The star Rho1 Cancri is 57 light-years from the earth and has a mass 0.85 times that of our sun. A planet has been detected in a circular orbit around Rho1 Cancri with an orbital radius equal to 0.11 times the radius of the earth’s orbit around the sun. What are (a) the orbital speed and (b) the orbital period of the planet of Rho1 Cancri?
Solution 25E Step 1 Orbital speed of earth can be calculated by equating the equations for gravitational force and centripetal force. 2 Gravitational force between earth and sun, F = GMm/g Where, G - Universal gravitational constant M - Mass of the sun m - Mass of the earth R - radius of earth’s orbit Centripetal force, F = mv /R2 c Both these forces will be equal for a revolving planet Then, mv /R = GMm/R 2 Rearranging the equation, v = GM/R2 Taking square roots on both sides, v = GM R