Escape velocity - Revision history

Michel Lamontagne at 14:53, 27 August 2021

2021-08-27T14:53:09Z

Michel Lamontagne: /* Values of interest for a Mars mission */

2019-12-28T22:28:05Z

Values of interest for a Mars mission

Michel Lamontagne at 22:23, 28 December 2019

2019-12-28T22:23:51Z

Michel Lamontagne: /* Values of interest for a Mars mission */

2019-12-28T22:22:59Z

Values of interest for a Mars mission

Michel Lamontagne: /* Values of interest for a Mars mission */

2019-12-28T22:21:51Z

Values of interest for a Mars mission

Michel Lamontagne at 22:19, 28 December 2019

2019-12-28T22:19:28Z

Michel Lamontagne at 22:10, 28 December 2019

2019-12-28T22:10:52Z

Michel Lamontagne at 21:54, 28 December 2019

2019-12-28T21:54:07Z

ChristiaanK: Internal links

2013-02-16T19:42:28Z

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ChristiaanK: Created page

2013-02-16T19:15:07Z

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When a spacecraft (or any celestial body) is in the region gravitationally dominated by a celestial body (such as a star), it will either orbit the celestial body in an [[elliptical orbit]] or, if it is moving fast enough, away from the celestial body (possibly after first passing by it) and never return unless a third body exerts some force on it. (Ignoring the trivial case where the spacecraft's movement is aimed sufficiently close to the celestial body to crash into it.) '''Escape velocity''', also known as '''parabolic velocity''', refers to the precise speed at which a spacecraft must be moving so that it will escape rather than enter an elliptical orbit ''irrespective of which direction it is moving in''. The further the spacecraft is from the celestial body, the lower the escape velocity.<br />
An object moving at exactly escape velocity moves in a [[parabolic trajectory]] and an object moving faster than escape velocity moves in a [[hyperbolic trajectory]].
The escape velocity at any distance <math>R</math> from the centre of a spherically symmetric celestial body with [[gravitational parameter]] <math>\mu</math> is given by<ref name=Wertz>J.R. Wertz - ''Orbits and astrodynamics'' in J.R. Wertz, D.F. Everett & J.J. Pushcell eds. ''Space mission engineering: The new SMAD'' ISBN 978-1-881883-15-9 p. 201</ref><br />
<math>V_e = \sqrt{{2 \mu} \over {R}}</math><br />

==Relation to hyperbolic velocity==
A spacecraft's [[hyperbolic velocity]] is exactly zero when it is moving at escape velocity, positive when it is moving faster than escape velocity and undefined when it is moving at less than escape velocity.

==Relation to specific energy==
[[Specific energy]] is defined so as to be zero when a body moves at escape velocity, negative when moving at less than escape velocity and positive when moving at more than escape velocity.

==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.
Note also that the escape velocity does not take drag into account, so a body at the surface of Earth or Mars would not escape if launched at exactly escape velocity.
{| class="wikitable"
|-
! Central body !! Escape velocity at surface<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>617,542 ms^{-1}</math>
|-
| Earth || <math>11,179.9 ms^{-1}</math>
|-
| Luna || <math>2,375.7 ms^{-1}</math>
|-
| Mars || <math>5,022.1 ms^{-1}</math>
|-
| Phobos || <math>10.3 ms^{-1}</math>
|-
| Deimos || <math>5.3 ms^{-1}</math>
|}

==See also==
* [[Circular velocity]]
* [[Hyperbolic velocity]]

==References==
<references />

[[Category:Orbital Mechanics]]

