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

a) 8.27 ×10^4m/s = Orbital speed

b) The period,T = 1.25×10^6 seconds

Explanation:

b) The orbital period T is given by :

T =( 2pi × r ^(3/2))/(SqrtGM)

Where G = gravitational constant = 6.67×10^-11

M = mass = 1.99×10^30kg

Substituting into the equation

T =( 2 ×3.142(0.11×1.5×10^11)^3/2) / (Sqrt(6.67×10^-11)×(0.85)×(1.99×10^30)

T = 1.25 ×10^6 seconds

a) The orbital speed can be determined using the equation:

T = (2pi ×r)/v

Rearranging the equation, we get:

v = (2 pi × r)/T

Substituting the values

v = [2 ×3.142)(0.11) × (1.5×10^-11)] / (1.25×10^6)

v = 8.27 × 10^4m/s