Unpowered separation of artificial celestial bodiesGravity of the earthThe minimum speed required for binding.If air resistance is not considered, its value is 11.2km/s.yesFirst cosmic velocity√ 2 times of.
Escape Velocity: An object is shot vertically upward on the surface of the planet. If the initial velocity is less than the escape velocity of the planet, the object will only rise for a certain distance, and then the acceleration generated by the gravity of the planet will eventually make it fall.
If the initial speed reaches the escape speed of the planet, the object will completely escape the gravitational binding of the planet and fly out of the planet.The speed at which an object needs to escape from the gravity of the planet is called escape speed.The minimum speed required for an object on the surface of a celestial body to fly to space without being bound by the universal gravitation of the celestial body.For example, the Earth's breakaway speed is 11.2 km/s (the second cosmic speed)[1]。
The second cosmic speed - when the object (spacecraft) flies at a speed of 11.2 km/s, it can get rid of the constraints of the earth's gravity and fly away from the earth into the orbit around the sun, no longer around the earth.This minimum speed away from the earth's gravity is the second cosmic speed.The initial flight speed of various planetary or satellite probes is higher than the second cosmic speed.
The second cosmic speed v When the spacecraft exceeds the first cosmic speed v and reaches a certain value, it will break away from the earth's gravitational field and become an artificial planet orbiting the sun. This speed is called the second cosmic speed, also called the breakaway speed[5]。According to the mechanical theory, the second cosmic velocity v=11.2km/s can be calculated.
The second cosmic velocity is the escape velocitykinetic energyEqual toGravitational potential energyThe size of the objectrate。Escape speed is generally described as getting rid of onefield of gravityThe lowest rate required to fly away from a gravitational field.
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Escape speed
The escape speed depends on the mass of the planet.If a star has a large mass, its gravity will be strong and its escape speed will be high.Conversely, a lighter planet will have a smaller escape velocity.The escape speed also depends on the distance between the object and the center of the planet.The closer the distance, the greater the escape speed.The escape speed of the earth is 11.2 km/s, and that of the sun is 617.7 km/s.If the mass and surface gravity of an object are so large that the escape speed reaches or exceeds the speed of light, the object isblack hole。The escape speed of the black hole reaches 300000 km/s.It is generally believed that the universe has no boundary. It is meaningless to say that the matter in the universe escapes to other places. Therefore, it seems meaningless to say that the escape speed of the universe[2]。
However, the universe is expanding, that is, galaxies are moving far away (away from each other), which has such a problem: if the expansion speed of the universe is large enough, galaxies will overcome the total gravity of the universe and expand forever.It's like galaxies are fleeing.Here, the expansion speed is equal to the escape speed.Of course, if the expansion speed is not large enough, the expansion will eventually stop, and the total gravity of the universe will make galaxies close to each other, just like objects flying off the earth fall back.
Therefore, to understand the escape speed of the universe in this way has become a very meaningful problem.Whether the universe will expand or shrink forever depends on the expansion speed and the total gravity.Since the expansion speed can be measured, it depends on the total gravity of the universe, which is actually how heavy the universe is.
From the general view of the physics world, the universe originates from a singularity, that is, a black hole.Black holes are connectedlight speedMoving objects cannot escape.The speed of light is the speed limit of continuous motion, and any object in continuous motion cannot exceed the speed of light.Therefore, there is no escape velocity in the universe.
Satellite launch speed
The escape speed of a star is the lowest speed to escape the gravitational binding of the star.
Having escape velocity does not mean that you can escape from the gravitational range (because the gravitational range is infinite).The escape speed is only a mathematical limit.
Escaping from the binding of gravity does not mean that the object is not subject to gravity, it only means that the object will not be able to reach farther places because of gravity.Gravity is a long-term one-way force. No matter how far away from the gravitational source, gravity will not disappear.Just because when the distance from the gravitational source is far enough, the gravitational effect becomes extremely weak and can be ignored.Therefore, gravity has no so-called scope, it is always there.
In conclusion, the calculation of escape velocity is not related to the distance from the gravitational source, but only to the mass of the gravitational source.
computing method
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An object with mass m has a velocity v, and its kinetic energy is mv ^ 2/2.At infinityGravitational potential energyIs zero (it should be that when the object is infinitely far from the earth, the gravitational potential energy of the object is zero, so this assumption is reasonable).
The potential energy of the object can be written as - GmM/r, where M isEarth mass。Let the speed of the object on the ground be V,Earth radiusR, according toconservation of energyIt can be seen that the kinetic energy of objects on the earth's surfacepotential energyThe sum is equal to the sum of kinetic energy and potential energy at r, namely
mVtwo/2+（-GMm/R）=mvtwo/2+（-GmM/r)。
When the object gets rid of the gravity of the earth, r can be regarded as infinity, and the gravitational potential energy is zero, then the above formula becomes
mVtwo/2-GmM/R=mvtwo/2.
