Surface gravity
From CreationWiki, the encyclopedia of creation science
The surface gravity of any celestial body, like a star, a planet, a dwarf planet, or a moon, is actually the acceleration due to gravity of a falling object at or near the surface.
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Terminology
Surface gravity is an acceleration, and is commonly measured in the units of acceleration, which are mass per square unit of time. The SI units of acceleration are m/s².
But surface gravity has another unit, g. The lowercase g is always italicized in the technical literature, mainly to distinguish it from g for gram, and also from g as a symbol for the quantity called surface gravity as opposed to its value. The quantity g is the standard surface gravity of the earth. By definition this is 9.80665 m/s².
In the discussion below, body refers to a celestial body and object refers to a much smaller object that might rest on a body.
Mass v. Weight
Mass and weight are often confused, especially in the US Customary system of units or any other system of ancient or medieval origin. In such systems, mass and weight are regarded as fundamentally the same. But weight can change with altitude or even with latitude.
Weight and mass are related in the following manner:
where g is the surface gravity at any given point on any given body and m is an object's mass.
The concept of weight still has a practical meaning in the planning of missions, crewed or non-crewed, to various celestial bodies. Weight is the force that a spacecraft's engines will need to counteract during liftoff and landing. Moreover the difference in the weight of a man on Earth and on a body to be explored will dictate how much equipment an exploratory crewman can carry on that body.
Calculation of surface gravity
Surface gravity derives directly from the Newtonian law of gravity:
where G is Cavendish's gravitational constant, M is the mass of the body, and R is the radius of the body at any given point on its surface.
Table
The following table lists several celestial bodies for which the surface gravity is known:
| Name | Mass | Mean radius | Equatorial radius | Surface gravity | Escape speed |
|---|---|---|---|---|---|
| Deimos | 1.4E+151.9052e-8 M☾1.4e+15 kg 2.34271e-10 M⊕ |
62006.2 km3.853 mi | 0.00252.54929e-4 g0.0025 m/s² 0.0082 ft/s² |
5.60.0056 km/s20.16 km/h 0.00348 mi/s 12.527 mph |
|
| Phobos | 1.073E+161.4602e-7 M☾1.073e+16 kg 1.79552e-9 M⊕ |
1110011.1 km6.897 mi | 0.005815.92455e-4 g0.00581 m/s² 0.0191 ft/s² |
11.40.0114 km/s41.04 km/h 0.00708 mi/s 25.501 mph |
|
| Miranda | 6.59E+198.96806e-4 M☾6.59e+19 kg 1.10275e-5 M⊕ |
234200234.2 km145.525 mi | 240000240 km149.129 mi | 0.08020.00818 g0.0802 m/s² 0.263 ft/s² |
1940.194 km/s698.4 km/h 0.121 mi/s 433.966 mph |
| Tethys | 6.18E+200.00841 M☾6.18e+20 kg 1.03414e-4 M⊕ |
536300536.3 km333.241 mi | 0.1430.0146 g0.143 m/s² 0.469 ft/s² |
3920.392 km/s1,411.2 km/h 0.244 mi/s 876.879 mph |
|
| Umbriel | 1.17E+210.0159 M☾1.17e+21 kg 1.95783e-4 M⊕ |
584700584.7 km363.316 mi | 0.22870.0233 g0.229 m/s² 0.75 ft/s² |
5170.517 km/s1,861.2 km/h 0.321 mi/s 1,156.496 mph |
|
| Rhea | 2.309E+210.0314 M☾2.309e+21 kg 3.86379e-4 M⊕ |
764500764.5 km475.038 mi | 0.26340.0269 g0.263 m/s² 0.864 ft/s² |
634.60.635 km/s2,284.56 km/h 0.394 mi/s 1,419.56 mph |
|
| Charon | 1.9E+210.0259 M☾1.9e+21 kg 3.17939e-4 M⊕ |
