228:
849:
466:
2557:
376:
203:. Given the speed at which such a fall would occur, it is doubtful that Galileo could have extracted much information from this experiment. Most of his observations of falling bodies were really of bodies rolling down ramps. This slowed things down enough to the point where he was able to measure the time intervals with
1360:
density cannot be assumed to be constant, such as for objects falling from high altitude, the equation of motion becomes much more difficult to solve analytically and a numerical simulation of the motion is usually necessary. The figure shows the forces acting on meteoroids falling through the Earth's upper atmosphere.
1587:
461:
This is the "textbook" case of the vertical motion of an object falling a small distance close to the surface of a planet. It is a good approximation in air as long as the force of gravity on the object is much greater than the force of air resistance, or equivalently the object's velocity is always
1380:
It can be said that two objects in space orbiting each other in the absence of other forces are in free fall around each other, e.g. that the Moon or an artificial satellite "falls around" the Earth, or a planet "falls around" the Sun. Assuming spherical objects means that the equation of motion is
433:
on August 2, 1971. He simultaneously released a hammer and a feather from the same height above the Moon's surface. The hammer and the feather both fell at the same rate and hit the surface at the same time. This demonstrated
Galileo's discovery that, in the absence of air resistance, all objects
137:
In the
Western world prior to the 16th century, it was generally assumed that the speed of a falling body would be proportional to its weightāthat is, a 10 kg object was expected to fall ten times faster than an otherwise identical 1 kg object through the same medium. The ancient Greek
1359:
Using the figure of 56 m/s for the terminal velocity of a human, one finds that after 10 seconds he will have fallen 348 metres and attained 94% of terminal velocity, and after 12 seconds he will have fallen 455 metres and will have attained 97% of terminal velocity. However, when the air
2357:
426:, and relative surface area and will only be achieved if the fall is from sufficient altitude. A typical skydiver in a spread-eagle position will reach terminal velocity after about 12 seconds, during which time they will have fallen around 450 m (1,500 ft).
422:. With air resistance acting on an object that has been dropped, the object will eventually reach a terminal velocity, which is around 53 m/s (190 km/h or 118 mph) for a human skydiver. The terminal velocity depends on many factors including mass,
2728:
The experimental observation that all objects in free fall accelerate at the same rate, as noted by
Galileo and then embodied in Newton's theory as the equality of gravitational and inertial masses, and later confirmed to high accuracy by modern forms of the
311:
Technically, an object is in free fall even when moving upwards or instantaneously at rest at the top of its motion. If gravity is the only influence acting, then the acceleration is always downward and has the same magnitude for all bodies, commonly denoted
207:
and his own pulse (stopwatches having not yet been invented). He repeated this "a full hundred times" until he had achieved "an accuracy such that the deviation between two observations never exceeded one-tenth of a pulse beat." In 1589ā1592, Galileo wrote
1019:
1974:
1354:
1432:
1166:
2552:{\displaystyle y(t)=y_{0}\left(x-{\frac {1}{5}}x^{2}-{\frac {3}{175}}x^{3}-{\frac {23}{7875}}x^{4}-{\frac {1894}{3031875}}x^{5}-{\frac {3293}{21896875}}x^{6}-{\frac {2418092}{62077640625}}x^{7}-\cdots \right)\ ,}
1245:
1855:
2346:
610:
2071:
2018:
1740:
1075:
523:
2682:
926:
412:
1866:
1256:
1582:{\displaystyle t(y)={\sqrt {\frac {{y_{0}}^{3}}{2\mu }}}\left({\sqrt {{\frac {y}{y_{0}}}\left(1-{\frac {y}{y_{0}}}\right)}}+\arccos {\sqrt {\frac {y}{y_{0}}}}\right),}
727:
644:
759:
676:
1664:
1042:
360:
Descending to the Earth using a parachute, which balances the force of gravity with an aerodynamic drag force (and with some parachutes, an additional lift force).
1774:
826:
803:
780:
697:
50:. An object moving upwards might not normally be considered to be falling, but if it is subject to only the force of gravity, it is said to be in free fall. The
1684:
1635:
1613:
918:
894:
874:
330:
200:
194:
175:, al-BaghdÄdÄ«'s theory of motion was "the oldest negation of Aristotle's fundamental dynamic law , anticipation in a vague fashion of the fundamental law of
2705:
is flat, the
Newtonian theory of free fall agrees with general relativity. Otherwise the two disagree; e.g., only general relativity can account for the
364:
The example of a falling skydiver who has not yet deployed a parachute is not considered free fall from a physics perspective, since they experience a
840:, the distance fallen in successive time intervals grows as the odd numbers. This description of the behavior of falling bodies was given by Galileo.
1382:
1090:
836:
If the initial velocity is zero, then the distance fallen from the initial position will grow as the square of the elapsed time. Moreover, because
307:
An object thrown upward or a person jumping off the ground at low speed (i.e. as long as air resistance is negligible in comparison to weight).
