Question

What is the mass of the star?You are the science officer on a visit to a distant solar system. Prior to landing on a planet you measure its diameter to be 1.8×107m and its rotation period to be 22.3 hours . You have previously determined that the planet orbits 2.2×1011m from its star with a period of 422 earth days. Once on the surface you find that the free-fall acceleration is 12.2m/s2.

Answer 1

M=4.736×10³⁰kg

Step-by-step explanation:

Given Data

Diameter of planet= 1.86×10⁷m

Radius R=Diameter/2=1.86×10⁷/2⇒0.93×10⁷m

Period of rotation of planet t=22.3 hr⇒80280 seconds

Period of revolution around star T=422 earth days⇒3.646×10⁷ seconds

Radius of orbit r=2.2×10¹¹m

Acceleration of gravity on surface of planet g=12.2 m/s²

To Find

Mass of star

Solution

To find mass of star.For that we will consider the revolution of planet around the star with given period

`T^(2)=(4\pi ^(2)r^(3)  )/(GM)\\  M=(4\pi ^(2)r^(3)  )/(GT^(2))\\M=(4\pi ^(2)(2.2*10^(11) )^(3)  )/((6.67*10^(-11) )(3.646*10^(7) )^(2))\\M=4.736*10^(30) kg`