Tidal force refers to the difference in the gravity of different parts of a volume object in an uneven gravitational field (for example, the gravitational field excited by a point source).Specifically, the gravitational difference between any two points on the object represents the strength of tidal force between them.[1]
Chinese name
Tidal force
Foreign name
tidal force
Noun domain
Celestial mechanics
Cause
Gravitational difference caused by different gravity of each point
Take people near black holes as an example. Black holes are special celestial bodies. For stellar black holes, they are smaller than stars of the same mass. Therefore, the change of gravity is more obvious near the surface of black holes.If a person's head is toward a black hole.Each part of the human body is attracted by the black hole. The closer the person is to the black hole, the greater the attraction. Obviously, the head is closer to the black hole, so the attraction is stronger, while the foot is weaker. Such uneven forces tend to stretch people;For the arms on both sides, although the force is the same, the direction of gravity always points to the center of mass (black hole), which tends to squeeze people on both sides.The force generated by the uneven gravitational force is tidal force, or more accurately described as the impact of tidal force.
Figure: Schematic diagram of human forces near the black hole.The length of the arrow in the figure represents the magnitude of the force. The uneven force on the head and foot makes people stretched, while the force on the arms makes people squeezed due to the direction.
A Calculation Method of Tidal Force
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Taking the earth moon system as an example, consider the tidal force of the moon on the earth.
The gravity of the Earth's center of mass on the moon is:
Where r is the distance between the earth and the moon's centroid, G is the gravitational constant,
And
Represents the mass of the moon and the earth, respectively.However, the side of the earth toward the moon is obviously closer to the moon, and the gravity is stronger, as follows:
R is the radius of the earth, while the side of the earth facing away from the moon receives less gravity, which is:
The difference between the two gravitations can reflect the magnitude of this tidal force:
This uneven gravitational action makes the side close to the moon tend to be stretched. For the earth moon system, the acceleration provided to the earth by the tidal force defined by the two points close to the moon and far from the moon is
The magnitude is far from enough to cause significant deformation of the earth structure.However, the tidal force still has a great impact on the sea water. The tidal force, together with the centrifugal force brought by the revolution of the earth and the moon, is called the tidal force, which causes the potential surface of the earth surface, such as the tidal force, to appear ellipsoidal. Under certain assumptions, this ellipsoid will also be the sea level, thus explaining the tide phenomenon[4]。
Tidal force related phenomena
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Tidal phenomenon
The term "tidal force" was first proposed to explain tidal phenomena. In 1687, Newton proposed that the gravity of the moon and the sun, as well as the revolution of the earth and the moon or the sun, caused tidal phenomena on the earth.
Taking the earth and the moon as an example, the moon and the earth are strictly rotating around each other, ignoring the rotation of the earth. At the same time, the earth is assumed to be a rigid body, so that each point on the earth will have the same size of revolution centrifugal force, the same size as the moon's gravity on the earth's center, and the direction is away from the moon;The moon's gravity on the earth is stronger on the side close to the moon and weaker on the side far from the moon.In particular, for the two points along the line between the earth and the moon, the water near the moon receives stronger lunar gravity, and then there is an acceleration toward the moon (the water rises);On the other side, on the contrary, the centrifugal force is stronger than the moon's gravity, which makes it have an acceleration far away from the moon, but also makes the sea water rise.
However, this simple discussion can only show that the sea water will rise on the earth moon line, and cannot specifically calculate the height of the tide.Others believe that when discussing tides in practice, we should also take into account the horizontal flow of seawater at other points under the action of gravity and centrifugal force, so that the seawater will converge at both ends close to the moon and far away from the moon;At the same time, the sea water is not a rigid body, which has viscosity and friction. In addition, the rotation of the earth also has an impact on the tide phenomenon.
In oceanography, the combined force of the gravitational force of the moon/sun and the centrifugal force of revolution is called the tidal force, and the work done to overcome the tidal force and the gravitational force of the earth from the center of the earth to a certain point is defined as potential, thus it can be found that on the surface of the earth, the equipotential surface of this potential energy is ellipsoidal and its major axis points to the moon.If the earth is further assumed to be a sphere and covered by water of equal depth, the water is free from viscosity and inertia, friction and geostrophic deflection, and the sea surface always coincides with the equipotential surface, the specific height of tides can be calculated according to this equipotential surface.
Figure: Schematic diagram of tide phenomenon and tide generating force: ellipsoid outline in the figure is the schematic outline of tide
Tidal locking
The tide locking of the moon shows that the revolution period of the moon is consistent with its rotation period, so the moon always faces the earth on the same side.This phenomenon can be explained by tidal force. If there is a time when the moon's revolution is inconsistent with its rotation period, it is assumed that its rotation is faster at this time. As the gravity near the earth is stronger, the moon itself, as an elastic solid, will appear a bulge of surface rock due to the pull of the earth's gravity, but the recovery of this bulge cannot occur immediately,When the moon itself turns an angle, the gravity of the earth will further pull the bulge, causing the change of the angular momentum of the moon's rotation until the moon's rotation is consistent with the revolution period - at this time, the rock bulge is always facing the earth, and the gravity of the earth cannot change the angular momentum of the moon's rotation[9]。
Mutual accretion between binary stars and Roche limit
Similarly, the influence of tidal force also exists in the binary system. When two stars are close enough, one star can take away the material of the other star through tidal force.Usually, this happens in a binary star system. A star enters the red giant stage earlier, and then its volume increases significantly. When the volume reaches a certain size, the atmosphere of the red giant will be accreted to the companion star.Detailed calculation can prove that the potential around the binary star (gravitational potential energy plus potential energy brought by revolution) is an equipotential surface of different shapes, called the Roche equipotential surface, in which the equipotential surface containing the first Lagrange point L1 is a critical equipotential surface. When the star's surface is filled with this equipotential surface, the gravity of the companion star can absorb the matter of the star through L1.
Figure: Schematic diagram of Roch equipotential surface, where L1 is the first Lagrange point, and the equipotential surface passing through L1 is the critical equipotential surface;M1 and M2 are the main star and companion star respectively
Tidal collapse event
Near the black hole, the closer to the surface of the black hole, the greater the gradient of gravitational change. For a person who is two meters tall and weighs 90 kg, at a distance of 100 km from the horizon of a stellar black hole (three solar masses), assuming that his head is facing the black hole, the gravitational difference between his head and his feet, that is, the tidal force at this time, is, such acceleration is enough to tear a person apart,However, in the same case, near one million supermassive black holes with solar mass, the tidal force felt 100 km away from the event horizon is very weak, and the magnitude of the tidal force is only
。
Tidal Disruption Event (TDE) describes a situation where when a star is captured by a black hole, when it is close enough to the black hole, the tidal force it receives is enough to tear the star apart and then be absorbed by the black hole, while the remaining debris will emit electromagnetic radiation on different wavebands, accompanied by a specific light curve.[6]
Art of Tidal Collapse Event (source NASA)
Tidal detachment
When galaxies are close enough, there is also tidal force between galaxies. In this interaction, depending on the mass of the galaxy at this time, the proportion of gas, the depth of potential well, orbital parameters and other factors, the galaxy may appear overall disturbance, leading to the formation of the bar structure of the host galaxy, the stripping of gas components, the cessation of star formation and other situations, and then the shape of the galaxy,Physical attributes such as dynamic parameters[2-3][7-8]。
Figure: NGC2207+IC2163, the two galaxies are interacting because they are close enough, including Tidal Stripping
