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

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 as mentioned by Michael Kjörling's comment.

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.)
• so it will not be sufficient to get your orbital speed? At all, stuff in space isn't moving in a straight line but in... trajectories (?)... okay, with 0.9 c you might not have to worry about this, but I still wonder: will orbital speed be sufficient? Nov 11 '15 at 7:35
• @ConfusedMerlin: You are right anyway I'm also thinking about better solution to work around relativity, I remember 1 interesting notion in special relativity is you can never tell whether you are moving in total vacuum space. Nov 11 '15 at 7:48
• I took the liberty to remove the hard science tag. For this to apply, it says: All answers to this question should be backed up by equations, empirical evidence, scientific papers, other citations, etc.. I think this is not necessary here. Feel free to add it back if i got that wrong. Nov 11 '15 at 8:00
• @Burki: no problem as I thought I can see some equations and numbers :) Nov 11 '15 at 8:02
• @MichaelKjörling: thanks for the clarification Nov 11 '15 at 8:32

A spaceship could measure red/blue shift from stars around it.

This would require a database of light frequency distributions of stars measured "at rest". Comparing observed values of stars at different angles relative to the ship would give both speed and direction of the ship (peak blue-shift is where you're heading).. By incorporating relativity into the calculation this should work for speeds close to light speed as well.

Inside a planetary system your speed is normally slow enough that measuring the position of the stars and planets should work.

In space combat, absolute speed doesn't matter, only relative speed and especially acceleration. For that, gyroscopes and lasers should work.

• <shakes fist> damn you stole my answer. If only I had stayed past 3AM awake!!! here is a +1 Nov 11 '15 at 12:04
• In space combat you can triangulate to the mother ship and the mother ship triangulate to the nearby stars. That way they could navigate. Nov 11 '15 at 14:45
• Yeah, this was my first idea. You don't even need a catalogue of stars - assuming your moving from star system A to star system B, all you need is the data on one of those stars, which you'll obtain before your acceleration. Nov 11 '15 at 14:48
• Note that one need not use the stars nearby. Doppler shifting and red/blue shifting of pulsars (of precisely known positions) works. Same with red/blue shifting galaxies of precisely known angles (and positions if one is planning on moving galactically-relevant distances). But the "coolest" version of this is to measure the red/blue anisotropy of the CMB. (Amusingly, if one were to do this, one could detect nearby strong gravity sinks via surges of Unruh radiation.) This only requires a database with one entry. Nov 12 '15 at 0:37
• This is known as Peculiar velocity. You create an artificial frame of reference at "rest" relative to you and your destination. You take an average measurement of the velocity of objects close enough that you can measure their velocity accurately enough for your purpose that are also far enough to have negligible gravitational influence on you and your destination. This rest reference frame has nothing to do with "absolute rest"(which is a murky if not fictitious concept). It's a local calibration of what "rest" means, but it can be used to calculate your relative velocity to your destination. Nov 12 '15 at 2:45

The star ship is (presumably) moving from one point to another point.

This means, the only relevant information is the distance from the departure point and / or the distance to the target location.

Your speedometer gives you a speed as measured in distance per time. Now, provided you can measure the distance to your target, you can compare two measurements and get the delta distance in the time between the measurements.

This is your speed. Now all you need is a display where this number is shown.