2899:
164:
2029:
1394:
1181:
379:
Measured fall time of a small steel sphere falling from various heights. The data is in good agreement with the predicted fall time of
2808:
2756:
1361:
1785:
2817:
2082:
418:
Near the surface of the Earth, an object in free fall in a vacuum will accelerate at approximately 9.8 m/s, independent of its
271:
238:
1743:
1397:. This connection between falling objects close to the Earth and orbiting objects is best illustrated by the thought experiment,
108:
drag forces in such situations prevent them from producing full weightlessness, and thus a skydiver's "free fall" after reaching
160:
challenged this argument and said that, by observation, two balls of very different weights will fall at nearly the same speed.
2698:
132:
1386:
531:
1426:
for two point objects on a radial path. The solution of this equation of motion yields time as a function of separation:
2746:
900:
well above the critical
Reynolds number, so that the air resistance is proportional to the square of the fall velocity,
89:, a condition that also occurs when the gravitational field is weak (such as when far away from any source of gravity).
253:
1419:
435:
168:
20:
249:
92:
The term "free fall" is often used more loosely than in the strict sense defined above. Thus, falling through an
1250:
The object's speed versus time can be integrated over time to find the vertical position as a function of time:
2761:
2730:
2697:
In general relativity, an object in free fall is subject to no force and is an inertial body moving along a
2034:
335:
Since all objects fall at the same rate in the absence of other forces, objects and people will experience
1398:
1982:
1690:
2734:
77:
gravity acts on each part of a body approximately equally. When there are no other forces, such as the
1014:{\displaystyle m{\frac {\mathrm {d} v}{\mathrm {d} t}}=mg-{\frac {1}{2}}\rho C_{\mathrm {D} }Av^{2}\,,}
1051:
852:
Acceleration of a small meteoroid when entering the Earth's atmosphere at different initial velocities
3080:
3028:
2981:
2932:
2846:
1969:{\displaystyle y(t)=y_{0}~Q\left(1-{\frac {t}{t_{\text{ff}}}};{\frac {3}{2}},{\frac {1}{2}}\right)~,}
1409:
1349:{\displaystyle y=y_{0}-{\frac {v_{\infty }^{2}}{g}}\ln \cosh \left({\frac {gt}{v_{\infty }}}\right).}
476:
153:
2567:
382:
2718:
2714:
451:
176:
144:
74:
27:
1084:
Assuming an object falling from rest and no change in air density with altitude, the solution is:
3046:
2971:
2692:
210:
120:
116:
47:
3109:
67:
2997:
2895:
2813:
2766:
2021:
1369:
369:
109:
63:
2889:
704:
621:
3135:
3130:
3088:
3036:
2989:
2940:
2025:
1405:
1078:
734:
651:
423:
1642:
1027:
293:(in space) with propulsion off (e.g. in a continuous orbit, or on a suborbital trajectory (
1390:
897:
188:
157:
35:
2917:
1753:
810:
787:
764:
681:
3084:
3032:
2985:
2936:
465:
2960:"From Cavitation to Astrophysics: Explicit Solution of the Spherical Collapse Equation"
2959:
2771:
2722:
1777:
1669:
1620:
1598:
1423:
1172:
1045:
903:
879:
859:
336:
315:
86:
3124:
3050:
3041:
3016:
2710:
1365:
837:
59:
2863:
1081:, assumed to be constant although in general it will depend on the Reynolds number.
354:
347:
172:
78:
46:
acting upon it. A freely falling object may not necessarily be falling down in the
2829:
Abel B. Franco (October 2003). "Avempace, Projectile Motion, and
Impetus Theory",
112:
produces the sensation of the body's weight being supported on a cushion of air.
2993:
430:
204:
105:
3065:
2737:, from which basis Einstein's theory of general relativity initially took off.
2706:
365:
294:
290:
93:
1161:{\displaystyle v(t)=v_{\infty }\tanh \left({\frac {gt}{v_{\infty }}}\right),}
2702:
848:
301:
149:
139:
97:
82:
3001:
2076:
This solution can also be represented exactly by the analytic power series
434:
experience the same acceleration due to gravity. On the Moon, however, the
414:, where h is the height and g is the free-fall acceleration due to gravity.
85:
in orbit) and its surrounding objects, it will result in the sensation of
3114:
856:
This case, which applies to skydivers, parachutists or any body of mass,
2751:
829:
353:
Standing on the ground: the gravitational force is counteracted by the
39:
3092:
375:
1404:
The motion of two objects moving radially towards each other with no
2944:
256:. Statements consisting only of original research should be removed.
2976:
2888:
Olenick, Richard P.; Apostol, Tom M.; Goodstein, David L. (2008).
2812:. Vol. 1. New York: Charles Scribner's Sons. pp. 26ā28.
