- #1

uSee2

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- Homework Statement
- A planet orbits a star in an elliptical orbit, is the planet faster when it is farther away from the planet or closer to the planet? Explain in terms of momentum

- Relevant Equations
- ##\tau = Fr\sin(\theta)##

The planet is faster when it is closer to the planet because when it is closer to the planet it has less rotational inertia, and rotational momentum is conserved in this system, so less rotational inertia means a greater angular velocity. This explains why it is slower when it is farther away from the planet because has more rotational inertia which means it has slower angular velocity to keep momentum conserved.

I believe that my explanation above is correct, however what I am confused about is to how angular velocity can change without a net torque. There is no net torque done on the planet because the force due to gravity is always pointing towards the star, and since ##\tau = Fr\sin(\theta)## combined with the fact that ##\sin(\theta) = 0## always, so net torque done the system equals 0 as well. However, there is an angular acceleration of the system because angular velocity changes as it orbits.

How could there be an angular acceleration in this case if there was no torque being done?

I believe that my explanation above is correct, however what I am confused about is to how angular velocity can change without a net torque. There is no net torque done on the planet because the force due to gravity is always pointing towards the star, and since ##\tau = Fr\sin(\theta)## combined with the fact that ##\sin(\theta) = 0## always, so net torque done the system equals 0 as well. However, there is an angular acceleration of the system because angular velocity changes as it orbits.

How could there be an angular acceleration in this case if there was no torque being done?

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