@@ Line 1: / Line 1: @@
 __NOTOC__
-When a spacecraft (or any celestial body) is in the region gravitationally dominated by a celestial body (such as a star), it will either orbit the celestial body in an [[elliptical orbit]] or, if it is moving fast enough, away from the celestial body (possibly after first passing by it) and never return unless a third body exerts some force on it. (Ignoring the trivial case where the spacecraft's movement is aimed sufficiently close to the celestial body to crash into it.) '''Escape velocity''', also known as '''parabolic velocity''', refers to the precise speed at which a spacecraft must be moving so that it will escape rather than enter an elliptical orbit ''irrespective of which direction it is moving in''. The further the spacecraft is from the celestial body, the lower the escape velocity.<br />An object moving at exactly escape velocity moves in a [[parabolic trajectory]] and an object moving faster than escape velocity moves in a [[hyperbolic trajectory]].
+In [[Astronautics]], when a spacecraft (or any celestial body) is in the region gravitationally dominated by a celestial body (such as a star), it will either orbit the celestial body in an [[elliptical orbit]] or, if it is moving fast enough, away from the celestial body (possibly after first passing by it) and never return unless a third body exerts some force on it. (Ignoring the trivial case where the spacecraft's movement is aimed sufficiently close to the celestial body to crash into it.) '''Escape velocity''', also known as '''parabolic velocity''', refers to the precise speed at which a spacecraft must be moving so that it will escape rather than enter an elliptical orbit ''irrespective of which direction it is moving in''. The further the spacecraft is from the celestial body, the lower the escape velocity.<br />An object moving at exactly escape velocity moves in a [[parabolic trajectory]] and an object moving faster than escape velocity moves in a [[hyperbolic trajectory]].
 The escape velocity at any distance <math>R</math> from the centre of a spherically symmetric celestial body with [[gravitational parameter]] <math>\mu</math> is given by<ref name="Wertz">J.R. Wertz - ''Orbits and astrodynamics'' in J.R. Wertz, D.F. Everett & J.J. Pushcell eds. ''Space mission engineering: The new SMAD'' ISBN 978-1-881883-15-9 p. 201</ref>.  R is often taken at the surface of the celestial body.

@@ Line 1: / Line 1: @@
 __NOTOC__
 When a spacecraft (or any celestial body) is in the region gravitationally dominated by a celestial body (such as a star), it will either orbit the celestial body in an [[elliptical orbit]] or, if it is moving fast enough, away from the celestial body (possibly after first passing by it) and never return unless a third body exerts some force on it. (Ignoring the trivial case where the spacecraft's movement is aimed sufficiently close to the celestial body to crash into it.) '''Escape velocity''', also known as '''parabolic velocity''', refers to the precise speed at which a spacecraft must be moving so that it will escape rather than enter an elliptical orbit ''irrespective of which direction it is moving in''. The further the spacecraft is from the celestial body, the lower the escape velocity.<br />An object moving at exactly escape velocity moves in a [[parabolic trajectory]] and an object moving faster than escape velocity moves in a [[hyperbolic trajectory]].
 The escape velocity at any distance <math>R</math> from the centre of a spherically symmetric celestial body with [[gravitational parameter]] <math>\mu</math> is given by<ref name="Wertz">J.R. Wertz - ''Orbits and astrodynamics'' in J.R. Wertz, D.F. Everett & J.J. Pushcell eds. ''Space mission engineering: The new SMAD'' ISBN 978-1-881883-15-9 p. 201</ref>.  R is often taken at the surface of the celestial body.
@@ Line 23: / Line 24: @@
 !Gravitational parameter
 m3/s2
 |-
 |Sol||617 540
 |1,32e20
 |-
 |Earth||11 180
 |3,98e14
 |-
 |Luna||2 370
 |4,90e12
 |-
 |Mars||5 020
 |4,28e13
 |-
 |Phobos||10,3
 |7,16e5
 |-
 |Deimos||5,3
 |1,05e5
 |}