1860:
The separation can be expressed explicitly as a function of time
847:
374:
201:
dropped two objects of unequal mass from the
Leaning Tower of Pisa
55:
43:
2806:
Pines, Shlomo (1970). "Abu'l-BarakÄt al-BaghdÄdÄ« , Hibat Allah".
1240:{\displaystyle v_{\infty }={\sqrt {\frac {2mg}{\rho C_{D}A}}}\,.}
199:
According to a tale that may be apocryphal, in 1589ā1592 Galileo
419:
51:
1850:{\displaystyle t_{\text{ff}}=\pi {\sqrt {y_{0}^{3}/(8\mu )}}~.}
2826:
2341:{\displaystyle y(t)=\sum _{n=1}^{\infty }\left\right)\right].}
221:
214:, an unpublished manuscript on the motion of falling bodies.
464:
346:
Flying in an aircraft: there is also an additional force of
2891:
The
Mechanical Universe: Introduction to Mechanics and Heat
2701:. Far away from any sources of space-time curvature, where
1408:
can be considered a special case of an elliptical orbit of
646:
is the initial vertical component of the velocity (m/s).
2795:. Cambridge, MA: Harvard University Press. p. 220.
245:
2847:"The Feynman Lectures on Physics Vol. I Ch. 8: Motion"
605:{\displaystyle y(t)=v_{0}t+y_{0}-{\frac {1}{2}}gt^{2}}
3017:"From Moon-fall to motions under inverse square laws"
2570:
2360:
2085:
2037:
1985:
1869:
1788:
1756:
1693:
1672:
1645:
1623:
1601:
1435:
1259:
1184:
1093:
1054:
1030:
929:
906:
882:
862:
813:
790:
767:
737:
707:
684:
654:
624:
534:
479:
385:
318:
3066:"Radial Motion of Two Mutually Attracting Particles"
429:
Free fall was demonstrated on the Moon by astronaut
2676:
2551:
2340:
2065:
2012:
1968:
1849:
1768:
1734:
1678:
1658:
1629:
1607:
1581:
1348:
1239:
1160:
1069:
1036:
1013:
912:
888:
868:
820:
797:
774:
753:
721:
691:
670:
638:
604:
517:
462:much less than the terminal velocity (see below).
457:Uniform gravitational field without air resistance
406:
324:
100:, or lifting device, is also often referred to as
1637:is the distance between the centers of the bodies
368:that equals their weight once they have achieved
123:, a body in free fall has no force acting on it.
2128:
2791:Cohen, Morris R.; Drabkin, I. E., eds. (1958).
1372:'s record jumps, also belong in this category.
844:Uniform gravitational field with air resistance
438:is approximately 1.63 m/s, or only about ā
2858:
2856:
678:is the vertical component of the velocity at
8:
297:) going up for some minutes, and then down).
2894:. Cambridge University Press. p. 18.
838:the odd numbers sum to the perfect squares
285:Examples of objects in free fall include:
195:Galileo's Leaning Tower of Pisa experiment
142:(384ā322 BC) discussed falling objects in
3040:
2975:
2661:
2657:
2638:
2631:
2626:
2614:
2598:
2583:
2569:
2526:
2512:
2503:
2489:
2480:
2466:
2457:
2443:
2434:
2420:
2411:
2397:
2380:
2359:
2305:
2301:
2285:
2273:
2260:
2238:
2226:
2202:
2201:
2192:
2179:
2178:
2173:
2170:
2154:
2148:
2131:
2116:
2105:
2084:
2042:
2036:
1984:
1945:
1932:
1921:
1912:
1889:
1868:
1822:
1816:
1811:
1805:
1793:
1787:
1755:
1723:
1710:
1692:
1671:
1650:
1644:
1622:
1600:
1562:
1552:
1528:
1519:
1500:
1491:
1489:
1467:
1460:
1455:
1451:
1434:
1331:
1317:
1290:
1285:
1279:
1270:
1258:
1233:
1220:
1198:
1189:
1183:
1143:
1129:
1113:
1092:
1060:
1059:
1053:
1029:
1007:
1001:
987:
986:
969:
946:
936:
933:
928:
905:
881:
861:
832:(9.81 m/s near the surface of the earth).
817:
812:
794:
789:
771:
766:
750:
736:
718:
712:
706:
688:
683:
667:
653:
635:
629:
623:
596:
579:
570:
554:
533:
514:
499:
478:
394:
386:
384:
317:
272:Learn how and when to remove this message
16:Motion of a body subject only to gravity
2783:
2713:or inspiral of compact binaries due to
1615:is the time after the start of the fall
148:(Book VII), one of the oldest books on
2914:An analysis of such jumps is given in
1376:Inverse-square law gravitational field
342:Examples of objects not in free-fall:
2066:{\displaystyle I_{x}(\alpha ,\beta )}
1383:Newton's law of universal gravitation
189:Galileo Galilei Ā§ Falling bodies
7:
2030:regularized incomplete beta function
119:, where gravitation is reduced to a
2717:, and the relativity of direction (
2013:{\displaystyle Q(x;\alpha ,\beta )}
1735:{\displaystyle \mu =G(m_{1}+m_{2})}
2958:Obreschkow, Danail (7 June 2024).
