Corotation speed and energy

[Imagin_e]

Homework Statement

Hi!
I need help with a problem regarding the corotational speed en energies for oxygen ions around Jupiter. I'm stuck

Homework Equations

See below

The Attempt at a Solution

I know that the maximum magnetospheric plasma density is about 1000-50000 cm^-3.
I also know that the formula for the circumference of Jupiter (or any other planet if I'm correct) is: 2*pi*L*Rj.
The L values should be between 1-10.
The critical velocity has a formula and it is: (v_crit)^2=Omega_gyro*Omega_rotation*Rj^2*L^2 and I believe that I need to use this. In that case, I need to know how to calculate Omega_gyro and Omega_rotation (which are the rotational frequencies). What should I do?
When it comes to the energy, I believe that I can use E=mv^2/2 , where m is the mass of the ion. Correct?

Thanks!

 

[Asim Riaz]

Yes, you are correct about the circumference of Jupiter formula. For the critical velocity equation, Omega_gyro is the gyroscopic frequency of the ion and Omega_rotation is the rotational frequency of the planet. You can calculate the rotational frequency of the planet by taking the angular velocity which is 2*pi/T where T is the rotation period. The gyroscopic frequency depends on the particle's charge to mass ratio, so you would need to know the charge and mass of the oxygen ion in question. For the energy, yes you can use the equation E=mv^2/2, where m is the mass of the ion and v is the velocity.