# Decelerating a spaceship, is the exhaust spectra Doppler shifted red or blue?

Gold Member
TL;DR Summary
spectra deceleration doppler shift red blue
Let's imagine we have a ship heading towards our planet. It fires forward thrusters to brake. The ship is long way away. Because the ship decelerates, (slows down towards us) would we see particles from its exhaust doppler shifted blue or red? On the one hand the gas is flying towards Earth, so that would imply a blue doppler shift. On the other hand, the ship is slowing down, but would that decleration manifest itself as a red doppler shift somehow? I feel like the fact that the exhaust gas points towards, and is liberated from the ship, the gas would be Doppler blue shifted, but I'm not sure.

Gold Member
Not acceleration but velocity to the observer matters for Doppler shift. Which direction of speed to the Earth observer does exhaust gas have in your setting ?

russ_watters
Staff Emeritus
2022 Award
The velocity is the only thing that matters, not acceleration, when it comes to redshit/blueshift. If the exhaust is coming towards the planet it will be blueshifted. If it is moving away then it will be redshifted. With respect to an observer on the planet of course. Someone viewing the exhaust from a different location or frame of reference may see it completely different.

Gold Member
Summary:: spectra deceleration doppler shift red blue

I feel like the fact that the exhaust gas points towards, and is liberated from the ship, the gas would be Doppler blue shifted, but I'm not sure.
Correct in principle and you got the 'sign' right. However there are two problems here. Firstly the ejecta from rockets is going far to slowly (relative to the rocket) for any relativistic effects to be observed and secondly, there will be a massive range in speeds of ejecta from a conventional rocket which(imo) would mask any subtle frequency shift in the observed light.

There are a number of possible alternatives for spaceship propulsion (e.g. Ion drive) which involve much higher speeds of ejecta. Relativistic shift would be more visible in that case but non-chemical propulsion involves small forces over a long time so actually observing the drive at work would be a huge problem as the emitted light would be so faint.

Is this a SF enquiry?

Gold Member
"Which direction of speed to the Earth observer does exhaust gas have in your setting ?"

The observer is on the Earth. They look up in space and see the braking gas coming towards them. The ship is moving towards Earth, but slowing down. The ship's velocity vector is dead-on pointing towards Earth.

"If the exhaust is coming towards the planet it will be blueshifted. If it is moving away then it will be redshifted."

Okay, sounds good. Appears to be what I'm looking for.

"Firstly the ejecta from rockets is going far to slowly (relative to the rocket) for any relativistic effects to be observed and secondly, there will be a massive range in speeds of ejecta from a conventional rocket which(imo) would mask any subtle frequency shift in the observed light."

I know that stars can eject gas that comes towards the Earth which astronomers see blue-shifted for a variety of situations. Does gas from stars then, need to be relativistic to have a noticeable blue-shift? So for a spaceship, the ejected exhaust traveling towards Earth would travel much more slowly than light from gas ejected from a star, is this correct? How much energy would a spaceship need whose braking exhaust would be blue-shifted, or would the wide range of speeds from braking exhaust erase any gas that blue-shifts, regardless of speed, relativistic or not?

Yes, this is an SF inquiry.

"There are a number of possible alternatives for spaceship propulsion (e.g. Ion drive) which involve much higher speeds of ejecta."

Gold Member
So for a spaceship, the ejected exhaust traveling towards Earth would travel much more slowly than light from gas ejected from a star, is this correct?
Speeds of around 3km/s for your average rocket engine exhaust gasses. That would be about 1/1000% of c which is, indeed, a lot slower than some particles ejected from stars at a sizeable fraction of c. Any shift in frequency would be hard to detect, bearing in mind the wide (continuous) spectrum of the hot exhaust.

Alternative forms of propulsion: A quick google of Spacecraft Propulsion yields quite a few hits. This Wiki link is a start for you. Any SF story needs to take account of the enormous time involved in accelerating and decelerating a rocket with what's available for long journeys.

If your story involves finding out the approach speed of a craft then there are other possible methods - say lidar (laser radar). If you don't know that a craft is approaching then you have the same problem as finding other small objects out there. Things are getting better in that respect, though, with dedicated satellite systems looking for rogue asteroids. How big would the craft be, though?
So many questions and the particular scenario would probably need a particular solution.
Good luck with that. SF can turn round and bite you if you overstretch the suspension of disbelief.

Klystron
Gold Member
Excellent everyone. I think I'm good to go.

sophiecentaur and berkeman