2809:Dictionary of Scientific Biography
2757:High-altitude military parachuting
2193:
2174:
2117:
1422:). This allows one to compute the
1332:
1286:
1190:
1144:
1114:
1061:
988:
947:
937:
300:An object dropped at the top of a
14:
2869:. Green Harbor Publications. 2010
1395:Kepler's laws of planetary motion
156:). Although, in the 6th century,
2916:Mohazzabi, P.; Shea, J. (1996).
2020:is the quantile function of the
1744:standard gravitational parameter
1070:{\displaystyle C_{\mathrm {D} }}
446:Free fall in Newtonian mechanics
226:
171:of falling bodies. According to
81:exerted between a body (e.g. an
54:is thus in free fall around the
2831:Journal of the History of Ideas
518:{\displaystyle v(t)=v_{0}-gt\,}
133:History of gravitational theory
2793:A Source Book in Greek Science
2677:{\displaystyle x=\left^{2/3}.}
2370:
2364:
2293:
2267:
2257:
2248:
2135:
2095:
2089:
2060:
2048:
2007:
1989:
1879:
1873:
1836:
1827:
1729:
1703:
1445:
1439:
1387:gravitational two-body problem
1103:
1097:
747:
741:
664:
658:
544:
538:
489:
483:
407:{\displaystyle {\sqrt {2h/g}}}
1:
2747:Equations for a falling body
920:, has an equation of motion
876:, and cross-sectional area,
729:is the initial altitude (m).
167:gave an explanation for the
3110:Freefall formula calculator
3021:European Journal of Physics
2994:10.1103/PhysRevE.109.065102
2925:American Journal of Physics
828:is the acceleration due to
252:the claims made and adding
3152:
3042:10.1088/0143-0807/29/5/012
2690:
1420:radial elliptic trajectory
449:
436:gravitational acceleration
192:
186:
169:gravitational acceleration
130:
21:Free fall (disambiguation)
18:
2918:"High altitude free fall"
165:Abu'l-BarakÄt al-BaghdÄdÄ«
3064:Mungan, Carl E. (2009).
2762:Reduced-gravity aircraft
2351:Evaluating this yields:
1666:is the initial value of
1385:, with solutions to the
722:{\displaystyle y_{0}\,}
639:{\displaystyle v_{0}\,}
3117:an educational website
2733:, is the basis of the
2678:
2553:
2342:
2121:
2067:
2014:
1970:
1851:
1770:
1736:
1680:
1660:
1631:
1609:
1583:
1350:
1241:
1162:
1071:
1038:
1015:
914:
890:
870:
853:
822:
799:
776:
755:
754:{\displaystyle y(t)\,}
723:
693:
672:
671:{\displaystyle v(t)\,}
640:
606:
519:
470:
415:
408:
326:
163:In 12th-century Iraq,
2735:equivalence principle
2691:Further information:
2687:In general relativity
2679:
2554:
2343:
2101:
2068:
2015:
1971:
1852:
1771:
1737:
1681:
1661:
1659:{\displaystyle y_{0}}
1632:
1610:
1584:
1351:
1242:
1163:
1072:
1039:
1037:{\displaystyle \rho }
1016:
915:
891:
871:
851:
823:
800:
777:
756:
724:
694:
673:
641:
607:
520:
468:
409:
378:
339:in these situations.
327:
73:In a roughly uniform
2568:
2358:
2083:
2035:
2024:, also known as the
1983:
1867:
1786:
1754:
1691:
1670:
1643:
1621:
1599:
1433:
1257:
1182:
1091:
1052:
1028:
927:
904:
880:
860:
811:
805:is time elapsed (s).
788:
765:
735:
705:
682:
652:
622:
532:
477:
383:
316:
154:Aristotelian physics
121:space-time curvature
19:For other uses, see
3115:The Way Things Fall
3085:2009PhTea..47..502M
3073:The Physics Teacher
3033:2008EJPh...29..987F
3015:Foong, S K (2008).
2986:2024PhRvE.109f5102O
2937:1996AmJPh..64.1242M
2836:(4), pp. 521ā546 .)
