Standard gravitational parameter Guide, Meaning , Facts, Information and Description

In astrodynamics, the standard gravitational parameter () is a useful value in two-body problems:

where:

• is the mass of the orbiting body,
• is the mass of the central body,
• is the gravitational constant.

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

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Body
-	[km3s-2]
Sun	132,712,440,000
Mercury	22,032
Venus	324,859
Earth	398,600
Mars	42,828
Jupiter	126,686,534
Saturn	37,931,187
Uranus	5,793,947
Neptune	6,836,529
Pluto	1,001

Under standard assumptions in astrodynamics where standard gravitational parameter is usually computed as:

For all circular orbits around a given central body, rv² = r³ω² = 4π²r³/T² = μ

where r is the orbit radius, v the orbital speed, ω the angular speed, and T the orbital period.

The last equality has a very simple generalization to elliptic orbits: 4π²a³/T² = μ, where a is the semi-major axis.

For all parabolic trajectories rv² is constant and equal to 2μ.

For elliptic and hyperbolic orbits μ is twice the semi-major axis times the absolute value of the specific orbital energy.

Two bodies orbiting each other

In the more general case where the bodies need not be a large one and a small one, we define:

• the vector r is the position of one body relative to the other
• r, v, and in the case of an elliptic orbit, the semi-major axis a, are defined accordingly (hence r is the distance)
• (the sum of the two μ-values)

where:

• and are the masses of the two bodies.

Then:

• for circular orbits
• for elliptic orbits:
• for parabolic trajectories is constant and equal to

Terminology and accuracy

The value for the Earth is called geocentric gravitational constant and equal to 398,600.441,8 ± 0.000,8 km³s^-2

The value for the Sun is called heliocentric gravitational constant.

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