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pargeterw
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*Please Help* Question related to Orbital speed of star, Keep getting *10^4 to high??
A star has a mass of 2.2*1030kg, there is a planet of mass 4.5*1027kg orbiting it at a distance of 3.1*1011m (also told that it has a "period of wobble" of 9.2*107s due to the orbiting of the planet)
The start is orbiting about the centre of mass of the star/planet system.
Show that the speed of the star in its circular orbit is about 50m/s
v=sqrt((G*M)/r)
where G=6.67*10-11m3/kg/s2
M=mass of orbiting object
r=radius of orbit
I know M=2.2*1030
I know G=6.67*10-11
so I only need r
r is the distance from C.O.M of the Star/planet system to the star, and it follows that this would equal ((4.5*1027)*(3.1*1011))/((4.5*1027)+(2.2*1030)) = 6.33*108
because <x>=(∑mixi)/(∑mi)
therefore substituting M, G, and r into the equation for v should, one would hope, give about 50m/s
it does in fact, give 48*104.
this is slightly hopeful, as 48≈50, although not correct, as 104 ≠ 1!
does anybody have any idea what I got wrong?
Homework Statement
A star has a mass of 2.2*1030kg, there is a planet of mass 4.5*1027kg orbiting it at a distance of 3.1*1011m (also told that it has a "period of wobble" of 9.2*107s due to the orbiting of the planet)
The start is orbiting about the centre of mass of the star/planet system.
Show that the speed of the star in its circular orbit is about 50m/s
Homework Equations
v=sqrt((G*M)/r)
where G=6.67*10-11m3/kg/s2
M=mass of orbiting object
r=radius of orbit
The Attempt at a Solution
I know M=2.2*1030
I know G=6.67*10-11
so I only need r
r is the distance from C.O.M of the Star/planet system to the star, and it follows that this would equal ((4.5*1027)*(3.1*1011))/((4.5*1027)+(2.2*1030)) = 6.33*108
because <x>=(∑mixi)/(∑mi)
therefore substituting M, G, and r into the equation for v should, one would hope, give about 50m/s
it does in fact, give 48*104.
this is slightly hopeful, as 48≈50, although not correct, as 104 ≠ 1!
does anybody have any idea what I got wrong?
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