Escape speed
Obviously, when v equals zero, the requiredDisengagement speedV minimum, that is, V=2GM/R open root,
Where g is theGravitational acceleration, the value is 9.8Newton/Kg.The radius of the earth R is about 6370 km, so the final separation speed of the earth is 11.17 km/s.
Different celestial bodies have different escape velocities, and the escape velocity formula is also applicable to other celestial bodies.
Cosmic velocity classification
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First cosmic velocity
First cosmic velocity
Human spaceflight activities are not blindly trying to escape from the earth.In particular, the current application spacecraft needs to fly around the earth, that is, let the spacecraftCircular motion。To make circular motion, there must always be a force acting on the spacecraft.Its size is equal to the operation of the spacecraftLinear velocityIs multiplied by its mass and divided by the radius of revolution, that is, F=mvtwo/R. Where vtwo/R is that the object moves in a circleCentripetal acceleration。Here, we can just use the gravity of the earth. Under the appropriate orbital radius and speed, the gravity of the earth on the object is just equal to the centripetal force of the circular motion of the object.The first cosmic speed is also calledOrbit speed。In fact, there are denseatmosphereIt is impossible for a spacecraft to move in a circle close to the earth's surface, and it must fly at an altitude of 150 kilometers to move in a circle around the earth.The orbit speed at this altitude is 7.9 km/s.
First cosmic velocity
Second cosmic speed
The second cosmic speed is also called breakaway speed,[3]It refers to the minimum initial speed required for an object to fly away from the earth completely free from the constraints of the earth's gravity.Similarly, due to the dense atmosphere on the earth's surface, it is difficult for the spacecraft to take off at such a high initial speed. In fact, the spacecraft leaves the atmosphere first, then accelerates to complete the separation (for example, first reaches the low Earth orbit, and then accelerates in that orbit).At this altitude, the disengagement speed of the spacecraft is low, about 11.2 km/s.
Third cosmic speed
Third cosmic speed
The third cosmic speed is also called escape speed,[4]It refers to the minimum initial speed required for an object launched from the earth to fly out of the solar system, which is about 16.7km/s.Originally, inEarth orbitThe initial speed required to break away from the sun's gravity is 42.1 km/s, butThe earth revolves around the sunAt that time, all objects on the ground have an initial speed of 29.8 km/s, so if they follow the direction of the earth's revolutionlaunch, just leaveGravity of the earthIn addition to the speed of 12.3 km/s, the escape speed was originally a directionless concept, but the third cosmic speed should rely on the initial speed of the earth's revolution, so the speed direction of the additional 12.3 km/s should be the same as that of the earth's revolution.
Fourth cosmic speed
The fourth cosmic speed refers to the minimum initial speed required for objects launched from the earth to get rid of the gravitational constraints of the Milky Way and fly out of the Milky Way.However, as people have not yet known the exact size and mass of the Milky Way, they can only roughly estimate its value between 110 and 120 km/s.In fact, no spacecraft can reach this speed.
The concept of cosmic velocity can also be applied to the launch of spacecraft from other celestial bodies.For example, to calculate the orbit speed and escape speed of Mars, we only need to replace M, R, g in the formula with the mass, radius, and surface gravity acceleration of Mars.
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The escape speed depends on the mass of the planet.If a star has a large mass, its gravity will be strong and its escape speed will be large.Conversely, a lighter planet will have a smaller escape velocity.The escape speed also depends on the distance between the object and the center of the planet. The closer the distance is, the greater the escape speed will be.If the mass and surface gravity of an object are so large that the escape speed reaches or exceeds the speed of light, the object is a black hole.The escape speed of the black hole reaches 300000 km/s.It is generally believed that the universe has no boundary, and it is meaningless to say that the matter in the universe escapes to other places.Therefore, it seems meaningless to discuss the escape speed of the universe.
However, the universe is expanding, that is, galaxies are moving far away (away from each other), which has such a problem: if the expansion speed of the universe is large enough, galaxies will overcome the total gravity of the universe and expand forever, which is like galaxies escaping.Here, the expansion speed is equal to the escape speed.Of course, if the expansion speed is not large enough, the expansion will eventually stop, and the total gravity of the universe will make galaxies close to each other, just like objects flying off the earth fall back.
Therefore, to understand the escape speed of the universe in this way has become a very meaningful problem.Whether the universe will expand or shrink forever depends on the expansion speed and the total gravity.Since the expansion speed can be measured, it depends on the total gravity of the universe, which is actually how heavy the universe is.
Escape speed is the minimum speed that a particle must have when it is permanently separated from the gravity of the parent body. If only the particle is separated from the gravity of the parent body after it has greater than the escape speed, this understanding is not comprehensive, and the escape speed has far-reaching significance. This paper will discuss that the escape speed is the transmission speed of the gravity of the parent body.
