The star Rho1Rho1 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 Rho1Rho1 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 Rho1Rho1 Cancri

8.27 * 10^4 m/s ; 14.51 days

Explanation:

Mass of star, Ms = 0.85 mass of earth

Radius of star, Rs = 0.11 radius of earth

Mass of earth = 1.99 * 10^30 kg

Radius of earth round the sun = 1.5 * 10^11 m

Ms = 0.85 * 1.99 * 10^30 = 1.6915 * 10^30 kg

Rs = 0.11 * 1.5 * 10^11 = 0.165 * 10^11 m

1.) The Orbital speed, v

V = sqrt(Gm/r) ; G = 6.67 * 10^11

V = sqrt(6.67 * 10^-11 * 1.6915 * 10^30) / 0.165 * 10^11

V = sqrt(11.282 * 10^19 / 0.165 * 10^11)

V = sqrt(68.377606 * 10^8)

V = 82690.752

V = 8.27 * 10^4 m/s

2.)

T = 2πr / v

(2π * 0.165 * 10^11) /8.27 * 10^4

1.03672 * 10^11 / 8.27 * 10^4

1253598.0 s

Converting seconds to days:

1 sec = 1/ (60 * 60 * 24) = 1/86400 days

Hence,

1253598.0 * (1/86400)

= 14.509236 days

= 14.51 days

the answer would be 32*f