Q: What are some laws derived from gravitation?

To give you two sets of summaries, please choose:

1. Gravitational force.

1.Kepler's third law: t2 r3 k( 4 2 gm) {r: orbital radius, t: period, k: constant (independent of the mass of the planet, depending on the mass of the central object)}

2.The law of gravitation: f gm1m2 r2 g ?m2 kg2, the direction is on their line)

3.Gravity and acceleration due to gravity on celestial bodies: gmm R2 mg; g gm r2{r: celestial radius (m), m: celestial mass (kg)}

4.Satellite orbit velocity, angular velocity, period: v (gm r)1 2;ω＝gm/r3)1/2；t 2 (r3 gm)1 2 {m: central object mass}

5.1 (2, 3) cosmic velocity v1 (g r ) 1 2 (gm r ) 1 2 ; v2＝；

v3＝6.Geosynchronous satellites gmm (R+H)2 m4 2(R+h) t2{H 36000km, H: height above the Earth's surface, R: radius of the Earth}

Note: 1) The centripetal force required for the motion of celestial bodies is provided by gravitational force, f to f thousand;

2) the law of gravitation can be applied to estimate the mass density of celestial bodies;

3) Geosynchronous satellites can only operate over the equator, and the period of operation is the same as that of the Earth's rotation;

4) The orbital radius of the satellite becomes smaller, the potential energy becomes smaller, the kinetic energy becomes larger, the velocity becomes larger, and the period becomes smaller (together with three antis);

5) The maximum orbital velocity and the minimum launch velocity of the Earth satellite are both.

2. Gravitational force.

13 Kepler's first law states that all planets orbit around the Sun in an elliptical orbit and that the Sun is at a focal point in the elliptical orbit.

The third law states that the ratio of the quadratic half major axis to the square of the orbital period of all planets is equal, i.e.

14.A commonly used relationship between the mass of the Earth m, the radius of R, the gravitational constant of g, and the gravitational acceleration of the Earth's surface is g. (Analogies apply to other planets as well).

15.The expression for the first cosmic velocity (the orbital velocity of the near-Earth satellite) , the magnitude is , which is the minimum velocity of the launched satellite and the maximum orbital velocity of the Earth satellite. As the altitude of the satellite increases, V decreases, decreases, A decreases, and T increases.

16.The second cosmic velocity (detachment velocity), which is the minimum velocity of emission that frees an object from the gravitational constraints of the Earth.

17.The third cosmic velocity (escape velocity), which is the minimum velocity of emission that frees an object from the gravitational constraints of the Sun.

18.For a binary star in space, its orbital radius is inversely proportional to its mass, and its orbital velocity is inversely proportional to the mass of its mass.

There are so many that all the formulas of celestial motion contain this.

Write out the formula and mark the same physical quantities as equal to the ratio of the algebraic equation obtained by approximating the same term.

It depends.

For example, gm=gr 2

The derivation of the law of gravitation is based on Kepler's third law, which r3 t2=c(c is.

constant), and the derivation gives f=gmm r2, and the magnitude of the gravitational force is proportional to the product of their mass and inversely to the square of their distance.

ratio, independent of the chemical composition of the two objects and the type of medium between them.

1. Derivation of the gravitational force formula.

Kepler's third law r2 t2 = c (c is a constant).

The gravitational force f, the form is unknown, but it must be equal to the centripetal force f=mr (2 t) 2

Bring in 1 t2 = c r2

f=mr4π2* (c/r3 ) c' *m/r2

Because the symmetry of gravity f=c"*m r2

So, f=gmn r2 and g are constants.

2. The scientific significance of gravitation.

The discovery of the law of gravitation was one of the greatest achievements of natural science in the 17th century. It moves objects on the ground.

The laws and the laws of the motion of celestial bodies were unified, which had a profound impact on the development of physics and astronomy in the future.

It is the first to explain (one of the four types of interactions in nature) the laws of fundamental interactions that are recognized by human beings.

A milestone has been set in the history of nature awareness.

The law of gravitation reveals the laws of celestial motion, and has a wide range of applications in astronomy and in the calculation of astronautics.

Use. It provides a set of calculation methods for actual astronomical observations, which can be calculated from only a few observations.

