Question

medal!!!
can someone explain about kepler's 3rd law..

Answer 1

The formula for the law is as follows:\[\frac{ T ^{2} }{ r ^{3} }=\frac{ 4 \pi ^{2} }{ GM }\]where T is the orbital period; r is the mean orbital radius; G is the gravitational constant; and M is the mass of the star being orbited.

The beauty of this law is this: if you know the period and orbital radius for one planet in a solar system; you can use that info to find either the radius or the period of another planet in the same solar system.\[\frac{ T _{1}^{2} }{ r _{1}^{3} }=\frac{ T _{2}^{2} }{ r _{2}^{3} }\]where T1 is the period of planet one; r1 is the mean orbital radius of planet 1; T2 is the period of planet 2; and r2 is the mean orbital radius for planet 2. This is because for any planet in a solar system:\[\frac{ 4\pi ^{2} }{ GM }=constant\]This also applies to moons orbiting a planet. In that case, M is the mass of the planet.

Answer 2

Note that this equation can even be used to calculate the period or radius of satellites orbiting Earth.