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用户:DrizzleD/地月转移轨道

< User:DrizzleD
地月转移，相对视角。在近地的红点处开始TLI。

月球转移轨道（Lunar Transfer Orbit, LTO，亦称为地月转移轨道）是探测器从环绕地球运行转变为环绕月球运行所经历的轨道，常常是类霍曼转移轨道。

月球转移入轨（Trans-Lunar Injection, TLI）是一种经由月球转移轨道到达月球的轨道机动。

历史

 
GRAIL-A的入轨机动模拟动画
  GRAIL-A ·   Moon ·   Earth
 
Chandrayaan-2的入轨机动模拟动画
  Earth ·   Moon ·   Chandrayaan-2
 
LRO的入轨机动模拟动画
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第一次月球转移入轨的尝试是由苏联的月球一号做出的。这枚探测器于1959年1月2日发射，计划在月球上硬着陆。然而，其入轨精度未达预期，最终以超过三倍月球半径的距离错过月球。[1]月球二号于同年9月2日执行了同样的机动，并改进了入轨精度，于两天后成功撞击月球。[2]苏联人之后在1959至1976年间又成功执行了22项月球计划任务和5项探测器计划任务。[3]

美国于1962年1月26日启动其首次月球硬着陆尝试徘徊者3号，但同样未能成功达成目标。随后，美国于同年4月23日成功发射了徘徊者4号。[4] Another 27 missions to the Moon were launched from 1962 to 1973, including five successful Surveyor soft landers, five Lunar Orbiter surveillance probes,[5]:166 and nine Apollo missions, which landed the first humans on the Moon. 1968年发射的阿波罗8号是人类首次载人月球转移入轨任务。[6]

For the Apollo lunar missions, TLI was performed by the restartable J-2 engine in the S-IVB third stage of the Saturn V rocket. This particular TLI burn lasted approximately 350 seconds, providing 3.05 to 3.25 km/s (10,000 to 10,600 ft/s) of change in velocity (delta-v), at which point the spacecraft was traveling at approximately 10.4 km/s (34150 ft/s) relative to the Earth.[7] The Apollo 8 TLI was spectacularly observed from the Hawaiian Islands in the pre-dawn sky south of Waikiki, photographed and reported in the papers the next day.[8] In 1969, the Apollo 10 pre-dawn TLI was visible from Cloncurry, Australia.[9] It was described as resembling car headlights coming over a hill in fog, with the spacecraft appearing as a bright comet with a greenish tinge.[9]

In 1990 Japan launched its first lunar mission, using the Hiten satellite to fly by the Moon and place the Hagoromo microsatellite in a lunar orbit. Following that, it explored a novel low delta-v TLI method with a 6-month transfer time (compared to 3 days for Apollo).[10][5]:179

The 1994 US Clementine spacecraft, designed to showcase lightweight technologies, used a 3 week long TLI with two intermediate earth flybys before entering a lunar orbit.[10][5]:185

In 1997 Asiasat-3 became the first commercial satellite to reach the Moon's sphere of influence when, after a launch failure, it swung by the Moon twice as a low delta-v way to reach its desired geostationary orbit. It passed within 6200 km of the Moon's surface.[10][5]:203

The 2003 ESA SMART-1 technology demonstrator satellite became the first European satellite to orbit the Moon. After being launched into a geostationary transfer orbit (GTO), it used solar powered ion engines for propulsion. As a result of its extremely low delta-v TLI maneuver, the spacecraft took over 13 months to reach a lunar orbit and 17 months to reach its desired orbit.[5]:229

China launched its first Moon mission in 2007, placing the Chang'e 1 spacecraft in a lunar orbit. It used multiple burns to slowly raise its apogee to reach the vicinity of the Moon.[5]:257

India followed in 2008, launching the Chandrayaan-1 into a GTO and, like the Chinese spacecraft, increasing its apogee over a number of burns.[5]:259

The soft lander Beresheet from the Israel Aerospace Industries, used this maneuver in 2019, but crashed on the Moon.

In 2011 the NASA GRAIL satellites used a low delta-v route to the Moon, passing by the Sun-Earth L1 point, and taking over 3 months.[5]:278

理论

典型的地月转移入轨和霍曼转移相仿，不过低能量转移有时也被使用，飞天号探测器就是。[11]对于没有显著地月系外摄动的短期任务，快霍曼转移往往更实际。

A spacecraft performs TLI to begin a lunar transfer from a low circular parking orbit around Earth. The large TLI burn, usually performed by a chemical rocket engine, increases the spacecraft's velocity, changing its orbit from a circular low Earth orbit to a highly eccentric orbit. As the spacecraft begins coasting on the lunar transfer arc, its trajectory approximates an elliptical orbit about the Earth with an apogee near to the radius of the Moon's orbit. The TLI burn is sized and timed to precisely target the Moon as it revolves around the Earth. The burn is timed so that the spacecraft nears apogee as the Moon approaches. Finally, the spacecraft enters the Moon's sphere of influence, making a hyperbolic lunar swingby.

