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 m_{1} = mass of Sun and m_{2} = mass of
planet.

As m_{2}<<m_{1}, therefore m_{2}
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)

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