586000586 km364.124 mi | 0.2780.0283 g0.278 m/s² 0.912 ft/s² |
5800.58 km/s2,088 km/h 0.36 mi/s 1,297.423 mph |
|
| Oberon | 3.01E+210.041 M☾3.01e+21 kg 5.03682e-4 M⊕ |
761400761.4 km473.112 mi | 0.34690.0354 g0.347 m/s² 1.138 ft/s² |
726.80.727 km/s2,616.48 km/h 0.452 mi/s 1,625.805 mph |
|
| Titania | 3.52E+210.0479 M☾3.52e+21 kg 5.89024e-4 M⊕ |
788900788.9 km490.2 mi | 0.37810.0386 g0.378 m/s² 1.24 ft/s² |
7680.768 km/s2,764.8 km/h 0.477 mi/s 1,717.967 mph |
|
| Pluto | 11950001,195 km742.539 mi | 0.580.0591 g0.58 m/s² 1.903 ft/s² |
12001.2 km/s4,320 km/h 0.746 mi/s 2,684.324 mph |
||
| Eris | 13000001,300 km807.783 mi | 0.65540.0668 g0.655 m/s² 2.15 ft/s² |
13051.305 km/s4,698 km/h 0.811 mi/s 2,919.202 mph |
||
| Nereid | 3.09E+194.20505e-4 M☾3.09e+19 kg 5.17069e-6 M⊕ |
170000170 km105.633 mi | 0.7130.0727 g0.713 m/s² 2.339 ft/s² |
1560.156 km/s561.6 km/h 0.0969 mi/s 348.962 mph |
|
| Triton | 2.14E+220.291 M☾2.14e+22 kg 0.00358 M⊕ |
13534001,353.4 km840.964 mi | 0.779550.0795 g0.78 m/s² 2.558 ft/s² |
1452.61.453 km/s5,229.36 km/h 0.903 mi/s 3,249.374 mph |
|
| Callisto | 1.076E+231.464 M☾1.076e+23 kg 0.018 M⊕ |
24103002,410.3 km1,497.691 mi | 1.235770.126 g1.236 m/s² 4.054 ft/s² |
24502.45 km/s8,820 km/h 1.522 mi/s 5,480.494 mph |
|
| Europa | 4.8E+220.653 M☾4.8e+22 kg 0.00803 M⊕ |
15608001,560.8 km969.836 mi | 1.32390.135 g1.324 m/s² 4.344 ft/s² |
20202.02 km/s7,272 km/h 1.255 mi/s 4,518.611 mph |
|
| Titan | 1.34553E+231.831 M☾1.34553e+23 kg 0.0225 M⊕ |
25755002,575.5 km1,600.342 mi | 1.35350.138 g1.354 m/s² 4.441 ft/s² |
2640.52.641 km/s9,505.8 km/h 1.641 mi/s 5,906.63 mph |
|
| Ganymede | 1.48186E+232.017 M☾1.48186e+23 kg 0.0248 M⊕ |
26312002,631.2 km1,634.952 mi | 1.42820.146 g1.428 m/s² 4.686 ft/s² |
2741.52.742 km/s9,869.4 km/h 1.703 mi/s 6,132.561 mph |
|
| Io | 8.93194E+221.216 M☾8.93194e+22 kg 0.0149 M⊕ |
18216001,821.6 km1,131.89 mi | 1.796110.183 g1.796 m/s² 5.893 ft/s² |
2558.052.558 km/s9,208.98 km/h 1.589 mi/s 5,722.195 mph |
|
| Mercury (planet) | 24397002,439.7 km1,515.959 mi | 24397002,439.7 km1,515.959 mi | 3.70.377 g3.7 m/s² 12.139 ft/s² |
43004.3 km/s15,480 km/h 2.672 mi/s 9,618.826 mph |
|
| Mars | 33895003,389.5 km2,106.138 mi | 33962003,396.2 km2,110.301 mi | 3.710.378 g3.71 m/s² 12.172 ft/s² |
50305.03 km/s18,108 km/h 3.125 mi/s 11,251.79 mph |
|
| Uranus | 2536200025,362 km15,759.216 mi | 2555900025,559 km15,881.626 mi | 8.690.886 g8.69 m/s² 28.51 ft/s² |
2130021.3 km/s76,680 km/h 13.235 mi/s 47,646.743 mph |
|
| Venus | 60518006,051.8 km3,760.414 mi | 60518006,051.8 km3,760.414 mi | 8.870.904 g8.87 m/s² 29.101 ft/s² |
1036010.36 km/s37,296 km/h 6.437 mi/s 23,174.66 mph |
|
| Saturn | 5823200058,232 km36,183.687 mi | 6026800060,268 km37,448.799 mi | 8.960.914 g8.96 m/s² 29.396 ft/s² |
3549035.49 km/s127,764 km/h 22.052 mi/s 79,388.869 mph |
|
| Neptune | 2462200024,622 km15,299.401 mi | 2476400024,764 km15,387.636 mi | 111.122 g11 m/s² 36.089 ft/s² |
2350023.5 km/s84,600 km/h 14.602 mi/s 52,568.003 mph |
|
| Jupiter | 7149200071,492 km44,423.069 mi | 20.872.128 g20.87 m/s² 68.471 ft/s² |
5954059.54 km/s214,344 km/h 36.996 mi/s 133,187.187 mph |
||
| Sun | 696000000696,000 km432,474.35 mi | 695500000695,500 km432,163.664 mi | 27427.94 g274 m/s² 898.95 ft/s² |
617700617.7 km/s2,223,720 km/h 383.821 mi/s 1,381,755.548 mph |
See also
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