Any two particles are attracted to each other by the force in the direction of the line. The magnitude of gravity is directly proportional to their mass product and inversely proportional to the square of their distance, and has nothing to do with the chemical properties or physical states of two objects and intermediate substances.
The law of universal gravitation is the law of gravitation that explains the interaction between objects. It is the law of mutual attraction between objects (particles) because of their gravitational mass.
It was published by Newton in "Mathematical Principles of Natural Philosophy" in 1687 on the basis of predecessors' research (Kepler, Hooke, Rehn, Halley) and with his extraordinary mathematical ability.
In high school, the idea of simplification was mainly used to simplify the orbit of the planet from ellipse to proof under circle.
Specific proof can refer to p36-37, a textbook for senior one.
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Any two objects in nature are attracted to each other, and gravity is directly proportional to the product of the mass of the two objects and inversely proportional to the square of the distance between the two objects.
The formula shows that:
f = g * m 1 m2/(r * r)(g=6.67× 10^- 1 1n？ M 2/kg 2) can be read as f equals g times M 1M2 divided by the square quotient of R.
The attraction between two objects.
G: constant of universal gravitation
M 1: the mass of the object 1.
M2: mass of object 2
R: the distance between two objects
According to the international system of units, the unit of f is Newton (n), the unit of m 1 and m2 is kilogram (kg), the unit of r is meter (m), and the constant g is about 6.67 × 10? 1 1n·m2·kg？ 2 (square of Newton meters per kilogram).
It can be seen that the repulsive force F will never exist, that is to say, the force of net acceleration is absolute. This symbolic agreement is to be compatible with Coulomb's law, in which absolute force represents repulsive force between two electrons. )
Meaning:
The discovery of the law of universal gravitation is one of the greatest achievements of natural science in the17th century. It unifies the laws of motion of ground objects and celestial bodies, and has a far-reaching impact on the future development of physics and astronomy. A basic law of interaction (one of the four major interactions in nature) was explained for the first time, which set a milestone in the history of human understanding of nature.
The law of universal gravitation reveals the laws of celestial motion and is widely used in astronomy and space navigation calculation. It provides a set of calculation methods for practical astronomical observation. With only a small amount of observation data, we can calculate the orbit of celestial bodies for a long time. The discovery of Halley's comet, Neptune and Pluto in the history of science are all examples of great achievements made by applying the law of universal gravitation. Using the formula of universal gravitation and Kepler's third law, we can also calculate the mass of celestial bodies that cannot be directly measured, such as the sun and the earth. Newton also explained the tidal phenomena caused by the gravity of the moon and the sun. According to the law of gravity and other mechanical laws, he also successfully explained the reasons for the flat shape of the earth's poles and the complex motion of the earth's axis.
Gravity acceleration:
Let a 1 be the gravitational acceleration of the particle known in advance. According to Newton's second law. Replace the f in the previous equation.
A2 can be obtained in the same way.
According to the international system of units, the unit of gravity acceleration (like other general accelerations) is defined as meters per square second (m/s2 or m s? 2)。 Non-international system of units includes Galileo, unit G (see below) and square feet per second.
Please note that the acceleration of a 1 and mass m 1 in the above formula does not actually depend on the value of m 1. Therefore, it can be inferred that any object, regardless of its mass, will fall to the ground at the same speed (ignoring air resistance).
If there is only a slight change in R during the movement of an object, such as a free fall near the ground, the acceleration of gravity is almost constant (see the entry gravity). For a huge object, the change of gravity at different points caused by the change of R will cause huge and considerable tidal force effect.
Objects with spatial width:
If the objects in question have a spatial width (much larger than the theoretical particles), then the gravitational force between them can be calculated by the sum of the gravitational forces of each equivalent particle of the object. On the limit, when the constituent particles are close to "infinitesimal", it is necessary to integrate the force between two objects in space (see below for vector formula).
From this, it can be concluded that if the mass distribution of an object is uniform and spherical, then its attraction to external objects is the same as when all the mass is concentrated in the geometric center of the object. (This does not apply to aspheric symmetric objects).
Vector type:
Schematic diagram of gravity in the space near the earth: At this order of magnitude, the curvature of the earth's surface can be ignored, so the magnetic lines of force can be approximately parallel to each other and point to the center of the earth. Newton's law of universal gravitation can also be expressed in the form of vector equation to calculate the direction and magnitude of universal gravitation. In the following formula, the quantities shown in bold represent vectors.
These include:
F 12: the attraction of object 1 to object 2.
G: constant of universal gravitation
M 1 and m2: the mass of object 1 and object 2, respectively.
r2 1 = | r2？ R 1 |: the distance between object 2 and object 1.
