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# How would an interstellar spaceship's speedometer work if everything else is moving?

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A speedometer is a gauge or device used for measuring instantaneous speed of moving vehicle roughly speaking, so for example the reading shown on the speedometer of a car parked at road side displays zero implying it is at stationary position respective to the road or landmark etc as long the surrounding objects are at rest relatively to ground. I believe some of you already see where this is going...

Correction: This speedometer actually counts how many turns the wheel makes which then can be translated good indication of vehicle speed but not without flaw.

Another example is a speedometer or otherwise called pitometer log which is usually seen in boat or ship and I shall leave you to find out the working mechanism. (clue: differential pressure of water)

I know with GPS who is still using speedometer nowadays let alone in the future but I'm sure some of you are aware of the limitations.

Notes

• Please factor in time dilation when you approach closer to speed of light in vaccum. (e.g. Lorentz factor: <0.9)

Questions

1. How would interstellar spaceship without FTL or wrap capability measures instantaneous speed accurately?
2. If instantaneous speed is useless for space travel then what kind of measurement would be adopted instead? (e.g. light year is used instead of miles or kilometer etc.)
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The first question is: What is instantaneous speed measured against (that is, what is the “ground” relative to which the speed is measured)? Remember that there is no such thing as absolute speed.

The closest to an absolute speed would be the speed relatively to the cosmic microwave background. That speed would be measured by measuring the Doppler shift in different directions. In the direction you are heading to it is blue shifted, in the opposite direction it is red shifted. The amount of blue/red shift gives you the speed.

However the speed relative to the CMB is probably not the most useful. In particular, since you assume no sort of warp drive or similar, you're surely still in the Milky Way, and indeed probably quite close to the Sun. Probably the more useful measurement would be the speed relative to the interstellar medium (this would be the equivalent to measuring airspeed of an airplane or speed relative to the water for a ship). If you are very fast (relativistic speed), you probably encounter enough particles to measure the speed of those atoms directly when they hit your space ship (or whatever shielding you use to prevent them hitting the ship). Otherwise you'll probably resort to the Doppler effect again (either by taking radiation the gases emit naturally, or using a sort of gas radar).

Another possibility is to measure your speed against nearby stars. The movement of the stars is pretty predictable even over centuries; unless you're going to have very long travels, that should be sufficient. Moreover, your destination like is a star anyway, so the movement relative to the stars is ultimately what matters most. Measuring the speed relative to those stars is done by parallax for tangential velocity and again the Doppler effect for radial velocity.

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You would send out a small laser or radar retroreflector out of the side of your ship and observe the tracking angle. Knowing the speed of your marker you can calculate the speed of your ship with reasonable accuracy.

For large scale relative velocity you would use stars with known vectors and calculate your position and then recalculate after you can see perceptible change in the relative angles to establish you velocity vector.

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Whatever means you use, it would make sense to have two measurements: Time To Destination (TTD) relative to yourself, and TTD relative to the destination. E.g one year for you, two years for the people waiting for you

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I'd recommend a Kalman filter to increase measurement accuracy to the overlap of multiple system errors so that you get the best result.

For inputs, may I recommend -

• a calculation of doppler shift for known stars. You can do this realtime. Take a fast fourier transform of the incoming light for that star, and compare it to a catalog. Then calculate the redshift or blueshift. It accounts for Lorentz length contraction. And the measurement precision increases as you approach the speed of light.
• doppler shift of one or more known radio emitters back home.
• parallax shift of pre-positioned radio emitters, if you are flying in an area that has that kind of infrastruture
• change in radio distance to receiver over time, if you are flying through a region with that kind of infrastructure.
• parallax shift of nearby stars
• dead reckoning (compounded accelerometer over time, and fuel burn). This will work better at low velocities where doppler shift is small. This also may be your only way to measure at faster than light speeds, if some sort of superluminal shock wave makes seeing the outside impossible.
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