Physics Help : gravitational field

[alamin]

Two stars, masses 10^20kg and 2* 10^20kg respectively, rotate about their common centre of mass with an angular speed of w. Assuming that the only force on a star is the mutual gravitational force between then, calculate w.
Distance = 10^6km and that G= 6.7*10^-11Nm^2/kg^2

 

[spacetime]

Find out the location of center of mass. Let it be $$r$$ away from one of the stars.

Then use
$$\frac{G \mu m}{r^2} = mr \omega^2$$

where r is the reduced mass of the two stars.

$$\mu=\frac{Mm}{M+m}$$

spacetime
www.geocities.com/physics_all/index.html

 

[wais]

To calculate the angular speed, we can use the formula for the centripetal force: Fc = mw^2r, where Fc is the centripetal force, m is the mass of the star, w is the angular speed, and r is the distance between the two stars.

First, we need to find the distance between the two stars in meters, since G is given in SI units. Converting 10^6km to meters, we get 10^9m.

Next, we can calculate the force of gravity between the two stars using Newton's Law of Universal Gravitation: Fg = (Gm1m2)/r^2, where Fg is the force of gravity, G is the gravitational constant, m1 and m2 are the masses of the two stars, and r is the distance between them.

Plugging in the values, we get:

Fg = (6.7*10^-11Nm^2/kg^2)(10^20kg)(2*10^20kg)/(10^9m)^2
= 1.34*10^30N

Since the only force acting on the stars is the force of gravity, this must also be the centripetal force, so we can set Fc equal to Fg and solve for w:

Fc = Fg = mw^2r
1.34*10^30N = (10^20kg + 2*10^20kg)w^2(10^9m)
1.34*10^21 = 3*10^20kgw^2
w^2 = (1.34*10^21)/(3*10^20kg)
w^2 = 4.47
w = √4.47
w = 2.11 rad/s

Therefore, the angular speed of the stars rotating around their common center of mass is 2.11 rad/s.