Escape velocity
Minimum speed to escape a body's gravitational pull.
Last updated
Richard West · CC BY-SA 2.0
The escape velocity from Earth is 11.186 km/s, based on the standard gravity value of 9.80665 m/s².[1] The speed needed to escape a gravitational field without additional thrust is not a fixed value; it changes depending on how far the object is from the body's center.[2] For an object following a parabolic path, its instantaneous velocity matches the escape velocity corresponding to its present distance from the primary.[2]
Quick Facts
- Field
- Celestial mechanics
- Known for
- Minimum speed to escape a gravitational field
- Key principle
- Conservation of energy
Facts from the source article.
Key facts and history
Escape speed depends on the distance from the center of the primary body.[2] The formula for escape speed at distance d from a spherically symmetric body of mass M is v_e = √(2GM/d).[3] An alternative expression uses surface gravity: v_e = √(2gr), where r is the distance from the body's center.[4] When given an initial speed V greater than escape speed v_e, the object approaches a hyperbolic excess speed v_∞ satisfying v_∞² = V² - v_e².[5]
A relativistic calculation using the Schwarzschild metric yields the same result for escape velocity.[6] A body moving along a hyperbolic trajectory will possess a velocity exceeding the escape velocity at its current location.[2] At any given altitude, the escape velocity equals the circular orbital velocity multiplied by the square root of two.[7] The term "first cosmic velocity" denotes the speed for a circular orbit, while "second cosmic velocity" refers to the escape velocity.[7]
References
- Wikipedia, "Escape velocity" (CC BY-SA 4.0), which cites: Bureau International des Poids et Mesures, "Comptes Rendus des Séances de la Troisième Conférence· Générale des Poids et Mesures", Gauthier-Villars, 1901, p. 68; Lai, "Fundamentals of Spacecraft Charging: Spacecraft Interactions with Space Plasmas", Princeton University Press, 2011, p. 240 (original not read by us) en.wikipedia.org
- Wikipedia, "Escape velocity" (CC BY-SA 4.0), which cites: Giancoli, "Physics for Scientists and Engineers with Modern Physics", Addison-Wesley, 2008, p. 199 (we also read that source) en.wikipedia.org
- Wikipedia, "Escape velocity" (CC BY-SA 4.0), which cites: "New Understanding Physics for Advanced Level", Nelson Thornes, 2000, p. 231; "Black Holes: A Very Short Introduction", Oxford University Press, 2015, p. 4 (original not read by us) en.wikipedia.org
- Wikipedia, "Escape velocity" (CC BY-SA 4.0), which cites: Bate, Mueller and White, p. 35 (original not read by us) en.wikipedia.org
- Wikipedia, "Escape velocity" (CC BY-SA 4.0), which cites: Bate, "Fundamentals of Astrodynamics", Courier Corporation, 1971, p. 39 (original not read by us) en.wikipedia.org
- Wikipedia, "Escape velocity" (CC BY-SA 4.0), which cites: Taylor, "Exploring Black Holes: Introduction to General Relativity", Addison-Wesley, 21 July 2017, p. 2–22}} Sample chapter, page 2-22 {{Webarchive; Choquet-Bruhat, "Introduction to General Relativity, Black Holes, and Cosmology", Oxford University Press, 2015, p. 116–117 (original not read by us) en.wikipedia.org
- Wikipedia, "Escape velocity" (CC BY-SA 4.0), which cites: Teodorescu, "Mechanical systems, classical models", Springer, Japan, 2007, p. 580; "Physics of Planetary Ionospheres", Springer Science & Business Media, 2012, p. 28; "Classical Mechanics in Geophysical Fluid Dynamics", CRC Press, 2022, p. 195 (we also read that source) en.wikipedia.org
Each numbered sentence above was checked against the source it cites before publication. Sentences citing Wikipedia adapt text from the English Wikipedia article Escape velocity (contributors), used under CC BY-SA 4.0; this entry is available under the same licence. Other sources were used for facts only; no text or images are copied from them.
More in Orbits And Celestial Mechanics
Sources
Compiled from Wikipedia and the sources listed below. Text from Wikipedia is available under CC BY-SA 4.0; this entry is adapted from it.
- Wikipedia: Escape velocity (CC BY-SA 4.0).
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