Would you believe me if I said that Kepler s second law does not hold 15

Whether a law of physics holds or not depends on its application. If you use a rough calculation, the Newtonian system is sufficient, so that Kepler's second law holds, as evidenced by the large number of observations of Brother's then.

But if you look at it from the perspective of relativity, when mankind entered the twentieth century, the accuracy of observation also improved, and anomalies in the distribution of angular momentum in the solar system were discovered, it seems that Kepler's second law is not true. But people belong to the product of Newton's system, which is an approximation at a certain precision. The anomaly of the angular momentum distribution of the solar system is a more accurate observation than Newton's system, and it has to be considered from the perspective of relativity, and of course it will not work with Kepler's second law of Newton's system, which is like you specified pi five hundred years ago, and now you suddenly find that how to calculate it a little more?

You just say that the rules were wrong. In fact, everyone is right, the scope of application and accuracy are different. From this point of view, Kepler's second law is wrong, but don't deny the great contribution of others, after all, this law has unveiled the mystery of the universe for us in history, and we must not forget it and its discoverer.

Some theories, especially those in physics, tend to give people the illusion that they are wrong because they ignore small things. This is very normal, and Einstein made such mistakes. I think that everyone studying physics is for the happiness of mankind, since it is for the public, we should popularize some theories, so that everyone can put forward their own opinions, so that human beings will make faster progress!!

I also said that the theory of relativity is false.

Do you believe it?

1. Kepler's first law (orbital law): Each planet orbits the Sun in an elliptical orbit, and the Sun is in a focal point of the ellipse.

2. Kepler's second law (area law) Lazhou: A straight line from the sun to the planets sweeps the same area in equal time.

It is expressed by the formula: sab=scd=sek

3. Kepler's third law (periodic law): The ratio of the cubic of the semi-major axis of the orbit of all planets to the second quadratic of the orbital period is equal.

It is expressed by the formula: a 3 t 2 = k

a = semi-major axis of the planet's orbit.

t = period of planetary revolution.

k=constant =gm 4 2

Since gravitational forces act as a centripetal force, the conservation of angular momentum is given by the fluid or law (m is the mass of the planet, r is the distance from the planet to the sun, is the angle between the velocity of the planet and the line between the planet and the sun): l m(r 2)w const, solve r , get, r 2 l (mw).

At the same time, in the form of polar coordinates of the difference shirt, the area element is: ds (1 2)(r 2)d, and substituting the obtained r above can obtain: ds l (2mw)d.

w d dt, i.e.: ds l (2m)dt. Got Kepler's second law.

Kepler's first law, also known as the elliptic law, the law of orbit: each planet orbits the Sun in its own elliptical orbit, and the Sun is in a tung oak focal point of the ellipse.

Kepler's statement in The Harmony of the Universe states that each planet orbits the Sun in its own elliptical orbit, and the Sun is in a focal point of the ellipse.

Kepler's first law was proposed by the German astronomer Johannes Kepler, who published two laws on planetary motion in his scientific journal New Astronomy in 1609, and in 1618, discovered the third law. Before this law was disturbed by the imaginary chakra, it was believed that the orbits of celestial bodies were "perfectly circular".

In astronomy and physics, Kepler's laws posed great challenges to the Aristotelians and Ptolemaics. Kepler asserted that the earth is constantly moving; The orbits of the planets are not circular, but elliptical; The speed at which the stars rotate is unequal. These arguments greatly shook the astronomy and physics of the time.

After almost a century of research, physicists have finally been able to explain principles using physical theories. Newton applied his second law and the law of universal gravitation to mathematically rigorously prove Kepler's law and give an understanding of its physical significance. Thus, Kepler's three laws of planetary motion changed the entire astronomy, completely destroyed Ptolemy's complex cosmic system, perfected and simplified Copernicus's heliocentric theory, and he became a key figure in the scientific revolution of the seventeenth century.

Kepler's first law is that the orbit of the planets around the Sun is elliptical, and the Sun is located at a focal point of this elliptical orbit.

What was the trajectory of the planets like before Kepler? At the time when geocentrism was popular, we all now know that geocentrism itself is wrong, and the earth is not the center of the universe.

If we want to verify that the trajectory of the planet is an ellipse, then we need to find the equation of the trajectory, that is, the orbit equation, and compare it with the equation of the ellipse to determine whether it is consistent. But to know the equation of the ellipse, which coordinate system is more appropriate? Considering that the ellipse is a regular closed curve, it is more appropriate to use a polar coordinate system.

