Two newly discovered planets follow circular orbits around a star in a distant p

Question

Two newly discovered planets follow circular orbits around a star in a distant part of the galaxy. The orbital speeds of the planets are determined to be 43.5 km/s and 56.0 km/s. The slower planet's orbital period is 7.50 years.

(a) What is the mass of the star in kg?

Two newly discovered planets follow circular orbits around a star in a distant part of the galaxy. The orbital speeds of the planets are determined to be 43.5 km/s and 56.0 km/s. The slower planet's orbital period is 7.50 years. (a) What is the mass of the star? x kg (b) What is the orbital period of the faster planet, in years?

Explanation / Answer

For planet one is moving with a velocity is =43.5km/s =43.5*1000m/s

The second planet is moving with a velcoty =56.0km/s

Given that time T =7.50yrs =7.50*365*24*3600 =236520000s

G =6.67*10-11N.m2/kg2

Now we know that

GMm/r2 =mv2/r

GM/r2 =v2/r

Then M =v2*r/G

But we know tha v =2pir/T

then r =Tv/2pi

Fiinally for M =v3*T/2piG =(43.5*103)3*236520000/2*3.14*6.67*10-11 =4.647*1031kg

B)

The orbital velocity of the faster planet is given by

v=rw =w*GM/v2 =2pi/T*GM/vf2

Substitute all the above values to get the required answer

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