Atmospheric drag on an artificial satellite orbiting the Earth

[Cristiano]

Consider an artificial satellite orbiting the Earth and suppose that the atmosphere co-rotates with the Earth.

I need to calculate x, y and z components of the atmospheric drag.

I know how to calculate the drag in a non-spinning atmosphere and I have all the data to do that, but the Earth’s rotation confuses me.

I know the x, y and z components of the satellite state (position and velocity). The z-axis is the Earth’s rotation axis and the x-axis and y-axis lie on the equatorial plane. The exes do not rotate (it’s an inertial reference frame).

Please, could somebody help me?

 

[rcgldr]

The altitude of the satellite is not stated. Atmospheric drag is only significant for objects in low Earth orbits. The shape, size, and orientation of the satellite are also not stated.

 

[mfb]

You can calculate the x/y/z motion of the atmosphere at the position of the satellite and subtract that from the satellite velocity to find the relative velocity.

 

[Cristiano]

You can calculate the x/y/z motion of the atmosphere at the position of the satellite and subtract that from the satellite velocity to find the relative velocity.

There is no doubt, but how to calculate x/y of the atmosphere (rotating frame) in the satellite reference frame (inertial frame)?
I know that the atmosphere rotates with speed (with an adequate accuracy for me):
Vrot= (6378.137 + alt_satellite) * (2 * PI) / 86162 * cos(lat_satellite) [km/s]
the z component is always 0, but how to calculate x/y components?

 

[mfb]

$\vec v = \vec r \times \vec \omega$ with the cross product.