2719:geodetic precession
2715:gravitational waves
1821:
1769:{\displaystyle y=0}
1399:Newton's cannonball
1295:
821:{\displaystyle g\,}
798:{\displaystyle t\,}
775:{\displaystyle t\,}
761:is the altitude at
692:{\displaystyle t\,}
452:Newtonian mechanics
177:classical mechanics
96:without a deployed
75:gravitational field
34:is any motion of a
28:classical mechanics
2693:General relativity
2674:
2549:
2338:
2142:
2063:
2010:
1966:
1847:
1807:
1766:
1732:
1676:
1656:
1627:
1605:
1579:
1346:
1281:
1237:
1158:
1067:
1034:
1011:
910:
886:
866:
854:
818:
795:
772:
751:
719:
689:
668:
636:
602:
515:
471:
416:
404:
322:
237:possibly contains
211:De Motu Antiquiora
117:general relativity
115:In the context of
48:vertical direction
3093:10.1119/1.3246467
2901:978-0-521-71592-8
2864:"Free fall graph"
2767:Terminal velocity
2731:Eƶtvƶs experiment
2645:
2644:
2606:
2591:
2545:
2520:
2497:
2474:
2451:
2428:
2405:
2313:
2291:
2265:
2246:
2215:
2168:
2127:
2022:Beta distribution
1962:
1953:
1940:
1927:
1924:
1897:
1843:
1839:
1796:
1679:{\displaystyle y}
1630:{\displaystyle y}
1608:{\displaystyle t}
1569:
1568:
1541:
1534:
1506:
1482:
1481:
1370:Felix Baumgartner
1337:
1299:
1231:
1230:
1149:
977:
955:
913:{\displaystyle v}
889:{\displaystyle A}
869:{\displaystyle m}
587:
402:
370:terminal velocity
325:{\displaystyle g}
282:
281:
274:
239:original research
110:terminal velocity
3143:
3097:
3096:
3070:
3061:
3055:
3054:
3044:
3012:
3006:
3005:
2979:
2955:
2949:
2948:
2922:
2912:
2906:
2905:
2885:
2879:
2878:
2876:
2874:
2868:
2860:
2851:
2850:
2843:
2837:
2823:
2803:
2797:
2796:
2788:
2683:
2681:
2680:
2675:
2670:
2669:
2665:
2656:
2652:
2651:
2647:
2646:
2643:
2642:
2637:
2636:
2635:
2624:
2616:
2615:
2607:
2599:
2592:
2584:
2558:
2556:
2555:
2550:
2543:
2542:
2538:
2531:
2530:
2521:
2513:
2508:
2507:
2498:
2490:
2485:
2484:
2475:
2467:
2462:
2461:
2452:
2444:
2439:
2438:
2429:
2421:
2416:
2415:
2406:
2398:
2385:
2384:
2347:
2345:
2344:
2339:
2334:
2330:
2329:
2325:
2324:
2320:
2319:
2318:
2314:
2306:
2300:
2296:
2292:
2290:
2289:
2274:
2266:
2261:
2247:
2239:
2231:
2230:
2216:
2214:
2213:
2212:
2196:
2190:
2189:
2177:
2171:
2169:
2167:
2159:
2158:
2149:
2141:
2120:
2115:
2072:
2070:
2069:
2064:
2047:
2046:
2026:inverse function
2019:
2017:
2016:
2011:
1975:
1973:
1972:
1967:
1960:
1959:
1955:
1954:
1946:
1941:
1933:
1928:
1926:
1925:
1922:
1913:
1895:
1894:
1893:
1856:
1854:
1853:
1848:
1841:
1840:
1826:
1820:
1815:
1806:
1798:
1797:
1794:
1775:
1773:
1772:
1767:
1741:
1739:
1738:
1733:
1728:
1727:
1715:
1714:
1685:
1683:
1682:
1677:
1665:
1663:
1662:
1657:
1655:
1654:
1636:
1634:
1633:
1628:
1614:
1612:
1611:
1606:
1588:
1586:
1585:
1580:
1575:
1571:
1570:
1567:
1566:
1554:
1553:
1542:
1540:
1536:
1535:
1533:
1532:
1520:
1507:
1505:
1504:
1492:
1490:
1483:
1480:
1472:
1471:
1466:
1465:
1464:
1453:
1452:
1417:
1406:angular momentum
1355:
1353:
1352:
1347:
1342:
1338:
1336:
1335:
1326:
1318:
1300:
1294:
1289:
1280:
1275:
1274:
1246:
1244:
1243:
1238:
1232:
1229:
1225:
1224:
1211:
1200:
1199:
1194:
1193:
1167:
1165:
1164:
1159:
1154:
1150:
1148:
1147:
1138:
1130:
1118:
1117:
1079:drag coefficient
1076:
1074:
1073:
1068:
1066:
1065:
1064:
1043:
1041:
1040:
1035:
1020:
1018:
1017:
1012:
1006:
1005:
993:
992:
991:
978:
970:
956:
954:
950:
944:
940:
934:
919:
917:
916:
911:
895:
893:
892:
887:
875:
873:
872:
867:
827:
825:
824:
819:
804:
802:
801:
796:
781:
779:
778:
773:
760:
758:
757:
752:
728:
726:
725:
720:
717:
716:
698:
696:
695:
690:
677:
675:
674:
669:
645:
643:
642:
637:
634:
633:
611:
609:
608:
603:
601:
600:
588:
580:
575:
574:
559:
558:
524:
522:
521:
516:
504:
503:
424:drag coefficient
413:
411:
410:
405:
403:
398:
387:
357:from the ground.