← Older revision		Revision as of 22:23, 28 December 2019
Line 1:		Line 1:
		+	__NOTOC__
	When a spacecraft (or any celestial body) is in the region gravitationally dominated by a celestial body (such as a star), it will either orbit the celestial body in an [[elliptical orbit]] or, if it is moving fast enough, away from the celestial body (possibly after first passing by it) and never return unless a third body exerts some force on it. (Ignoring the trivial case where the spacecraft's movement is aimed sufficiently close to the celestial body to crash into it.) '''Escape velocity''', also known as '''parabolic velocity''', refers to the precise speed at which a spacecraft must be moving so that it will escape rather than enter an elliptical orbit ''irrespective of which direction it is moving in''. The further the spacecraft is from the celestial body, the lower the escape velocity.<br />An object moving at exactly escape velocity moves in a [[parabolic trajectory]] and an object moving faster than escape velocity moves in a [[hyperbolic trajectory]].		When a spacecraft (or any celestial body) is in the region gravitationally dominated by a celestial body (such as a star), it will either orbit the celestial body in an [[elliptical orbit]] or, if it is moving fast enough, away from the celestial body (possibly after first passing by it) and never return unless a third body exerts some force on it. (Ignoring the trivial case where the spacecraft's movement is aimed sufficiently close to the celestial body to crash into it.) '''Escape velocity''', also known as '''parabolic velocity''', refers to the precise speed at which a spacecraft must be moving so that it will escape rather than enter an elliptical orbit ''irrespective of which direction it is moving in''. The further the spacecraft is from the celestial body, the lower the escape velocity.<br />An object moving at exactly escape velocity moves in a [[parabolic trajectory]] and an object moving faster than escape velocity moves in a [[hyperbolic trajectory]].
	The escape velocity at any distance <math>R</math> from the centre of a spherically symmetric celestial body with [[gravitational parameter]] <math>\mu</math> is given by<ref name="Wertz">J.R. Wertz - ''Orbits and astrodynamics'' in J.R. Wertz, D.F. Everett & J.J. Pushcell eds. ''Space mission engineering: The new SMAD'' ISBN 978-1-881883-15-9 p. 201</ref>. R is often taken at the surface of the celestial body.		The escape velocity at any distance <math>R</math> from the centre of a spherically symmetric celestial body with [[gravitational parameter]] <math>\mu</math> is given by<ref name="Wertz">J.R. Wertz - ''Orbits and astrodynamics'' in J.R. Wertz, D.F. Everett & J.J. Pushcell eds. ''Space mission engineering: The new SMAD'' ISBN 978-1-881883-15-9 p. 201</ref>. R is often taken at the surface of the celestial body.

@@ Line 19: / Line 19: @@
 {| class="wikitable"
 |-
-!Central body!!Escape velocity at surface<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>m/s
+!Central body!!Escape velocity at surface<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> m/s
 !Gravitational parameter
 m3/s2

@@ Line 16: / Line 16: @@
 ==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.<br />
+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.<br />Note also that the escape velocity does not take [[aerodynamic drag]] into account, so a body at the surface of Earth or Mars would not escape if launched at exactly escape velocity.
 {| class="wikitable"
 |-
 !Central body!!Escape velocity at surface<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>m/s
-!Gravitational parameter GM
+!Gravitational parameter
 m3/s2
 |-
@@ Line 49: / Line 48: @@
 paper mission should search the literature for the most accurate and recent values.
 ==References==
 <references />
 [[Category:Orbital Mechanics]]

@@ Line 1: / Line 1: @@
 When a spacecraft (or any celestial body) is in the region gravitationally dominated by a celestial body (such as a star), it will either orbit the celestial body in an [[elliptical orbit]] or, if it is moving fast enough, away from the celestial body (possibly after first passing by it) and never return unless a third body exerts some force on it. (Ignoring the trivial case where the spacecraft's movement is aimed sufficiently close to the celestial body to crash into it.) '''Escape velocity''', also known as '''parabolic velocity''', refers to the precise speed at which a spacecraft must be moving so that it will escape rather than enter an elliptical orbit ''irrespective of which direction it is moving in''. The further the spacecraft is from the celestial body, the lower the escape velocity.<br />An object moving at exactly escape velocity moves in a [[parabolic trajectory]] and an object moving faster than escape velocity moves in a [[hyperbolic trajectory]].
-The escape velocity at any distance <math>R</math> from the centre of a spherically symmetric celestial body with [[gravitational parameter]] <math>\mu</math> is given by<ref name="Wertz">J.R. Wertz - ''Orbits and astrodynamics'' in J.R. Wertz, D.F. Everett & J.J. Pushcell eds. ''Space mission engineering: The new SMAD'' ISBN 978-1-881883-15-9 p. 201</ref><br /><math>V_e = \sqrt{{2 \mu} \over {R}}</math>   <br />
+The escape velocity at any distance <math>R</math> from the centre of a spherically symmetric celestial body with [[gravitational parameter]] <math>\mu</math> is given by<ref name="Wertz">J.R. Wertz - ''Orbits and astrodynamics'' in J.R. Wertz, D.F. Everett & J.J. Pushcell eds. ''Space mission engineering: The new SMAD'' ISBN 978-1-881883-15-9 p. 201</ref>.  R is often taken at the surface of the celestial body.
 ==Relation to hyperbolic velocity==
@@ Line 8: / Line 10: @@
 [[Specific energy]] is defined so as to be zero when a body moves at escape velocity, negative when moving at less than escape velocity and positive when moving at more than escape velocity.
-== Relation to orbital velocity ==
+==Relation to orbital velocity==
-<math>V_o = \sqrt{{ \mu} \over {r}}</math>
+The velocity of a body '''''V<sub>o</sub>''''' at a distance '''''R''''' of the center of gravity for a circular orbit is given by
-<math>V_o = \sqrt{{2 \mu} \over {R}}</math>
+<math>V_o = \sqrt{{ \mu} \over {R}}</math>   <math>V_o = V_e\sqrt{2}</math>      <math>V_o = \sqrt{{ GM} \over {R}}</math>
 ==Values of interest for a Mars mission==

