*39.  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 43.3 km/s and 58.6 km/s. The slower planet’s orbital period is 7.60 years. (a) What is the mass of the star? (b) What is the orbital period of the faster planet, in years?

 

Solving for

We also know the circular speed

So squaring that

Equating the two  relationships

 

Rearranging produces Kepler’s third law

 

Solve for Mass of star

Since we are given the velocity and not the radius, solve for R in terms of speed

 

Plug this into the Mass of Star equation

 

 

So the mass can be found from

 

 

 

To find the period of the other planet, lets consider

 

This reduces to

Solving for the unknown period

 

 

 

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This page last updated on January 11, 2020