Free return

主条目：Free return trajectory
 
Sketch of a circumlunar free return trajectory (not to scale)

In some cases it is possible to design a TLI to target a free return trajectory, so that the spacecraft will loop around behind the Moon and return to Earth without need for further propulsive maneuvers.[12]

Such free return trajectories add a margin of safety to human spaceflight missions, since the spacecraft will return to Earth "for free" after the initial TLI burn. The Apollos 8, 10 and 11 began on a free return trajectory,[13] while the later missions used a functionally similar hybrid trajectory, in which a midway course correction is required to reach the moon.[14][15][16]

Modeling

 
Artist's concept of NASA's Constellation stack performing the trans-lunar injection burn

Patched conics

TLI targeting and lunar transfers are a specific application of the n body problem, which may be approximated in various ways. The simplest way to explore lunar transfer trajectories is by the method of patched conics. The spacecraft is assumed to accelerate only under classical 2 body dynamics, being dominated by the Earth until it reaches the Moon's sphere of influence. Motion in a patched-conic system is deterministic and simple to calculate, lending itself for rough mission design and "back of the envelope" studies.

Restricted circular three body (RC3B)

More realistically, however, the spacecraft is subject to gravitational forces from many bodies. Gravitation from Earth and Moon dominate the spacecraft's acceleration, and since the spacecraft's own mass is negligible in comparison, the spacecraft's trajectory may be better approximated as a restricted three-body problem. This model is a closer approximation but lacks an analytic solution,[17] requiring numerical calculation.[18]

Further accuracy

More detailed simulation involves modeling the Moon's true orbital motion; gravitation from other astronomical bodies; the non-uniformity of the Earth's and Moon's gravity; including solar radiation pressure; and so on. Propagating spacecraft motion in such a model is numerically intensive, but necessary for true mission accuracy.

参见

参考文献

  1. ^ Luna 01. NASA. 
  2. ^ NASA - NSSDCA - Spacecraft - Details. nssdc.gsfc.nasa.gov. 
  3. ^ Soviet Missions to the Moon. nssdc.gsfc.nasa.gov. 
  4. ^ Ranger 4. NASA. 
  5. ^ 5.0 5.1 5.2 5.3 5.4 5.5 5.6 5.7 Beyond Earth (PDF). NASA. 
  6. ^ Mars, Kelli. 50 Years Ago: Apollo 8, You are Go for TLI!. NASA. December 20, 2018. 
  7. ^ Apollo By the Numbers. NASA. （原始内容存档于2004-11-18）. 
  8. ^ Independent Star News, Sunday, December 22, 1968.  "The TLI firing was begun at PST while the craft was over Hawaii and it was reported there that the burn was visible from the ground."
  9. ^ 9.0 9.1 French, Francis; Colin Burgess. In the Shadow of the Moon. University of Nebraska Press. 2007: 372. ISBN 978-0-8032-1128-5. 
  10. ^ 10.0 10.1 10.2 Alexander M. Jablonski1a; Kelly A. Ogden. A Review of Technical Requirements for Lunar Structures – Present Status (PDF). International Lunar Conference 2005. 2005. 
  11. ^ Hiten. NASA. 
  12. ^ Schwaninger, Arthur J. Trajectories in the Earth-Moon Space with Symmetrical Free Return Properties (PDF). Technical Note D-1833. Huntsville, Alabama: NASA / Marshall Space Flight Center. 1963. 
  13. ^ Mansfield, Cheryl L. Apollo 10. NASA. May 18, 2017. 
  14. ^ APOLLO 12. history.nasa.gov. 
  15. ^ Ways to the Moon (PDF) (报告): 93. 
  16. ^ Launch Windows Essay. history.nasa.gov. 
  17. ^ Henri Poincaré, Les Méthodes Nouvelles de Mécanique Céleste, Paris, Gauthier-Villars et fils, 1892-99.
  18. ^ Victor Szebehely, Theory of Orbits, The Restricted Problem of Three Bodies, Yale University, Academic Press, 1967.

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