Gravitational slingshot effect is to capture the characteristics of small mass aircraft through gravitational field by using large mass celestial experience to accelerate or decelerate small mass aircraft.Using the gravitational slingshot effect can easily change the trajectory of the aircraft and save fuel.
It should be noted that the gravitational slingshot effect is not limited to the use of aircraft, but a natural phenomenon, which is applicable to any acceleration or deceleration of small mass objects by using the gravitational effect of large mass objects.
Chinese name
Gravitational slingshot effect
Foreign name
Slingshot effect
Definition
Accelerating the space probe ship by using the planetary gravity field
To understand the gravitational slingshot, imagine a simple physical model: a ball with a large mass collides elastically with a ball with a small mass.For example, if a shot and a table tennis ball collide, both balls have good elasticity, and the collision process will not lose energy.
If the shot is not moving at first, the table tennis ball will
When hitting the shot, the shot is almost still after collision due to its great mass.The table tennis ball will bounce, and the speed is still
, remain unchanged.
If the initial shot is put at the speed of table tennis ball
Sports, table tennis with speed
Fly in.The speed of the table tennis ball after collision can be obtained directly from the conservation of energy and momentum. Considering that the mass of the shot is far greater than the table tennis ball, the speed of the table tennis ball after bounce should be
。It can also be solved by changing the reference system. First, take the shot as the reference system. The speed of the table tennis ball flying to the shot should be
, after the collision, the speed of the table tennis ball is opposite, the size remains the same, and is still
。
At this time, it is switched to the ground reference system. The speed of the table tennis ball is the speed of the table tennis ball relative to the shot plus the speed of the shot, so the speed of the table tennis ball leaving the shot after bouncing is
。
The acceleration process of the aircraft using the gravitational slingshot effect is similar to the collision process of table tennis ball and shot put, except that the aircraft does not collide with the planet, but exchanges energy through gravity.[2]
Since various details of the orbit are not considered, this is an oversimplified model.However, if the aircraft runs in a hyperbolic orbit, it can leave the planet in the opposite direction without starting the engine. At the same time, as long as it is out of the control of the planet's gravity, it can obtain an increment of twice the planet's speed.Of course, in reality, due to the influence of flight trajectory and other factors, the acceleration effect cannot reach twice the ideal planetary speed.
Here, the mass of the planet is far greater than that of the aircraft, so the impact of the aircraft on the speed of the planet is ignored, rather than violating the laws of energy conservation and momentum conservation.
Schematic diagram of velocity of gravitational slingshot effect
The gravitational slingshot effect can also be used to decelerate the aircraft. The acceleration process is "head-on collision" between the aircraft and the planet. The deceleration process is that the aircraft chases up the planet from "behind", which can achieve a deceleration of twice the speed of the planet.
analysis
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In the solar reference system, the speed of planet P is
, an aircraft at initial speed
Enter the gravitational field range of planet P from point A at infinity, and leave the gravitational field range of planet P from point B at infinity.When the aircraft moves in the range of planetary gravitational field, the gravitational force of the planet on the aircraft is far greater than that of the sun on the aircraft, and the time of the aircraft's movement in the range of planetary gravitational field is far less than the period of the planet's revolution around the sun. Therefore, the impact of solar gravity on the motion of the aircraft and the planetary assembly system can be ignored, and the aircraft and the planet are regarded as isolated two body systems.
And
The included angle of is
, the initial velocity of the aircraft relative to the planet
, the distance from the straight line along the direction to the center of the planet (i.e. aiming distance) is
, the mass of the aircraft is m, the mass of the planet is M, and the gravitational constant is G.[4]
Since the mass of the planet is far greater than that of the aircraft, it can be considered that the speed of the planet remains unchanged.The trajectory of the aircraft relative to the planet in the planetary gravitational field is a hyperbola, and planet P is the close focus of this hyperbola.
The velocity of the aircraft leaving the planetary gravitational field at point B can be calculated by using the hyperbolic geometric properties and hyperbolic orbital energy
among
by
And
Included angle of,
Is the deflection angle of aircraft speed direction.
Consider several special cases.
(1) When the initial speed direction of the aircraft is opposite to the planetary speed direction, the final speed is
If the aiming distance is 0, this is the ideal acceleration described previously, and the terminal velocity of the aircraft
(2) When the initial velocity direction of the aircraft is the same as that of the planet, the final velocity is
If the aiming distance is 0, this is the ideal deceleration condition, and the terminal speed of the aircraft
(3) When the angle between the initial speed direction of the aircraft and the speed direction of the planet is properly selected, the relative terminal speed direction of the aircraft when leaving the gravitational field can be in the same direction, that is, the aircraft leaves the gravitational field of the planet along the direction of the revolution speed of the planet.At this time, the final speed is
significance
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The significance of the gravitational slingshot effect is that it can use less fuel to achieve the flight mission of the aircraft, and greatly shorten the time required for the flight mission through the acceleration of the gravitational slingshot effect.
limit
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The biggest limitation of gravitational slingshot effect is that the massive objects used to accelerate or decelerate are not always in the ideal position.For example, Voyager 1 and Voyager 2 launched in the late 1970s, the next same ideal time will take 176 years.[3]
Application examples
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Gravitational slingshot definitely does not exist only in the minds of scientists and in science fiction movies, but in space technology that has long been mastered by humans.
