How to calculate relative doppler shift

[Link]

I am to measure the rotational velocity of Io relative to Jupiter, and will do so using a spectrograph.

I will measure the frequency change of a specific mineral emmision band in the spectra, and then check how much it has shifted from its original wavelength with a table. Then I use the formula:

$$v = (\Delta \lambda/\lambda) c$$

where $$\Delta \lambda$$ is the change of frequency and $$\lambda$$ is the rest wavelength. C is speed of light.

to calculate the velocity for each object.

The problem is how do I calculate the velocities relative to each other? Io rotates around jupiter, using my method i believe i can only calculate its speed moving relative to earth?

 

[Andrew Mason]

I am to measure the rotational velocity of Io relative to Jupiter, and will do so using a spectrograph.

I will measure the frequency change of a specific mineral emmision band in the spectra, and then check how much it has shifted from its original wavelength with a table. Then I use the formula:

$$v = (\Delta \lambda/\lambda) c$$

where $$\Delta \lambda$$ is the change of frequency and $$\lambda$$ is the rest wavelength. C is speed of light.

to calculate the velocity for each object.

The problem is how do I calculate the velocities relative to each other? Io rotates around jupiter, using my method i believe i can only calculate its speed moving relative to earth?

Can you not also measure the same emission band for Jupiter itself?

AM

 

[Link]

but the problem is, that I do not know how to integrate the shift of Io relative to jupiter... in order to measure the radial velocity of Io around jupiter, i need to integrate them both into the same formula in some way

 

[Andrew Mason]

but the problem is, that I do not know how to integrate the shift of Io relative to jupiter... in order to measure the radial velocity of Io around jupiter, i need to integrate them both into the same formula in some way

If you measure the Doppler shift from Jupiter itself you would simply subtract/add that from/to the Doppler shifts that you measure from Io.

AM