terms, an ordering of the class of objects to which
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For other meanings of the term "orbit", see orbit (disambiguation)

In astrodynamics or celestial mechanics a circular orbit is an elliptic orbit with the eccentricity equal to 0.
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Delta-v budget (or velocity change budget) is a term used in astrodynamics and aerospace industry for velocity change (or delta-v) requirements for the various propulsive tasks and orbital maneuvers over phases of the space mission.
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The Oberth effect is a feature of astronautics where using a rocket engine close to a gravitational body gives a higher final speed than the same burn executed further from the body.
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In stellar dynamics a box orbit refers to a particular type of orbit which can be seen in triaxial systems, that is, systems which do not possess a symmetry around any of its axes.
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For other meanings of the term "orbit", see orbit (disambiguation)

In astrodynamics or celestial mechanics a circular orbit is an elliptic orbit with the eccentricity equal to 0.
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A non-inclined orbit is an orbit which is contained in the plane of reference. It therefore has inclination equal to zero. If the plane of reference is the equator, these orbits are called equatorial; if the plane of reference is the ecliptic, they are called ecliptic.
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elliptic orbit can be computed from the Vis-viva equation as:

where:

is standard gravitational parameter,
is radial distance of orbiting body from central body,
is length of semi-major axis.

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Highly Elliptical Orbit (HEO) is an elliptic orbit characterized by a relatively low-altitude perigee and an extremely high-altitude apogee. These extremely elongated orbits can have the advantage of long dwell times at a point in the sky during the approach to and descent from
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A graveyard orbit, also called a supersynchronous orbit, junk orbit or disposal orbit, is an orbit significantly above synchronous orbit where spacecraft are intentionally placed at the end of their operational life.
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In astrodynamics or celestial mechanics a hyperbolic trajectory is an orbit with the eccentricity greater than 1. Under standard assumptions a body traveling along this trajectory will coast to infinity, arriving there with hyperbolic excess velocity relative to the central body.
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A satellite is said to occupy an inclined orbit around the Earth if the orbit exhibits an angle other than zero degrees with the equatorial plane. This angle is called the orbit's inclination.
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In astronomy, and in particular in astrodynamics, the osculating orbit of an object in space is the gravitational Keplerian orbit about a central body that it would have if other perturbations were not present.
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In astrodynamics or celestial mechanics a parabolic trajectory is an orbit with the eccentricity equal to 1. When moving away from the source it is called an escape orbit, otherwise a capture orbit.
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Bi Elliptic Transfer

Information about Bi Elliptic Transfer

Calculation

Example

References

See also

Impulsive maneuvers

Ellipse

Ellipse