Difference between revisions of "Gravitational parameter"
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| Deimos || <math>1.041 \times 10^{5} m^3s^{-2}</math> | | Deimos || <math>1.041 \times 10^{5} m^3s^{-2}</math> | ||
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| + | ==See also== | ||
| + | * [[Specific energy]] | ||
| + | * [[Gravity]] | ||
==References== | ==References== | ||
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[[Category:Orbital Mechanics]] | [[Category:Orbital Mechanics]] | ||
Latest revision as of 11:24, 17 December 2018
The gravitational parameter (symbol Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mu} of a body (normally a planet, moon or star) is a value which represents the strength of its gravitational pull. This value is used in calculations involving other bodies which orbit it. For a body with mass Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle M} and the universal gravitational constant Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle G} ,
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mu = GM}
Justification[1]
Experimental difficulties in determining Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle G} makes it one of the most inaccurate of the fundamental constants. Since the mass of heavenly bodies is also calculated from Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle G} according to the force equation for gravity (accurate to about 0.06%)
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle F_g = G {{m_1m_2} \over {r^2}}}
direct calculation of orbits using the force equation would be unacceptably inaccurate and prone to change whenever a better value for Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle G}
is found.
Because of this, it is better whenever possible to perform orbit calculations in terms of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mu}
and the mass ratios of bodies. Astronomical observations can determine Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mu}
to very high precision.
Values of interest for a Mars mission
Note: While most of these values are known to high precision, measurements still vary between observations and the less significant digits can change as the science advances. The table below gives the gravitational parameters to six significant digits or their full available accuracy (if less) when the source was published (2011). Anyone planning an actual or paper mission should search the literature for the most accurate and recent values.
| Central body | Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mu} [2] |
|---|---|
| Sol | Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 1.327,12 \times 10^{20} m^3s^{-2}} |
| Earth | Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 3.986,00 \times 10^{14} m^3s^{-2}} |
| Luna | Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 4.902,80 \times 10^{12} m^3s^{-2}} |
| Mars | Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 4.282,84 \times 10^{13} m^3s^{-2}} |
| Phobos | Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 7.161 \times 10^{5} m^3s^{-2}} |
| Deimos | Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 1.041 \times 10^{5} m^3s^{-2}} |
See also
References
- ↑ J.R. Wertz - Orbits and astrodynamics in J.R. Wertz, D.F. Everett & J.J. Puschell Space mission engineering: The new SMAD 2011. ISBN 978-1-881883-15-9 pp. 200-201
- ↑ N. Sarzi-Amade - Physical and orbit properties of the sun, earth, moon, and planets in J.R. Wertz, D.F. Everett & J.J. Puschell eds. Space mission engineering: The new SMAD 2011. ISBN 978-1-881883-15-9 p. 955
