Question

You discover a planet orbiting a distant star that has about the same mass as the sun, with an orbital period of 53 days. What is the planet’s orbital distance?.

Answer 1

Answer:

G M1 m1 / R1^2 = G M2 m2 / R2^2          gravitational equation

We can try Kepler's harmonic law

P2^2 = K R2^3

P1^2 = K R1^3     for earth

(P2 / P1)^2 = (R2 / R1)^3       dividing equations

R2^3 = (P2 / P1)^2 * R1^3

R2^3 = (53 / 365)^2 * R1^3

R2^3 = .145 R1^3

R2 = .526 R1

If one uses 93E6 miles as distance of sun from earth then

R2 = 49E6 miles