can someone help me with this space question?? (1 Viewer)

[ruwangi]

there is a net force acting on a satelite (m) in a stable orbit around a planet (M) at a distance (R) from the centre of the planet (R)

this net force provides the centripetal acceleration of the satelite

write an expression equating the two forces and hence derive an expression for the period (T1) of a satelite in terms of R, G (universal Gravvitational Constant) and M.

worth 2 marks

thanks

 

[Cara.Mel]

a = GM/r^2
a = (4pi^2*r)/T^2 (circular motion equation)

Equate the two so:

GM/r^2 = (4pi^2*r)/T^2
T^2 = (4pi^2*r^3)/GM
T = sqrt((4pi^2*r^3)/GM)

I come from victoria (and like to click the new post button ^_^) so I don't know if there is anything else you need to do, if you had to do anything to get the equations I started from etc, that's the answer anyway

 

[ruwangi]

a = GM/r^2
a = (4pi^2*r)/T^2 (circular motion equation)

Equate the two so:

GM/r^2 = (4pi^2*r)/T^2
T^2 = (4pi^2*r^3)/GM
T = sqrt((4pi^2*r^3)/GM)

I come from victoria (and like to click the new post button ^_^) so I don't know if there is anything else you need to do, if you had to do anything to get the equations I started from etc, that's the answer anyway

thanks for the help. good luck with the studying

 

[appleide]

If you wanna know where "a = (4pi^2*r)/T^2 (circular motion equation)" came from:
The sum of forces travelling in circular motion directed to the center is:
F=ma=(mv^2)/r
so,
a=(v^2)/r
and v=the perimeter of the circle (2pi*radius) divided by the time taken (period T).
=2pi*r / T

Sub the v into the v^2/r and you'll get it.