331:
329:
328:
323:
277:
270:
266:
263:
257:
254:inline citations
230:
229:
222:
3151:
3150:
3146:
3145:
3144:
3142:
3141:
3140:
3121:
3120:
3106:
3101:
3100:
3068:
3063:
3062:
3058:
3027:(5): 987ā1003.
3014:
3013:
3009:
2957:
2956:
2952:
2945:10.1119/1.18386
2920:
2915:
2913:
2909:
2902:
2887:
2886:
2882:
2872:
2870:
2866:
2862:
2861:
2854:
2845:
2844:
2840:
2824:
2820:
2805:
2804:
2800:
2790:
2789:
2785:
2780:
2743:
2709:of orbits, the
2695:
2689:
2627:
2625:
2617:
2597:
2593:
2582:
2578:
2577:
2566:
2565:
2522:
2499:
2476:
2453:
2430:
2407:
2390:
2386:
2376:
2356:
2355:
2281:
2237:
2233:
2232:
2222:
2221:
2217:
2197:
2191:
2172:
2160:
2150:
2147:
2143:
2126:
2122:
2081:
2080:
2038:
2033:
2032:
1981:
1980:
1917:
1905:
1901:
1885:
1865:
1864:
1789:
1784:
1783:
1752:
1751:
1719:
1706:
1689:
1688:
1668:
1667:
1646:
1641:
1640:
1619:
1618:
1597:
1596:
1558:
1524:
1512:
1508:
1496:
1488:
1484:
1473:
1456:
1454:
1431:
1430:
1412:
1391:elliptic orbits
1378:
1327:
1319:
1313:
1266:
1255:
1254:
1216:
1212:
1201:
1185:
1180:
1179:
1139:
1131:
1125:
1109:
1089:
1088:
1055:
1050:
1049:
1026:
1025:
997:
982:
945:
935:
925:
924:
902:
901:
898:Reynolds number
878:
877:
858:
857:
846:
809:
808:
786:
785:
763:
762:
733:
732:
708:
703:
702:
680:
679:
650:
649:
625:
620:
619:
592:
566:
550:
530:
529:
495:
475:
474:
459:
454:
448:
442:that on Earth.
441:
381:
380:
314:
313:
284:
278:
267:
261:
258:
243:
231:
227:
220:
197:
191:
185:
183:Galileo Galilei
158:John Philoponus
135:
129:
68:Earth's surface
24:
17:
12:
11:
5:
3149:
3147:
3139:
3138:
3133:
3123:
3122:
3119:
3118:
3112:
3105:
3104:External links
3102:
3099:
3098:
3079:(8): 502ā507.
3056:
3007:
2950:
2907:
2900:
2880:
2852:
2838:
2818:
2798:
2782:
2781:
2779:
2776:
2775:
2774:
2772:Weightlessness
2769:
2764:
2759:
2754:
2749:
2742:
2739:
2723:frame dragging
2688:
2685:
2673:
2668:
2664:
2660:
2655:
2650:
2641:
2634:
2630:
2623:
2620:
2613:
2610:
2605:
2602:
2596:
2590:
2587:
2581:
2576:
2573:
2560:
2559:
2548:
2541:
2537:
2534:
2529:
2525:
2519:
2516:
2511:
2506:
2502:
2496:
2493:
2488:
2483:
2479:
2473:
2470:
2465:
2460:
2456:
2450:
2447:
2442:
2437:
2433:
2427:
2424:
2419:
2414:
2410:
2404:
2401:
2396:
2393:
2389:
2383:
2379:
2375:
2372:
2369:
2366:
2363:
2349:
2348:
2337:
2333:
2328:
2323:
2317:
2312:
2309:
2304:
2299:
2295:
2288:
2284:
2280:
2277:
2272:
2269:
2264:
2259:
2256:
2253:
2250:
2245:
2242:
2236:
2229:
2225:
2220:
2211:
2208:
2205:
2200:
2195:
2188:
2185:
2182:
2176:
2166:
2163:
2157:
2153:
2146:
2140:
2137:
2134:
2130:
2125:
2119:
2114:
2111:
2108:
2104:
2100:
2097:
2094:
2091:
2088:
2062:
2059:
2056:
2053:
2050:
2045:
2041:
2009:
2006:
2003:
2000:
1997:
1994:
1991:
1988:
1977:
1976:
1965:
1958:
1952:
1949:
1944:
1939:
1936:
1931:
1920:
1916:
1911:
1908:
1904:
1900:
1892:
1888:
1884:
1881:
1878:
1875:
1872:
1858:
1857:
1846:
1838:
1835:
1832:
1829:
1825:
1819:
1814:
1810:
1804:
1801:
1792:
1778:free-fall time
1765:
1762:
1759:
1748:
1747:
1731:
1726:
1722:
1718:
1713:
1709:
1705:
1702:
1699:
1696:
1686:
1675:
1653:
1649:
1638:
1626:
1616:
1604:
1590:
1589:
1578:
1574:
1565:
1561:
1557:
1551:
1548:
1545:
1539:
1531:
1527:
1523:
1518:
1515:
1511:
1503:
1499:
1495:
1487:
1479:
1476:
1470:
1463:
1459:
1450:
1447:
1444:
1441:
1438:
1424:free-fall time
1377:
1374:
1357:
1356:
1345:
1341:
1334:
1330:
1325:
1322:
1316:
1312:
1309:
1306:
1303:
1298:
1293:
1288:
1284:
1278:
1273:
1269:
1265:
1262:
1248:
1247:
1236:
1228:
1223:
1219:
1215:
1210:
1207:
1204:
1197:
1192:
1188:
1173:terminal speed
1169:
1168:
1157:
1153:
1146:
1142:
1137:
1134:
1128:
1124:
1121:
1116:
1112:
1108:
1105:
1102:
1099:
1096:
1063:
1058:
1033:
1022:
1021:
1010:
1004:
1000:
996:
990:
985:
981:
976:
973:
968:
965:
962:
959:
953:
949:
943:
939:
932:
909:
885:
865:
845:
842:
834:
833:
816:
806:
793:
783:
770:
749:
746:
743:
740:
730:
715:
711:
700:
687:
666:
663:
660:
657:
647:
632:
628:
613:
612:
599:
595:
591:
586:
583:
578:
573:
569:
565:
562:
557:
553:
549:
546:
543:
540:
537:
526:
525:
513:
510:
507:
502:
498:
494:
491:
488:
485:
482:
458:
455:
450:Main article:
447:
444:
439:
401:
397:
393:
390:
362:
361:
358:
351:
337:weightlessness
321:
309:
308:
305:
298:
280:
279:
234:
232:
225:
219:
216:
184:
181:
131:Main article:
128:
125:
87:weightlessness
64:very far orbit
15:
13:
10:
9:
6:
4:
3:
2:
3148:
3137:
3134:
3132:
3129:
3128:
3126:
3116:
3113:
3111:
3108:
3107:
3103:
3094:
3090:
3086:
3082:
3078:
3074:
3067:
3060:
3057:
3052:
3048:
3043:
3038:
3034:
3030:
3026:
3022:
3018:
3011:
3008:
3003:
2999:
2995:
2991:
2987:
2983:
2978:
2973:
2970:(6): 065102.
2969:
2965:
2961:
2954:
2951:
2946:
2942:
2938:
2934:
2930:
2926:
2919:
2911:
2908:
2903:
2897:
2893:
2892:
2884:
2881:
2865:
2859:
2857:
2853:
2848:
2842:
2839:
2835:
2832:
2828:
2821:
2819:0-684-10114-9
2815:
2811:
2810:
2802:
2799:
2794:
2787:
2784:
2777:
2773:
2770:
2768:
2765:
2763:
2760:
2758:
2755:
2753:
2750:
2748:
2745:
2744:
2740:
2738:
2736:
2732:
2726:
2724:
2720:
2716:
2712:
2711:orbital decay
2708:
2704:
2700:
2694:
2686:
2684:
2671:
2666:
2662:
2658:
2653:
2648:
2639:
2632:
2628:
2621:
2618:
2611:
2608:
2603:
2600:
2594:
2588:
2585:
2579:
2574:
2571:
2563:
2546:
2539:
2535:
2532:
2527:
2523:
2517:
2514:
2509:
2504:
2500:
2494:
2491:
2486:
2481:
2477:
2471:
2468:
2463:
2458:
2454:
2448:
2445:
2440:
2435:
2431:
2425:
2422:
2417:
2412:
2408:
2402:
2399:
2394:
2391:
2387:
2381:
2377:
2373:
2367:
2361:
2354:
2353:
2352:
2335:
2331:
2326:
2321:
2315:
2310:
2307:
2302:
2297:
2286:
2282:
2278:
2275:
2270:
2262:
2254:
2251:
2243:
2240:
2234:
2227:
2223:
2218:
2209:
2206:
2203:
2198:
2186:
2183:
2180:
2164:
2161:
2155:
2151:
2144:
2138:
2132:
2123:
2112:
2109:
2106:
2102:
2098:
2092:
2086:
2079:
2078:
2077:
2074:
2057:
2054:
2051:
2043:
2039:
2031:
2027:
2023:
2004:
2001:
1998:
1995:
1992:
1986:
1963:
1956:
1950:
1947:
1942:
1937:
1934:
1929:
1918:
1914:
1909:
1906:
1902:
1898:
1890:
1886:
1882:
1876:
1870:
1863:
1862:
1861:
1844:
1833:
1830:
1823:
1817:
1812:
1808:
1802:
1799:
1790:
1782:
1781:
1780:
1779:
1763:
1760:
1757:
1750:Substituting
1745:
1724:
1720:
1716:
1711:
1707:
1700:
1697:
1694:
1687:
1673:
1651:
1647:
1639:
1624:
1617:
1602:
1595:
1594:
1593:
1576:
1572:
1563:
1559:
1555:
1549:
1546:
1543:
1537:
1529:
1525:
1521:
1516:
1513:
1509:
1501:
1497:
1493:
1485:
1477:
1474:
1468:
1461:
1457:
1448:
1442:
1436:
1429:
1428:
1427:
1425:
1421:
1415:
1411:
1407:
1402:
1400:
1396:
1392:
1388:
1384:
1375:
1373:
1371:
1367:
1366:Joe Kittinger
1363:
1343:
1339:
1328:
1323:
1320:
1314:
1310:
1307:
1304:
1301:
1296:
1291:
1282:
1276:
1271:
1267:
1263:
1260:
1253:
1252:
1251:
1234:
1226:
1221:
1217:
1213:
1208:
1205:
1202:
1195:
1186:
1178:
1177:
1176:
1174:
1155:
1151:
1140:
1135:
1132:
1126:
1122:
1119:
1110:
1106:
1100:
1094:
1087:
1086:
1085:
1082:
1080:
1056:
1047:
1031:
1008:
1002:
998:
994:
983:
979:
974:
971:
966:
963:
960:
957:
951:
941:
930:
923:
922:
921:
907:
899:
883:
863:
850:
843:
841:
839:
831:
814:
807:
791:
784:
768:
744:
738:
731:
713:
709:
701:
685:
661:
655:
648:
630:
626:
618:
617:
616:
597:
593:
589:
584:
581:
576:
571:
567:
563:
560:
555:
551:
547:
541:
535:
528:
527:
511:
508:
505:
500:
496:
492:
486:
480:
473:
472:
467:
463:
456:
453:
445:
443:
437:
432:
427:
425:
421:
399:
395:
391:
388:
377:
373:
372:(see below).
371:
367:
359:
356:
352:
349:
345:
344:
343:
340:
338:
333:
319:
306:
303:
299:
296:
292:
288:
287:
286:
276:
273:
265:
255:
251:
247:
241:
240:
235:This article
233:
224:
223:
217:
215:
213:
212:
206:
202:
196:
190:
182:
180:
178:
174:
170:
166:
161:
159:
155:
151:
147:
146:
141:
134:
126:
124:
122:
118:
113:
111:
107:
103:
99:
95:
90:
88:
84:
80:
76:
71:
69:
65:
61:
60:orbital speed
58:, though its
57:
53:
49:
45:
41:
37:
33:
29:
22:
3076:
3072:
3059:
3024:
3020:
3010:
2967:
2964:Phys. Rev. E
2963:
2953:
2931:(10): 1242.
2928:
2924:
2910:
2890:
2883:
2871:. Retrieved
2841:
2833:
2830:
2807:
2801:
2792:
2786:
2727:
2696:
2564:
2561:
2350:
2075:
1978:
1859:
1749:
1591:
1413:
1410:eccentricity
1403:
1381:governed by
1379:
1364:, including
1358:
1249:
1175:is given by
1170:
1083:
1023:
855:
835:
614:
460:
428:
417:
363:
355:normal force
341:
334:
310:
283:
268:
259:
236:
209:
205:water clocks
198:
173:Shlomo Pines
162:
143:
138:philosopher
136:
114:
101:
91:
79:normal force
72:
62:keeps it in
42:is the only
31:
25:
2518:62077640625
1776:we get the
1046:air density
431:David Scott
106:aerodynamic
3125:Categories
2977:2401.05445
2778:References
2707:precession
1362:HALO jumps
1171:where the
366:drag force
295:ballistics
291:spacecraft
246:improve it
193:See also:
187:See also:
94:atmosphere
3051:122494969
2703:spacetime
2622:μ
2609:−
2601:π
2536:⋯
2533:−
2510:−
2487:−
2464:−
2441:−
2418:−
2395:−
2303:−
2279:−
2271:−
2255:
2207:−
2184:−
2136:→
2118:∞
2103:∑
2058:β
2052:α
2005:β
1999:α
1910:−
1834:μ
1803:π
1695:μ
1550:
1517:−
1478:μ
1333:∞
1311:
1305:
1287:∞
1277:−
1214:ρ
1191:∞
1145:∞
1123:
1115:∞
1032:ρ
980:ρ
967:−
577:−
506:−
469:Free-fall
302:drop tube
262:July 2020
250:verifying
150:mechanics
140:Aristotle
102:free fall
98:parachute
83:astronaut
66:from the
32:free fall
3002:39021019
2873:14 March
2741:See also
2699:geodesic
2495:21896875
1393:obeying
218:Examples
3136:Gravity
3131:Falling
3081:Bibcode
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