Unit vector from object 1 to object 2
It can be seen that the form of the vector equation is similar to the scalar equation given before. The only difference is that F in the vector equation is a vector, and the right end of the vector equation is multiplied by the corresponding unit vector. Moreover, we can see: F 12 =? F2 1。
Similarly, the vector equation of gravity acceleration is similar to its scalar equation:
Gravity field:
The globular cluster M 13 proves the existence of gravity field. Gravity field is a vector field, which is used to describe the gravity per unit mass of an object at a certain point in any space. In fact, it is equal to the gravitational acceleration of the object at this point.
The following is a universal vector formula, which can be applied to the calculation of more than two objects (such as rockets going back and forth between the earth and the moon). For the case of two objects (for example, object 1 is a rocket and object 2 is the earth), we can replace the gravitational field with m, which is expressed as:
So we can get:
This formula is not limited by the object that produces the gravitational field. The unit of gravity field is the unit of force divided by mass; In the international system of units, it is stipulated as N kg? 1 (Newton per kilogram).
Problems in Newton's theory;
Although Newton's description of gravity is very accurate for many practical applications, it also has several theoretical problems, which have been proved to be incomplete.
Theoretical questions:
There is no indication that the propagation medium of gravity can be identified, and Newton himself is not satisfied with this unexplained action at a distance (see the latter "Limitations of Newton's Law").
Newton's theory needs to define that gravity can travel instantaneously. Therefore, the hypothesis of classical natural space-time view is given, which can also make the conservation of angular momentum observed by johannes kepler hold. However, this directly conflicts with Einstein's special theory of relativity, because the special theory of relativity defines the limit of speed-the speed of light in a vacuum-the speed at which signals can be transmitted.
Inconsistency of observation results:
Newton's theory can't fully explain the precession phenomenon when Mercury orbits to perihelion. Compared with the precession actually observed, Newton's theoretical prediction has an error of 43 arcsec/century.
Newton's theory predicts that the deflection of light under the action of gravity is only half of the actual observation results. General relativity regards it as a basic condition. See the principle of project equivalence.
Limitations of Newton's law:
When Newton's extraordinary work enabled the law of universal gravitation to be expressed in a mathematical formula, he was still dissatisfied with the idea of "action at a distance" implied in the formula. He never "gives the reason for this ability" in his writing. In other cases, he used the phenomenon of motion to explain why objects were acted by different forces, but for gravity, he could not prove that motion produced gravity by experiments. In addition, he even refused to put forward a hypothesis about the cause of the ground force, which violated the principle of scientific evidence.
Newton's discovery of gravity buried the truth that "philosophers have tried to explore nature", just as he thought that "there are various factors" made "various hitherto unknown reasons" the basis of all "natural phenomena". These basic phenomena are still under study. Although there are many hypotheses, the final answer has not been found. Although Einstein's hypothesis really explained the role of gravity in deciding a case more accurately than Newton's hypothesis, he never gave the reason for this ability in theory. In Einstein's equation, "matter tells space how to bend and space tells matter how to move" (and space tells matter how to move), but this new view, which is completely different from Newton's world, cannot make Einstein's "cause of this ability" more distort space than Newton's law of universal gravitation. Newton himself said:
I haven't been able to find out the reasons for these gravity characteristics from the phenomenon, and I can't guess ... The laws I explained and the rich calculation of celestial motion are enough to show that gravity does exist and can produce effects. It is a big fallacy for me that one object can act on another without any medium passing through the real space, and on top of that, their activities and forces can be transmitted to each other. So I believe that anyone with enough philosophical thinking ability will not be addicted to this.
If science can finally discover the cause of gravity, Newton's hope will finally come true.
Equator:
The equator is the longest circumferential line in the trajectory of each point on the earth's surface with the rotation of the earth, and the equatorial radius is 6378+037km；; The radius of the pole is 6359.752Km；; The average radius is 6371.012 km; The equatorial circumference is 40075.7Km. If the earth is regarded as an absolute sphere, the equator is equal to the north and south poles, which is a great circle. It divides the earth into two hemispheres, the northern hemisphere in the north and the southern hemisphere in the south. This is the baseline for dividing latitude, and the latitude of the equator is 0. The equator is the place with the least gravity on the earth.
The equator is the starting point of the north-south latitude (zero latitude) and the longest latitude on the earth.
Equatorial organism
The equator is the factory of species. Compared with other species less fortunate to enjoy this geographical advantage, equatorial animals live in an almost perfect environment, whether it is temperature, humidity or available food. The only disadvantage of living in this paradise is to share resources with more than half of the species on earth!
At the equator, animals and plants grow faster, bigger and weirder than anywhere else. Sunlight in the equatorial region is the most powerful energy on earth. Because the sunlight here evaporates a lot of oceans, this effect will form a humidity column in such a large area, then form wind and undercurrent, and finally provide energy for life in extremely distant places.