In astrodynamics, the standard gravitational parameter of a celestial body is the product of the gravitational constant G and the mass M:

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

Small body orbiting a central body

Under standard assumptions in astrodynamics we have:

where:

• is the mass of the orbiting body,
• is the mass of the central body,

and the relevant standard gravitational parameter is that of the larger body.

For all circular orbits around a given central body:

where:

• is the orbit radius,
• is the orbital speed,
• is the angular speed,
• is the orbital period.

The last equality has a very simple generalization to elliptic orbits:

where:

• is the semi-major axis.

See Kepler's third law.

For all parabolic trajectories is constant and equal to ;.

For elliptic and hyperbolic orbits 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 is the position of one body relative to the other
• , , and in the case of an elliptic orbit, the semi-major axis , are defined accordingly (hence is the distance)
• (the sum of the two values)

where:

• and are the masses of the two bodies.

Then:

• for circular orbits
• for elliptic orbits: (with a expressed in AU and T in years, and with M the total mass relative to that of the Sun, we get a³ / T² = M)
• for parabolic trajectories is constant and equal to
• for elliptic and hyperbolic orbits is twice the semi-major axis times the absolute value of the specific orbital energy, where the latter is defined as the total energy of the system divided by the reduced mass.

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. Thus the uncertainty is 1 to 500 000 000, much smaller than the uncertainties in G and M separately (1 to 7000 each).

The value for the Sun is called heliocentric gravitational constant and equals 1.32712440018×10²⁰ m³s^-2.

v • d • e Orbits   Types General Box · Capture · Circular · Elliptical / Highly elliptical · Escape · Graveyard · Hyperbolic trajectory · Inclined / Non-inclined · Osculating · Parabolic trajectory · Parking · Synchronous (semi · sub) Geocentric Geosynchronous · Geostationary · Sun-synchronous · Low Earth · Medium Earth · Molniya · Near-equatorial · Orbit of the Moon · Polar · Tundra Other Areosynchronous · Areostationary · Halo · Lissajous · Lunar · Heliocentric · Heliosynchronous   Parameters Classical  Inclination ·  Longitude of the ascending node ·  Eccentricity ·  Argument of periapsis ·  Semi-major axis ·  Mean anomaly at epoch Other  True anomaly ·  Semi-minor axis ·  Linear eccentricity ·  Eccentric anomaly ·  Mean longitude ·  True longitude ·  Orbital period   Maneuvers Bi-elliptic transfer · Geostationary transfer · Gravity assist · Hohmann transfer · Inclination change · Phasing · Rendezvous · Transposition, docking, and extraction   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 · Low energy transfers · n-body problem · Oberth effect · Orbit equation · Orbital speed · Orbital state vectors · Perturbation · Retrograde and direct motion · Specific orbital energy · Specific relative angular momentum List of orbits

References

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2. ^ D. T. Britt et al Asteroid density, porosity, and structure, pp. 488 in Asteroids III, University of Arizona Press (2002).
3. ^ Jacobson, R.A.; Campbell, J.K.; Taylor, A.H.; Synnott, S.P. (1992). "The masses of Uranus and its major satellites from Voyager tracking data and Earth-based Uranian satellite data". The Astronomical Journal 103 (6): 2068–2078. doi:10.1086/116211, http://adsabs.harvard.edu/abs/1992AJ....103.2068J. 
4. ^ M. W. Buie, W. M. Grundy, E. F. Young, L. A. Young, S. A. Stern (2006). "Orbits and photometry of Pluto's satellites: Charon, S/2005 P1, and S/2005 P2". Astronomical Journal 132: 290. doi:10.1086/504422. arΧiv:astro-ph/0512491, http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=2006AJ....132..290B&db_key=AST&data_type=HTML&format=&high=444b66a47d27727. 
5. ^ M.E. Brown and E.L. Schaller (2007). "The Mass of Dwarf Planet Eris". Science 316 (5831): 1585. doi:10.1126/science.1139415. PMID 17569855, http://www.sciencemag.org/cgi/content/full/316/5831/1585.