@@ Line 1: / Line 1: @@
-When a spacecraft (or any celestial body) is in the region gravitationally dominated by a celestial body (such as a star), it will either orbit the celestial body in an [[elliptical orbit]] or, if it is moving fast enough, away from the celestial body (possibly after first passing by it) and never return unless a third body exerts some force on it. (Ignoring the trivial case where the spacecraft's movement is aimed sufficiently close to the celestial body to crash into it.) '''Escape velocity''', also known as '''parabolic velocity''', refers to the precise speed at which a spacecraft must be moving so that it will escape rather than enter an elliptical orbit ''irrespective of which direction it is moving in''. The further the spacecraft is from the celestial body, the lower the escape velocity.<br />
+When a spacecraft (or any celestial body) is in the region gravitationally dominated by a celestial body (such as a star), it will either orbit the celestial body in an [[elliptical orbit]] or, if it is moving fast enough, away from the celestial body (possibly after first passing by it) and never return unless a third body exerts some force on it. (Ignoring the trivial case where the spacecraft's movement is aimed sufficiently close to the celestial body to crash into it.) '''Escape velocity''', also known as '''parabolic velocity''', refers to the precise speed at which a spacecraft must be moving so that it will escape rather than enter an elliptical orbit ''irrespective of which direction it is moving in''. The further the spacecraft is from the celestial body, the lower the escape velocity.<br />An object moving at exactly escape velocity moves in a [[parabolic trajectory]] and an object moving faster than escape velocity moves in a [[hyperbolic trajectory]].
-An object moving at exactly escape velocity moves in a [[parabolic trajectory]] and an object moving faster than escape velocity moves in a [[hyperbolic trajectory]].
+The escape velocity at any distance <math>R</math> from the centre of a spherically symmetric celestial body with [[gravitational parameter]] <math>\mu</math> is given by<ref name="Wertz">J.R. Wertz - ''Orbits and astrodynamics'' in J.R. Wertz, D.F. Everett & J.J. Pushcell eds. ''Space mission engineering: The new SMAD'' ISBN 978-1-881883-15-9 p. 201</ref><br /><math>V_e = \sqrt{{2 \mu} \over {R}}</math>   <br />
 ==Relation to hyperbolic velocity==
@@ Line 9: / Line 7: @@
 ==Relation to specific energy==
 [[Specific energy]] is defined so as to be zero when a body moves at escape velocity, negative when moving at less than escape velocity and positive when moving at more than escape velocity.
 ==Values of interest for a Mars mission==
@@ Line 15: / Line 18: @@
 {| class="wikitable"
 |-
-! Central body !! Escape velocity at surface<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>
+!Central body!!Escape velocity at surface<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>617,542 ms^{-1}</math>
+|Sol||<math>617,542 ms^{-1}</math>
 |-
-| Earth  || <math>11,179.9 ms^{-1}</math>
+|Earth||<math>11,179.9 ms^{-1}</math>
 |-
-| Luna   || <math>2,375.7 ms^{-1}</math>
+|Luna||<math>2,375.7 ms^{-1}</math>
 |-
-| Mars   || <math>5,022.1 ms^{-1}</math>
+|Mars||<math>5,022.1 ms^{-1}</math>
 |-
-| Phobos || <math>10.3 ms^{-1}</math>
+|Phobos||<math>10.3 ms^{-1}</math>
 |-
-| Deimos || <math>5.3 ms^{-1}</math>
+|Deimos||<math>5.3 ms^{-1}</math>
 |}
 ==See also==
 * [[Circular velocity]]
-* [[Hyperbolic velocity]]
+*[[Circular velocity]]
 ==References==