- #1
BOAS
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- 19
Hello :)
The Earth of mass [itex]m_{e}[/itex], moves with an approximately circular orbit of radius [itex] r = 1.5 * 10^{8}km[/itex] around the sun of mass [itex]M_{s} = 2 * 10^{30}kg[/itex].
(a) Determine the numerical value of the speed of the earth.
(done, got an answer of [itex]29821 ms^{-1}[/itex] by equating the gravitational equation with the centripetal force equation)
(b) Is the angular momentum [itex]L[/itex] of the Earth conserved? Why? Show that its module is given by [itex]L = m_{e} \sqrt{GM_{s}r}[/itex]
I do not understand how to show that angular momentum is conserved, one of the older students that help in our workshops gave an 'explanation' but I don't actually follow his argument.
I'll try to explain what I think he said.
[itex]L = I \omega[/itex]
[itex]\frac{dL}{dt} = \tau = f * r[/itex]
[itex]\tau = o[/itex]
[itex]\frac{dL}{dt} = 0[/itex]
∴ Angular momentum is conserved
The step that confuses me somewhat is why [itex]\tau = 0[/itex]
Thanks!
Homework Statement
The Earth of mass [itex]m_{e}[/itex], moves with an approximately circular orbit of radius [itex] r = 1.5 * 10^{8}km[/itex] around the sun of mass [itex]M_{s} = 2 * 10^{30}kg[/itex].
(a) Determine the numerical value of the speed of the earth.
(done, got an answer of [itex]29821 ms^{-1}[/itex] by equating the gravitational equation with the centripetal force equation)
(b) Is the angular momentum [itex]L[/itex] of the Earth conserved? Why? Show that its module is given by [itex]L = m_{e} \sqrt{GM_{s}r}[/itex]
Homework Equations
The Attempt at a Solution
I do not understand how to show that angular momentum is conserved, one of the older students that help in our workshops gave an 'explanation' but I don't actually follow his argument.
I'll try to explain what I think he said.
[itex]L = I \omega[/itex]
[itex]\frac{dL}{dt} = \tau = f * r[/itex]
[itex]\tau = o[/itex]
[itex]\frac{dL}{dt} = 0[/itex]
∴ Angular momentum is conserved
The step that confuses me somewhat is why [itex]\tau = 0[/itex]
Thanks!