• The tricky thing here is that the target point is also moving. Even if you're moving between solar systems, both solar systems are orbiting the galactic barycenter, so the point you're moving toward is in not moving in a straight line. This also means that your velocity relative to target actually doesn't give you a very good estimate of how long it will take to intercept (at least when approaching from a significant distance). You can compute interception time based on a transfer orbit, but it doesn't really simplify to a single 'speed' to target. Nov 11 '15 at 15:41
• @DanBryant this is of course correct, but the OP did not ask for ETA calculation, only for speed. Nov 11 '15 at 16:18
• @Burki, It really depends on what the speed is meant to be used for. We intuitively use speed on the ground to estimate time to arrival, so I think it's important to realize that it won't work that way when considering motion in orbits. Nov 11 '15 at 16:22
• Did you account for length contraction? Nov 11 '15 at 17:13
• @DanBryant Calculating ETA is certainly a use for a speedometer, but not the only possible use, and certainly not the definition of "speed". The idea of rendezvousing with a moving target is not unheard of on Earth. Ships can rendezvous at sea, airplanes sometimes meet up with tankers for in-flight refueling, etc. I would hope that spaceship crews would comprehend that when approaching a moving target, the time to arrive is not simply current distance divided by current speed.
– Jay
Nov 11 '15 at 19:56

For useful navigation, we want to know several velocity vectors

Assuming real-world physics and you're actually using orbital trajectories rather than 'warp-to-target' navigation:

1. Velocity vector to current position of target. This is highly relevant when you're already close to the target and trying to match velocities for a rendezvous maneuver. It's much less relevant for long-range interception, since the target is also moving along some orbital path and thus constantly driving 'toward' the object is not the most efficient way to arrive at the object.

2. Your orbital velocity vector relative to the dominating gravitational well in which you are moving. This allows you to predict your orbit with pretty good accuracy, presuming no encounters with other massive bodies along the way. Note that orbits include hyberbolic trajectories, such as escape from a planet's orbit.

3. Your velocity vector relative to the surface of a body you're orbiting. This takes into account the rotation of the body about its own axis and is quite relevant for things like landing or, say, plotting the path of your orbital bombardment laser across the surface.

How would these vectors be measured?

1. Receive information about our motion relative to an observer, such as Earth. This would be the most likely mode of operation in a typical space-faring society, as we would have a network of observation points and communication relays constantly tracking all objects in the system.

2. For navigation in isolation, one possibility is using transmissions from known Pulsars to compute position.

3. Another possibility is to find something else moving along a known orbit and watch it move. This requires us to either be fairly close to the object or to have really good sensors.

A motivating example for how these velocity vectors would be used

To give a sense for how this would work in practice, it's helpful to consider the Hohmann transfer orbit, which is an efficient way to intercept another object traveling in the same plane in orbit around the same body. This is the kind of maneuver you would use to transfer from one planet to another, for instance. The time to actually perform the intercept is not just determined by the distance between the targets (which changes as they move in their orbits), but depends on several things:

1. It takes time to achieve the correct orbital phase for the transfer. This is a 'waiting time' before you even start the maneuver. At this phase we care about our orbital velocities (and hence our orbits), as these determine the correct point to perform the transfer.

2. It takes time to actually get near to the object. This is the actual transfer orbit duration and is the closest analogy to 'travel velocity'.

3. Once you get close to your object, you can match velocity. This is where the velocity to target finally becomes useful. Once you've mostly matched velocities, you likely also follow up with a maneuver directly 'toward' the object. At this point, the distances and relative velocities are very small compared to orbital trajectories, so gravity is mostly negligible and we can pretend things are more like the intuitive picture of things floating freely in space.

Fair disclaimer, everything I know about orbital mechanics I learned by playing Kerbal Space Program. Obligatory xkcd.

Lets assume you are travelling at an appreciable fraction of C. Chances are you have some sort of shielding so the front of your ship (and then the front of you) doesn't get abraded away by the interstellar medium. Could you figure out some sort of measurement device that uses the activity of that shield? Could you then combine that with a known density of the interstellar medium?

• Ooh, fun idea. This also leads to the universe having a requirement for 'stellar-cartographers' to accurately map the density of the interstellar medium. It's a bit inaccurate though.. Nov 11 '15 at 16:54

It's very simple: you just need an accurate accelerometer. This is known as an inertial navigation system.

