Question

Using Newton’s formulation of Keller’s 3rd law (a^3= (m1+m2) x p^2) for any solar system planet ( except earth) discuss and demonstrate how Kepler was able to calculate a solar system planet’s orbit without mass.

Answer 1

From Kepler"s third law

where m₁ = mass of Sun and m₂ = mass of planet.

As m₂<<m₁, therefore m₂ can be ignored, therefore

As we know for earth

and  

As

Dividing (1) by (2)

we get

Putting the values of a_E and P_E, we get

(AU)----------- (3)

Therefore by putting the value of period P (in terms of earth years) of the planet around the sun, we can calculate the orbital radius of the planet in AU, using equation (3)