High school gravitational inference, derivation of gravitation

f=gmm/r^2

Proportional is a mathematical term that satisfies the relationship between variables of the f(x)=kx function. g is a constant, when m,r is constant, f=gmm r 2=k*m, indicating that gravitational force is proportional to the mass of the planet; Similarly, when m,r is constant, the gravitational force is proportional to the mass of the star to which m is directed; Then, it is not difficult to get that when r is constant, f=gmm r 2=k*mm, i.e., the gravitational force is proportional to the product of the mass of the two stars.

The derivation of the law of gravitation in high school treats the motion of celestial bodies as a simple derivation of circular motion.

It is based on Kepler's three laws as well as Newton's third law.

The details are as follows; f lead = f direction = mw2r mv2 r is then obtained from the linear velocity as a relation to the period.

F citation = m(2 r t)2 r = 4 2mr t2f citation = 4 2mr t2= 4 2(r3 t2) m r2f citation = 4 2km r2

So it can be concluded that the gravitational pull of the Sun on the planet is directly proportional to the mass of the planet and inversely proportional to the power of the distance from the planet to the Sun. i.e.: f m r2

Newton's bold conjecture based on Newton's third law is that since the gravitational pull of the sun on the planets is proportional to the mass of the planet, it should also be proportional to the mass of the sun.

F-quote mm r2, written as the equation: f-quote = gmm r2

The law of gravitation was published by Isaac Newton in 1687 in the Mathematical Principles of Natural Philosophy. Newton's universal law of gravitation is expressed as follows:

Any two particles are attracted to each other by a force in the direction of the 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.

Newton's conjecture.

The force of attraction between the Earth and the Sun and the gravitational pull of the Earth on the surrounding objects may be the same force and follow the same laws.

The basis for conjecture.

1) The gravitational force between the planet and the sun prevents the planet from flying away from the sun, and the gravitational force between the object and the earth prevents the object from leaving the earth; (2) At a very high distance from the ground, no significant weakening of gravity will be found, so this force must extend far away.

The results of the inspection.

The gravitational pull of the Earth on a ground object is the same force as the gravitational pull of the Earth on the Moon.

Derivation of gravitation: If the orbit of the planet is approximately circular, the angular velocity of the planet's motion can be determined from Kepler's second law, i.e.,

2 t (cycle).

If the mass of the planet is m, the distance from the Sun is r, and the period is t, then the magnitude of the force on the planet is .

mrω^2=mr（4π^2）/t^2

In addition, it can be obtained from Kepler's third law.

r3 t 2 = constant k'

Then the force along the direction of the sun is.

mr（4π^2）/t^2=mk'（4π^2）/r^2

From the relationship between the action and reaction forces, it can be seen that the sun is also subjected to the same magnitude of the above-mentioned forces. From the Sun's point of view, the Sun's mass m)(k''）4π^2）/r^2

It is the sun that is forced to clear the front by the force that balances in the direction of the planets. Since they are forces of the same magnitude, it can be seen from the comparison of these two equations that k'contains the mass of the Sun m,k''contains the mass m of the planet. From this, it can be seen that these two forces are proportional to the product of the masses of the two celestial bodies, which is called gravitational force.

If a new constant (called the gravitation constant) is introduced, and the masses of the Sun and the planets are considered, as well as the previously derived 4· 2, then it can be expressed as.

Gravitational force = gmm r 2

The law of gravitation: any two objects in nature are attracted to each other, and the magnitude of the gravitational force is directly proportional to the product of the masses of the two objects and inversely proportional to the square of the distance between the two objects.

The formula indicates: f=g*m1m2 (r*r).

g=f: The gravitational force between two objects.

g: gravitational constant.

m1: The mass of object 1.

m2: The mass of object 2.

r: The distance between two objects.

According to the International System of Units, f is measured in Newtons (n), m1 and m2 are measured in kilograms (kg), r is measured in meters (m), and the constant g is approximately equal to the power n·m2 -2 (the square of Newton-meters per kilogram squared).

Hello, :

From Newton's second law, it follows:

f magmm r mv r (gravitational force provides centripetal force) v (gm r).

By v r, substituting the formula, get:

gmm/r²＝mω²r ②

＝√gm/r³)

By 2 t, substituting the formula, get:

gmm/r²＝m(4π²/t²)r

t＝√(4π²r³/gm)

One is the force experienced by the object (celestial body), and the other is the centripetal force required for the uniform circular motion of the celestial body, and the gravitational force provides the centripetal force required for the circular motion of the celestial body.

First, Newton's second law f=ma, f=gmm (r 2)=m (v 2) r, where the acceleration a is in square brackets, the second substituting v=wr can be obtained, and the third generation w=(2) t.

Conclusion: v 2 = gm r; w^2=gm/（r^3）；t 2= 4(丌 2)(r 3) gm!

Note: "Denotes the power, followed by a number to the power of several times. "W" for angular velocity and "丌" for pi!

(1)gmm/r²=v²m/r

gm r=v

i.e. v=(gm r) (sorry, the root number won't be played) (2)gmm r =m r

Get =(gm r )

3）gmm/r²=4π²/t²mr

gm 4 r =t

i.e. t=(gm4r).

Kepler's third law: t 2 a 3 = 4*pi 2 (g*m). pi, pi; t 2, the quadratic of t.

It can be assumed that the smaller the orbital radius, the shorter the period. Therefore, when the artificial circumlunar satellite is close to the surface of the moon, the period is the shortest.

So t2r3=4*pi2(g*m).

And g*m*m r 2=m*g.

So t 2 r 3 = 4 * pi 2 (g*r 2), i.e. t 2 = 4 * pi 2 * r g.

Substituting the data yields t t=, which is about 1 hour and 43 minutes. This is the minimum period around the moon.

According to: g*m-month*m-r2 = m*g-month.

g*m-month = g-month*r2 (1).

Again: g*m-month*m-r 2 =m*(2 t) 2*rg*m-month = (2 t) 2*r 3 (2) joint solution (1)(2).

gmonth*r2 =(2 t) 2*r3

t= (4 2r g) substitute g= r=

4000 s >3600s

The minimum period of the spacecraft around the moon is 4000 s, and there is no artificial spacecraft around the moon, so the news is fake news.