What exactly is Cape Town s second law

Just a moment. But are you sure there really is this 2nd law?

Kepler published two laws of planetary motion in 1609:

Kepler's First Law (Law of Orbit): Each planet orbits the Sun in an elliptical orbit, and the Sun is in a focal point of the ellipse.

Kepler's second law (area law): 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

Brief proof: with the sun as the axis of rotation, since the tangential component of gravity is 0, the moment on the planet is 0, so the angular momentum of the planet is a constant value, and the angular momentum is equal to the mass of the planet multiplied by the velocity and distance from the sun, that is, l = mvr, where m is also a constant, so vr is a constant quantity, and in a short time t, the area swept by r is approximately equal to vr t 2, that is, it is only related to time, which explains Kepler's second law.

In 1609, these two laws were published in his book New Astronomy.

In 1618, Kepler discovered a third law:

Kepler's third law (the law of periods): The ratio of the cubic of the semi-major axis of the orbit of all planets to the square of the period of revolution 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

In 1619 he published the book The Harmony of the Universe, which introduced the third law, in which he wrote:

Recognizing this truth is beyond my best expectations. The overall situation has been decided, and this book has been written, which may be read by contemporary people or for future generations. It's likely to wait a century before it has a follower, I don't care. ”

This is detailed. Kepler's First Law.

Law of Orbit): Each planet orbits the Sun in an elliptical orbit, and the Sun is in a focal point of the ellipse.

Kepler's second law.

Area Law): 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

Short proof: With the Sun as the axis of rotation, the moment on the planet is 0 since the tangential component of gravity is 0, so the angular momentum of the planet.

is a constant value, and the angular momentum is equal to the mass of the planet multiplied by the velocity and distance from the sun, i.e., l = mvr, where m is also a constant, so vr is a constant quantity, and in a short time t, r sweeps an area approximately equal to vr t 2, that is, it is only related to time, which illustrates Kepler's second law.

In 1609, these two laws were published in his book New Astronomy.

In 1618, Kepler discovered a third law:

Kepler's third law.

Law of Periods): The semi-major axis of the orbit of all the planets.

The cubic is the second of the revolution period.

are all equal.

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

where r is the semi-major axis of the planet's orbit, t is the period of the planet's revolution, and k = gm 4 2 = constant.

Kepler's second law, also known as the law of area: the area swept by the line between the sun and the moving planets is equal in equal time. This law actually reveals the conservation of angular momentum around the Sun. sek=scd=sab

Let the orbits of planet 1 and planet 2 have radii r1 and r2 respectively, and when r1 is less than r2, then there are: (1) the linear velocity of planet 1 is greater than that of planet 2; (2) the angular velocity of planet 1 is greater than that of planet 2; (3) The acceleration of planet 1 is greater than that of planet 2; 4) the orbital period of Planet 1 is smaller than that of Planet 2; 5) Planet 1 travels a greater distance than planet 2 in the same amount of time; 6) In the same amount of time, Planet 1 swept at an angle greater than Planet 2 swept by. When the planet moves in an elliptical orbit, the area swept by the polar diameter (also known as the radial r) is proportional to the elapsed time, that is, the grazing velocity is conserved, that is, the vector product is conserved, and the momentum moment (angular momentum) is conserved. If the time of each step is the same, the area swept by the radial is also equal, that is, the surface velocity does not change and the shape changes.

The velocity of the sagittal surface is conserved, and the square root of the gravitational constant of the celestial body and the radius of the smallest curvature. Celestial velocity (vs) * polar diameter (r) * sine sin ( ) = (gml0) 1 2 = constant (j0). j0 = (gml0）1/2 = l0（gm/ l0）1/2 = l0·vc = a(1-e2)·vc = r·vs·sinα= vs·r·cosβ

Definition: Johannes Kepler's original statement in The New Astronomy: In equal time, the line between the sun and the moving planets sweeps the same area.

Common expression: The line between the central object and the surrounding object (called the sagittal diameter) [5] sweeps an equal area in equal time. Namely:

where k is the Kepler constant (and different systems have different Kepler constants)[6] and r is the vector leading from the center of mass of the central body to the planet.

is the angle between the planetary velocity and the sagittal diameter r.

As shown in the figure on the right, it is expressed by the formula: sek=scd=sab.

Kepler's second law is a more accurate description of the orbits of the planets, providing strong evidence for Copernicus's heliocentric theory, and providing an argument for Newton's later proof of gravitation, along with the other two Kepler's laws, which laid the cornerstone of classical astronomy.

Kepler's second law of planetary motion, also known as the law of area, states that the lines (sagittal diameters) of the Sun and the moving planets in the solar system sweep over an equal area in equal time. 1 This law is one of three Kepler's laws discovered by German astronomer Johannes Kepler. Originally published in the New Astronomy in 1609, the book also states that this law applies equally to other celestial systems that orbit around the center.

2 Kepler's second law is a more accurate description of the orbits of the planets, providing strong evidence for Copernicus's heliocentric theory, and an argument for Newton's later proof of gravitation, which, along with the other two Kepler's laws, laid the cornerstone of classical astronomy.

The content of Kepler's second law: the planets and the sun are equal in the same amount of time.

My research found that Kepler's first law: all planets orbit the Sun in elliptical orbits, and the Sun is at one focal point of the ellipse. Not accurately, but all planets orbit around the Sun in an oval circle.

Because if the Sun is in one focal point of the ellipse, the other focal point will not have the same celestial body as the Sun there, so there is no massive object in the other focal point to exert gravitational effect on the planet, and the orbit of the planet will change to an egg garden.

If I'm right, Kepler's second law says that the area swept by the planet and the sun is equal at the same time.

Keplon is generally translated as Kepler.

Kepler's second law states that the planets and the sun are equal in the same amount of time.

From this we know that planets have the highest linear velocity at perihelion and the smallest linear velocity at aphelion.

First of all, Kepler had three astronomical laws (all for the motion of planets around the sun).

The first law of planetary motion (the law of ellipse):

The orbit of all the planets around the Sun is elliptical, and the Sun is located on a focal point of the ellipse.

The Second Law of Planetary Motion (Area Law):

The straight lines connecting the planets and the Sun sweep the same area in equal time.

The Third Law of Planetary Motion (Law of Harmony):

The square of the orbital period of the planets around the Sun is proportional to the cube of the half-major diameter of their orbits.

Newton's law of universal gravitation is a hypothesis based on the law of harmony and has been verified by scientific observations.

The content of gravitation is expressed by the formula:

f=g*m1*m2/(r*r)

Kepler's law of harmony states:

t*t (r*r*r) = constant.

If we consider two stars moving in a star, and we take a star with mass m1 as a reference frame, then we can think of a star with mass m2 moving in a circle around m1, and the gravitational force between them provides the centripetal force for their circular motion.

That is: m2*(w*w)*r=g*m1*m2 (r*r).

And W 2* can be brought into the above equation to get that t squared is more than r to the third power is customized, which is what Kepler's law explains, so that Newton's law of gravitation is proved.

In fact, scientifically speaking, this is not called proof, because Newton's laws were thought out by Newton, and then verified through a series of scientific observation data, and cannot be proved from the root, Kepler is also an experimental astronomer, he guessed his three laws through long-term observation of astronomical data, and the discovery of physics is often through conjecture.