Data: twice grazing velocity (j0), twice elliptic area (2 ab), elliptical periodic law (t), polar diameter (r), deflection velocity (vs), deflection momentum (mvs), angle between velocity direction and polar diameter ( ), spherical velocity (vd), polar angular velocity (r), arc height (rl), minimum radius of curvature (l0), velocity coefficient (vc), celestial gravitational constant (gm).

Kepler's second law formula for conservation of grazing velocity:

j0 = (gml0）1/2 = l0（gm/ l0）1/2 = l0·vc = a(1-e²)·vc = r·vs·sinα= vs·r·cosβ。

This is the general sagittal velocity conservation formula for the deflection motion of celestial bodies: polar diameter * celestial velocity * sine of the two sagittal angles.

Kepler's second law is formulated in several ways:

Expression 1: Twice the grazing velocity (j0) = twice the ellipse area (2 ab) elliptic period (t).

j0 = 2πab/t = 2(πab/n)/(t/n) = 2da/dt

Expression 2: The product of the three variables of the polar diameter (r) * celestial velocity (vs) * the sine sin( ) of the angle between the two vectors is invariant.

j0 = vs·r·sinα= vs·r·cosβ

Expression 3: Celestial velocity (vs) * arc height (rl) The product of the two variables is invariant.

j0 = vs·（rcosβ）= vs·rl

Expression 4: The product of the two variables of polar diameter (r) * spherical velocity (vd) is invariant.

j0 =r·（vs cosβ）= r·vd = r·dd/dt

Expression 5: The product of the square of the polar diameter (r) * the angular velocity of the polar diameter (r) is invariant.

j0 = r·vd = r（rωr） = r²·ωr

Expression 6: Minimum radius of curvature (L0) * velocity coefficient (vc).

j0 = r·vd=（l0/k0）·（vc k0）= l0·vc = l0（gm/ l0）1/2

Formulation 7: The square root of the product of the gravitational constant (gm) of the celestial body and the minimum radius of curvature (l0).

j0 = l0·vc = l0·（gm/ l0）1/2 = （gm·l0）1/2

Special: Perihelion velocity is maximum: vm = j0 rn = j0 a(1-e) = a(1-e)(1+e)·vc a(1-e) = vc(1+e).

The velocity of the object at aphelion is minimal: vn = j0 rm = j0 a(1+e) = a(1-e)(1+e)·vc a(1+e) = vc(1-e).

Kepler's second law (also known as the law of area) reads as follows: For each planet, the line between the sun (star) and the planet sweeps the same area in equal time. As we all know, the graph swept by the line is an irregular curved triangle, for which its area seems to be found only by integrals, but Kepler lived before the founder of calculus--- Newton and Leibniz lived, so how did he discover and prove this strange but wonderful law of area?

In order to think about this problem, I also tried to prove, at first I used the kinetic energy theorem, the equation can be listed, but I can't determine the relationship between speed and time, and then I tried the momentum theorem, but the gravitational pull of the sun on the planets is a variable force, which is not suitable for the calculation of impulse.

About the night before yesterday, I looked up the information and learned that the "law of conservation of angular momentum" can deduce the second law. This afternoon, I went to Xinhua Bookstore and opened a college physics textbook, which explained in detail the concepts of angular momentum and moment.

As shown in Figure 1, the particle P rotates around the O point (P may have both circular motion and irregular centripetal motion), and its distance from the center point O is r, and the definition of angular momentum is the product of the distance from the rotating mass point to the center point and its momentum, so the angular momentum is a vector quantity, which is expressed by the formula: L=MVR. (where m is the mass around the rotating particle, v is the linear velocity around the rotating particle, r is the distance from the rotating particle, and the equation is the vector multiplication).

When I was in junior high school, I was exposed to the concept of moments. As shown in Figure 2, the force around the particle p is f, then the moment is equal to the product of the external force experienced by the particle p and the distance perpendicular to it to the center point. It is expressed by the formula as:

m=fr (vector multiplication, m is the moment, f is the resultant force around the rotating particle, r is the distance perpendicular to the rotating mass point to the center point), and the magnitude of the moment is expressed as m=frsina. If f is collinear with r, then the moment m is 0

An extremely important conclusion will be drawn below. Derivative: dl dt=d(mvr) dt=dr· (mv) dt+r·d(mv) dt。

This step is copied from the textbook, and I don't know the specific algorithm), and finally calculates m=dl dt.

As shown in Figure 3, in the elliptical orbit, the force on planet E is f, pointing to the star S, then f is collinear with r, so the moment of planet E is 0, then the rate of change of its angular momentum is 0, so the angular momentum of the planet at any point in its elliptical orbit has never changed. The unit of angular momentum is kg·m 2 s, which can be indirectly understood as the reciprocal of angular momentum equal to mass multiplied by area and then multiplied by time. So the area must be the same in the same time interval.