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The three law鈥檚 that Kepler discovereddescribed the motions of the planets accurately. These laws are for circular and elliptical orbits.

The above three laws are the law of Kepler.

Kepler鈥檚 third law states that the periods of the planets are directly proportional to thepowers of the significant axis lengths or aphelion distance of their orbits.

Kepler鈥檚 third law for the particular case of circular orbits states that the period of a satellite or planet in a circular orbit is proportional to the (3/2) power of the orbit radius r.

Newton shows that this equation is also true for an elliptical orbit, with the orbit radius r replaced by the semi-major axis a.

The period can be given as follows,

$T=\frac{2蟿蟿a^{{\displaystyle \raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}}{\sqrt{G{m}_s}}$

Elliptical orbit around the sun

$T=\frac{2蟿蟿a^{{\displaystyle \raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}}{\sqrt{G{m}_s}}$

Circular orbit around the sun

Here T is the period, G is the Gravitational constant, is the mass of the sun, rorbit radius, asemi-major axis.

If an amendment to Newton鈥檚 law of gravitation made the gravitational force inversely proportional to$r^3$ .

Then the equation can be given as,

$F_g=\frac{G{m}_{E}m}{r^3}$

Here,$F_g$ is Gravitational force, Gis Gravitational constant,$m_E$ is the mass of earth, mis mass of an object, r is the distance between planet and object.

Also, from Newton鈥檚 gravitational law,

$F_g=\frac{m{v}^2}{r}$

v is the velocity.

On equation both the above equation,

$$\begin{gathered} \frac{m{v}^2}{r}=\frac{G{m}_{E}m}{r^3} \\ v=\frac{\sqrt{G{m}_E}}{r} \\ T=\frac{2蟿蟿r}{v} \\ T=\frac{2蟿蟿r}{{\displaystyle \frac{\sqrt{G{m}_E}}{r}}} \end{gathered}$$

On solving further,

$T=\frac{2蟿蟿r^2}{\sqrt{G{m}_E}}$

By replacing the mass of the earth with the mass of the sun, the Kepler鈥檚 3^rd law will be given as,

$T=\frac{2蟿蟿r^2}{\sqrt{G{m}_s}}$

Here, T is the time period,$m_s$ is the sun鈥檚 mass.

Asthe orbital motion of planets and objects is balanced by thegravitational force,and gravitational force depends uponthis distance, any change in space will affect Kepler鈥檚 1st and 2nd laws.

The circular orbit of the earthwillbecome unstable becauseoftheunbalancedgravitational force. Thedifferent amount of area will get covered atotherperiodsbecause ofthechangeinthe acceleration rate of the plane.

Hence, due to unbalanced gravitational force, the 1st and 2nd laws will not apply to the planet鈥檚 motion.