Two planets p1 and p2 orbit around a star s in circular orbits with speeds v1 = 40.2 km/s, and v2 = 56.0 km/s respectively. if the period of the first planet p1 is 750 years what is the mass, in kg, of the star it orbits around?

Explanation:

We are told both planets describe a circular orbit around the star S. So, let's approach this problem begining with the angular velocity of the planet P1 with a period :

(1)

Where:

is the velocity of planet P1

is the radius of the orbit of planet P1

Finding :

(2)

(3)

(4)

On the other hand, we know the gravitational force between the star S with mass and the planet P1 with mass is:

(5)

Where is the Gravitational Constant and its value is

In addition, the centripetal force exerted on the planet is:

(6)

Assuming this system is in equilibrium:

(7)

Substituting (5) and (6) in (7):

(8)

Finding :

(9)

(10)

Finally:

(11) This is the mass of the star S

can be answered using momentum.

momentum = p

p1= mass1 * velocity1

p1 = p2

therefore

p1 = 6kg * 4m/s

p1 = 24kgm/s

p2=m2 * v2

24 kgm/s = 7kg * v2

v2 = 24 kgm/s / 7kg

v2= 3.42 m/s