Determine the mass of the star?

[ohheytai]

Uploaded the PDF someone please help me i have no idea what to do!

Homework Equations

(-G*m1*m2)/r^2
dP/dt

The Attempt at a Solution

I don't even know where to start i drew everything out and i think dP/dT is 0 cause its at a constant speed someone please help! :(

 

[Ambidext]

At constant speed in circular motion, acceleration would be constant towards the centre, creating the centripetal force, F<sub>c.

In the case of orbit, Fc = Fg = GMstarMplanet / R²

R, T and G are given, so all you need to do is to derive the mass of the planet in terms of the given quantities.

Rearranging the expression to find star's mass, I get:
Mstar = Fc R² / G Mplanet

The only unknowns left will be Fc and mass of planet.

However, it is known that Fc = Mplanet v² / R. Thus, the mass of planet in Fc can be canceled with the mass of planet in my arranged expression above to give:

Mstar = v² R / G

v = 2pi R / T (given in question as well), thus, final expression being:

Mstar = 4 pi² R ³ / G T ²

This is just my first try. please let me know if I've made any errors or if you disagree.</sub>

 

[ohheytai]

is it possible to do this without centripetal force? and using vectors?

 

[Ambidext]

Dimension for G is m³ kg^-1 s^-2, making the overall expression's dimension kg as well. So my expression SHOULD be correct.

 

[Ambidext]

is it possible to do this without centripetal force? and using vectors?

The purpose of this problem is to emphasize that in an orbit, the centripetal force is the gravitational force, and thus using simple algebra, master the variables of the expression for F_g.

Vectors will point only the tangential velocity and F_c, but to determine the mass, you need expression for F_g.

 

[ohheytai]

okay thank youuu!