Question

What is keepers law? Explain in your won words.

​

Answer 1

$\mathcal{KEPLER'S\:\:LAWS}$

The motion of natural satellites and planets can be studied with the help of Kepler's Laws, as stated in the following:

Law of orbit: Each planet moves around the Sun in an elliptical orbit with the Sun at one of the foci(fig.1). The eccentricity of an ellipse is defined as the ratio of the distance SO and AO, i.e., e=SO/AO.

$\sf{\therefore\:e=\dfrac{SO}{a}}$

$\sf{SO=ae}$

The distance of closest approach with Sun at $\sf{F_1}$ is AS. This distance is called perigee. The greatest distance (BS) of the planet from the Sun is called apogee.

Perigee (AS) = AO-OS = a-ae = a(1-e)

Apogee (BS) = OB+OS = a+ae = a(1+e)

Law of areas: The line joining the Sun and a planet sweeps out equal areas in equal intervals of time. A planet takes same time to travel from A to B as from C to D (fig.2 shaded region). Naturally, the planet has to move faster from C to D. In other words, areal velocity of a planet is constant at dA/dt = constant. The law of areas is identical with the law of conservation of angular momentum.

$\sf{Areal\:velocity=\dfrac{Area\:swept}{Time}}$

$\sf{\dfrac{\dfrac{r\left(rd\theta\right)}{2}}{dt}}$

$\sf{=\dfrac{1}{2}r^2\dfrac{d\theta}{dt}=constant}$

Hence, $\sf{\dfrac{1}{2}r^2\omega=constant}$

$\sf{mr^2\omega=constant}$

$\sf{where\:mr^2=MI\:of\:planet\:rel.\:to\:Sun=I}$

$\sf{I\omega=constant\:or\:\vec{L}=constant}$

Law of periods: The square of the time for a planet to complete a revolution about the Sun is proportional to the cube of semimajor axis of the elliptical orbit.

$\sf{T^2\:\propto\:a^3.....(1)}$

where T = Time period of revolution of the planet, a = semimajor axis of the ellipse. The orbits of all the planets except Mercury and Pluto are very close to being circular since the semi-major axis becomes the radius of circle. Hence, Eq. (1) can be written as

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

Answer 2

Answer:

Kepler’s laws describes the laws of planetary motion. Kepler's laws consist of three laws explaining the motions of the planets in the solar system. These laws were derived by the German astronomer Johannes Kepler.

Kepler’s three laws of planetary motion can be stated as follows: (1) All planets move around the Sun in elliptical orbits, with the Sun as one focus of the ellipse. (2) Kepler's second law describes the speed of a planet traveling in an elliptical orbit around the sun. It states that a line between the sun and the planet sweeps equal areas in equal times. Thus, the speed of the planet increases as it nears the sun and decreases as it recedes from the sun. (3) Third Law states that the ratio of the square of the period of revolution and the cube of the ellipse semimajor axis is the same for all planets.