Constant speed of light - scenario

[Silvestru]

I  understand how in free space, c is constant. And if I travel at let's say 0.5c and turn on a flash light I will record that the light is traveling away from me at c. 

I was hoping you could clear up the scenario that I was thinking of below

Let's say we have two stationary satellites that are located exactly 1 light hour away from each other and they exactly 1 light hour away at all times.
Satellite 2 starts shooting a light beam once every minute directly towards Satellite 1. A rocket starts traveling at a constant 0.6c (let's say) from Satellite 1 directly towards Satellite 2.
Would the rocket also record the "frequency" of the light beam signal once every minute the entire journey? (I understand that time would be relative and would pass differently for the rocket and Satellite 1 but I mean relative to each of these observers.)

I have follow up questions depending on the answer

Side question: From my understanding of Doppler shifting, for Satellite 2(who is emitting the light) the light would look normal("white") but for the rocket the light would be more blue? (would it be Doppler shifted to a higher level of energy? It gains energy from your motion but not speed.)

Or is that in the scenario that the rocket would be the one emitting the light? (and the light emitted would actually "slow down the rocket" by robbing energy from it's motion and converting it to energy)

[Janus]

A rocket moving from Satellite 1 to Satellite 2 at 0.6 c would measure the light beams as arriving 30 sec apart.

The frequency of the light received will be twice that of the frequency as measured by the source at Satellite 2 ( the duration of each light beam will also be half as long.)

As far as light emitted forward by the rocket goes, yes it would have a slowing effect on the rocket, as light has momentum and the forward momentum of the light would subtract from the forward momentum of the Rocket in order to conserve momentum.  The rate of this deceleration of the rocket depends on the frame from which you measure it.

[swansont]

1 hour ago, Silvestru said:

 Or is that in the scenario that the rocket would be the one emitting the light? (and the light emitted would actually "slow down the rocket" by robbing energy from it's motion and converting it to energy)

The force exerted by photons absorbed or emitted is F = P/c, where P is the optical power. (There's a factor of 2 if light is being reflected)

IOW, it's 3.3 millinewtons per Megawatt. It's very small. (On an atomic scale the absorption/emission of a photon is large enough to move atoms and even small molecules around, but by the point where you are getting near Avogadro's number of them, it's all but vanished) 

[Silvestru]

Thank you guys, and can you please tell me about the "color" of the light? Would it be different for each observer?

[swansont]

12 hours ago, Silvestru said:

Thank you guys, and can you please tell me about the "color" of the light? Would it be different for each observer?

Light will experience a doppler shift, depending on the relative motion between the observers. Moving toward each other there is a blue-shift, and moving apart gives a red-shift.