Question

State The Keplers law of planetory motion ? please give correct answer !!! i have foolow you!!!!​

Answer 1

Kepler's Laws Of Planetary Motion -

There are three laws , which can be stated as follows -

First Law -

The first law states that a planet's orbit is an ellipse with the Sun at a focus .

This law is also referred to as the law of ellipses .

See the first attachment .

Second Law -

The line between a planet and the sun sweeps out equal areas in the plane of the planet's orbit over equal times.

This is also referred to as the law of Harmony .

According to this law -

The area swept out in each orbit , $/ sf{ \dfrac{ dA }{ dt } }$ is constant .

The rate at which a planet sweeps out area on its orbit is equal to -

$\sf{ \dfrac{ Angular \: Momentum } { 2 \times Mass }}$

Refer to the second attachment .

Third Law -

This is also known as the laws of periods and can be stated as -

The square of the period of any planet is proportional to the cube of the semimajor axis of its orbit.

This can be written Mathematically as -

$\sf{ T ^ 2 = a ^ 3 }$

Here , T is the orbital Period and a is the mean distance from the sun .

This can be expressed in a more general form after applying the Newton's laws as -

$\sf{ T ^ 2 = \dfrac{ 4 { \pi } ^ 2 }{ G ( M_1 + M_2 ) } \times a ^ 3 }$

Where -

T is the orbital Period .

a is the mean distance from the sun .

G is the universal gravitational constant .

M1 and M2 are the masses of the two orbiting objects in terms of solar masses .

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