The first person who proposed this technology was the Soviet scientist Yuri Kondratuk. He put forward the concept of gravity boosting in his paper "To those who are interested in building interstellar rockets and read this article" published around 1918.This person also designed the way of human landing on the moon, which was finally adopted by NASA. The Apollo spacecraft was basically built according to Yuri's idea.
However, the orbit design of gravitational slingshot requires a lot of calculation, and its official application is about 50 years later.In 1961, Michael Minovich, a 25-year-old graduate student at the University of California, Los Angeles, used the most advanced IBM 7090 computer at that time to study the three body problem, and calculated the orbit of a gravitational slingshot incidentally.He found that in the late 1970s, the solar system would provide an excellent opportunity for gravitational slingshots: Jupiter, Saturn, Uranus and Neptune were all on the same side of the sun. If you launch an aircraft and use the gravitational slingshots of the four stars to accelerate, you can visit the four stars with little fuel in 12 years.If we miss this opportunity, we will have to wait another 176 years.NASA took this opportunity to start the Voyager program. In 1977, NASA launched Voyager 1 and Voyager 2 aircraft.Today, the two travelers have completed their respective missions and have roamed the universe for 42 years. They have successfully flown to the edge of the solar system with the help of the gravitational slingshot effect.[1][3]
Other aircraft
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Asteroid 3753
Asteroid 3753 is a near Earth asteroid that periodically changes its orbit by exchanging energy with the Earth through gravitational boost.
Mariner 10
Mariner 10 is the first probe to reach another planet with the help of gravity. It passed Venus on February 5, 1974 and arrived at Mercury after the deceleration of gravity.It was the first spacecraft to explore Mercury.
Galileo
In 1989, NASA launched the Galileo probe into space through the space shuttle Atlantis.Galileo originally planned to use the Hermann transfer orbit method, but due to the Challenger space shuttle accident, Galileo's "Centaurus" propulsion rocket was no longer allowed to be transported to space through the space shuttle, and instead was a solid fuel propulsion rocket with low power.In this case, Galileo flew past Venus once and Earth twice in its orbit, and planned to reach Jupiter in December 1995.
After investigation, Galileo's engineers believed (but could not confirm) that the lubricant of Galileo's main antenna failed due to the long-term contact between the aircraft and Venus during the flyby.This technical failure forced Galileo to use a backup antenna with poor function.
Later, during Galileo's exploration of Jupiter's satellite, the gravitational propulsion method was also used for many times, thus extending the use time of fuel and increasing the chances of its close contact with Jupiter's satellite.
Ulysses detector
In 1990, the European Space Agency launched the Ulysses probe to study the polar regions of the sun.Since the orbits of all planets in the solar system are basically located on the ecliptic plane, in order to move to the polar orbit around the sun, the detector must reduce the speed of 30km/s inherited from the orbit around the earth to zero, and at the same time obtain the orbital speed around the solar polar plane - but the existing spacecraft propulsion system cannot complete this task.
So Ulysses was launched to Jupiter. When it reached a region "in front of and below" Jupiter, it fell into the gravitational field of the planet. After a minute of gravitational propulsion, the orbit of Ulysses finally bent upward, broke away from the orbit around Jupiter, and entered the polar orbit around the sun.This strategy only needs enough fuel for Ulysses to travel to Jupiter.
Messenger
Messenger spacecraft frequently uses gravitational boosting to reduce speed, and finally enters orbit around Mercury.During its flight, it flew over the Earth once, over Venus twice, and over Mercury three times. It will finally arrive near Mercury in March 2011. At this time, its speed has dropped low enough to use the remaining fuel to send the aircraft into orbit around Mercury.Although each flyby during this period is mainly for gravitational boosting, it also provides rare scientific observation opportunities.
Cassini
Cassini flew past Venus twice, then passed through Earth, Jupiter, and finally reached Saturn.Its 6.7 year journey is slightly longer than that of the Hohmann transfer orbit method - 6 years, but the required speed increment is 2 km/s less, so Cassini, which is large in size and mass, can reach Saturn with less propulsion fuel.The total acceleration required by the Hermann transfer orbit method to reach Saturn is 15.7 km/s (the gravitational potential well of the Earth and Saturn and the atmospheric braking effect are ignored here), which exceeds the propulsion capability of the existing vehicle propulsion system.
Rosetta
"Rosetta" project is a milestone bold exploration plan. Its goal is to track and finally enter the orbit of a comet, and then release a lander to the surface of the comet. It is the first time in human history to land and detect the comet nucleus.The target of its investigation is Comet 67P/Chuliumov Grasimenko, a Jupiter family comet.
On March 2, 2004, the Rosetta spacecraft was launched from the Kuru Space Center in French Guiana, South America, by an Arian-5 rocket, followed by three Earth gravity slingshot borrows and one Mars gravity slingshot borrows.On his way to chase a comet, Rosetta flew over asteroids Steins 2867 and Lutetia 21 in 2008 and 2010.On August 6, 2014, after ten years of pursuit, Rosetta safely entered the orbit around the target comet.In November 2014, Rosetta landed on Comet 67P.
