7.1 Kepler's first law

  Gravitation

This law is also known as the law of orbits.

Every planet revolves around the sun in an elliptical orbit. The sun is situated at one focus of the ellipse.

This law of orbits can be better explained by the total energy of the system.

As we know the bound system (i.e. planet and the sun) the total energy is negative. So, the orbit is elliptical.

Elliptical orbit of planet-sun system

where,

$a:$ Length of major axis
$b:$ Length of minor axis
$e:$ Eccentricity of ellipse (i.e. $e<1$)
$S:$ Focus of an ellipse (position of sun)
$P:$ Perigee
$A:$ Apogee

Perigee: It is also known as perihelion. It is the nearest position of a planet from the sun while orbiting around sun in an elliptical orbit.

It is denoted by $P$.
The speed of the planet is maximum $\left( {{v_{\max }}} \right)$.
Distance $PS$ is minimum $\left( {{r_{\min }}} \right)$.

Apogee: It is also known as aphelion. It is the farthest position of a planet from the sun while orbiting around sun in an elliptical orbit.

It is denoted by $A$.
The speed of the planet is minimum $\left( {{v_{\min }}} \right)$.
Distance $AS$ is maximum $\left( {{r_{\max }}} \right)$.