Jburk at 18:24, 17 December 2018

2018-12-17T18:24:10Z

← Older revision		Revision as of 19:24, 17 December 2018
Line 38:		Line 38:


	~~[[Category:Physics]]~~
	[[Category:Orbital Mechanics]]		[[Category:Orbital Mechanics]]

ChristiaanK: Internal links

2013-02-16T19:48:33Z

Internal links

← Older revision		Revision as of 20:48, 16 February 2013
Line 29:		Line 29:
	\| Deimos \|\| <math>1.041 \times 10^{5} m^3s^{-2}</math>		\| Deimos \|\| <math>1.041 \times 10^{5} m^3s^{-2}</math>
	\|}		\|}

			==See also==
			* [[Specific energy]]
			* [[Gravity]]

	==References==		==References==

ChristiaanK: Rounding error

2013-02-16T19:46:25Z

Rounding error

← Older revision		Revision as of 20:46, 16 February 2013
Line 23:		Line 23:
	\| Luna \|\| <math>4.902,80 \times 10^{12} m^3s^{-2}</math>		\| Luna \|\| <math>4.902,80 \times 10^{12} m^3s^{-2}</math>
	\|-		\|-
	\| Mars \|\| <math>4.282,83 \times 10^{13} m^3s^{-2}</math>		\| Mars \|\| <math>4.282,84 \times 10^{13} m^3s^{-2}</math>
	\|-		\|-
	\| Phobos \|\| <math>7.161 \times 10^{5} m^3s^{-2}</math>		\| Phobos \|\| <math>7.161 \times 10^{5} m^3s^{-2}</math>
Line 29:		Line 29:
	\| Deimos \|\| <math>1.041 \times 10^{5} m^3s^{-2}</math>		\| Deimos \|\| <math>1.041 \times 10^{5} m^3s^{-2}</math>
	\|}		\|}


	==References==		==References==

ChristiaanK: Created page

2013-02-16T17:02:35Z

Created page

New page

The '''gravitational parameter''' (symbol <math>\mu</math> 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 <math>M</math> and the universal gravitational constant <math>G</math>,

<math>\mu = GM</math>

==Justification<ref name=Wertz>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</ref>==
Experimental difficulties in determining <math>G</math> makes it one of the most inaccurate of the fundamental constants. Since the mass of heavenly bodies is also calculated from <math>G</math> according to the force equation for gravity (accurate to about 0.06%)

<math>F_g = G {{m_1m_2} \over {r^2}}</math>

direct calculation of orbits using the force equation would be unacceptably inaccurate and prone to change whenever a better value for <math>G</math> is found.<br />
Because of this, it is better whenever possible to perform orbit calculations in terms of <math>\mu</math> and the mass ratios of bodies. Astronomical observations can determine <math>\mu</math> 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.
{| class="wikitable"
|-
! Central body !! <math>\mu</math><ref name=SarziAmade>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</ref>
|-
| Sol || <math>1.327,12 \times 10^{20} m^3s^{-2}</math>
|-
| Earth || <math>3.986,00 \times 10^{14} m^3s^{-2}</math>
|-
| Luna || <math>4.902,80 \times 10^{12} m^3s^{-2}</math>
|-
| Mars || <math>4.282,83 \times 10^{13} m^3s^{-2}</math>
|-
| Phobos || <math>7.161 \times 10^{5} m^3s^{-2}</math>
|-
| Deimos || <math>1.041 \times 10^{5} m^3s^{-2}</math>
|}

==References==
<references />

[[Category:Physics]]
[[Category:Orbital Mechanics]]

Gravitational parameter - Revision history

Jburk at 18:24, 17 December 2018

ChristiaanK: Internal links

ChristiaanK: Rounding error

ChristiaanK: Created page