The orbits of celestial bodies that orbit periodically, and the discoveries of Halley's Comets, Neptune, and Pluto in the history of science are all applied to millions.

There are examples of significant achievements made by the law of gravity. Using the gravitational formula, Kepler's third law, etc., can also be calculated.

The essence of celestial bodies such as the sun and the earth that cannot be directly measured. Newton also explained that the gravitational pull of the moon and the sun is caused.

tidal phenomena. He relied on the laws of gravitation and other laws of mechanics to flatten the earth's poles and.

The complex movement of the earth's axis has also been successfully illustrated. Overthrows the gravitational pull of the gods that ancient humans believed.

It is of great significance to the development of culture: it enables people to build confidence in the ability to understand all kinds of things in heaven and earth, and liberates.

People's thinking has played a positive role in promoting the development of science and culture.

The law of gravitation was proposed by Isaac Newton.

The Law of Gravitation:

1. The law of gravitation is the law of gravity that explains the interaction between objects. This law was published by Isaac Newton in 1687 in the Principia Mathematica of Natural Philosophy.

2. The content of the law is that any two particles are attracted to each other by the force in the direction of the concentric line. The magnitude of this gravitational force is directly proportional to the product of the masses of the two of them, inversely proportional to the square of the distance between the two of them, and has nothing to do with the chemical nature or physical state of the two objects and the intermediary matter.

3. The force of attraction between the Earth and the Sun and the gravitational pull of the Earth on surrounding objects may be the same force and follow the same law. The gravitational pull between the planet and the sun prevents the planet from flying away from the sun, and the gravitational pull between the object and the earth prevents the object from leaving the earth.

4. In the bucket infiltration at a high distance from the ground, there will be no obvious weakening of gravity, so this force must extend far away.

The reasoning basis for the law of gravitation:

1. Galileo actually put forward the initial idea of centrifugal force and centripetal force in 1632. Briard proposed the idea of the gravitational square ratio relation in 1645.

2. In his manuscript of 1665-1666, Newton proved the law of centrifugal force in his own way, but the word centripetal force may have first appeared in the first manuscript of On Motion.

3. It is generally believed that the law of centrifugal force was proposed by Huygens in his book "Pendulum Clock" published in 1673. According to the manuscript of the article "On the Motion of Rotating Objects" from August to October 1684, Newton probably proposed centripetal force and its definition for the first time in this manuscript.

4. The gravitational force is proportional to the mass product of the interacting object, which is a necessary stage for the transition from the discovery of the inverse square law of gravitation to the discovery of the law of gravitation.

5. From 1665 to 1685, it took Newton a full 20 years to follow the evolutionary sequence of the concept of centrifugal force-centripetal force-gravity-gravitational force, and finally put forward the concept and vocabulary of "gravitational force".

Isaac newton.

Newton's universal law of gravitation is stated as follows: any two particles have a force that attracts each other in the direction of their concentric line. The magnitude of this gravitational force is directly proportional to the product of their masses and inversely proportional to the square of their distance, independent of the chemical composition of the two objects and the type of medium in between.

Introduction to Newton:

Isaac Newton (January 4, 1643 – March 31, 1727), Sir Laurel, President of the Royal Society, a famous English physicist, mathematician, encyclopedic "all-rounder", author of "Mathematical Principles of Natural Philosophy" and "Optics".

In his 1687 book The Laws of Nature, he described gravitation and the three laws of motion. These descriptions laid the foundation for the scientific view of the physical world for the next three centuries and became the basis of modern engineering.

By demonstrating the consistency between Kepler's laws of planetary motion and his theory of gravity, he showed that the motion of terrestrial objects and celestial bodies follows the same laws of nature; It provided strong theoretical support for the heliocentric theory and promoted the scientific revolution.

In mechanics, Newton clarified the principle of conservation of momentum and angular momentum and proposed Newton's laws of motion. Optically, he invented the reflecting telescope and developed a theory of color based on the observation that a prism diverges white light into the visible spectrum. He also systematically formulated the law of cooling and studied the speed of sound.

In mathematics, Newton shared the honor of developing calculus with Gottfried Wilhelm Leibniz. He also proved the generalized binomial theorem, proposed the "Newtonian method" to approximate the zero point of a function, and contributed to the study of power series.

In economics, Newton proposed the gold standard.