Acceleration is measurable without external reference points. Just make sure to measure your starting speed $v_0$ accurately when you're still navigating out of the solar system, before you turn on the warp drive. From then, you just look at the accelerometer, and compute your new speed from the measured acceleration: for every second of acceleration at $a\;ms^{-2}$, you add $a$ to $v_0$.

If you're accelerating in complicated ways, you'll need one accelerometer per axis. If you get close to a planet you'll need to correct for the planet's gravity, but then you have an external reference, so you can recalibrate.

• Hopefully you don't start measuring your speed near any mass (like a planet or star), or else you'll measure gravity as a change in velocity. Nov 11 '15 at 17:17
• @Samuel, Acceleration due to gravity is very difficult to measure 'locally' if the gradient is small, as all parts of the object are being accelerated by almost exactly the same amount. This is why astronauts in orbit experience 'free fall'. Nov 11 '15 at 17:42
• @Dan I'm measuring local acceleration due to gravity fairly strongly from my chair right now. But really, if the ship is planning on moving in or out of gravity wells and not simply orbiting them, it will have to be accounted for. Nov 11 '15 at 17:51
• @Samuel True, but if there's mass nearby, then you also have an external reference point, so you can measure your speed by that. I suppose an invisible, unknown source of gravity, like dark matter, might pose a problem. But hey, that would be a good plot point :)
– PTm
Nov 12 '15 at 5:43

If you're a sufficiently advanced race then placing a series of 'beacons' that pulse with known combinations of frequencies might be advantageous.

The beacons would have to be very close together (in interstellar terms), due to the limitations of our signal broadcasting technology (We aren't as powerful as the stars yet), but this system could be used to string together known highways through space with the beacons acting as both 'mile' markers and GPS satellites.

The relative power of various beacon's signals can be used to compute location in space, and if you couple this approach with Cyrus' answer on redshift you also get speed with a bit more accuracy. 'Speed' then becomes a value relative to this network of beacons.

Obviously this approach doesn't work in a stellar system unless you have an unlimited amount of delta-V with which to hold the beacons in place, but if you're in-system you can use signals pumped from known celestial bodies (like Earth) to calculate speed. Any network in interstellar space will have to shift occasionally based on the relative motion of the stars, but any system using the stars as a reference for interstellar travel will have to compensate for that anyway. Oh, and it will be expensive to build and maintain, but depending upon your tech level and need for solid navigational information it might be worth it.

One more upside: When you've got at least 66 different beacon-pathways, you get to build some awesome space diners.

1.How would interstellar spaceship without FTL or wrap capability measures instantaneous speed accurately?

Other answers implied but no one blatantly stated the answer: you CANNOT measure an absolute velocity, which becomes especially obvious when in outer space. As far as we can tell, there is no such thing. Even on Earth, your "instantaneous speed" is actually relative to... the surface of the Earth! (Note that by definition, "speed" is independent of direction, and for a ship moving in 3-dimensions, the directional vector of its velocity is vital. Shades of Wrath of Khan!)

Unless the exact timing is important, such as plotting out an intricate "battlefield" or going (fairly slowly) between planets inside a stellar system, you can usually assume that your planets aren't moving. Only the relative speed between the stars might be of any interest at all, and rarely that would be either. Relative position in 3-d space might be of interest, since there could be a considerable Z-axis distance between 2 stars that have similar X & Y coordinates.

You didn't ask, but fortunately, several good suggestions about how to measure relative velocity were suggested.

In practice, you would probably use a combination of things to describe your velocity, depending on your technology, location, and relative velocity; (continued in explanation for #2).

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.)

That will depend on how "fast" you are going relative to other bodies in space (that you care about), i.e. your "delta v(elocity)". Some examples could be:

• small velocities/small scale objects - meters/second up to km/h -- typically for small boats, space-walkers and small to mid-sized ships approaching airlocks, space stations or other ships, missiles
• inside stellar system cruising - likely in km/h up to km/s, which could get very large depending on your thrust technology and travel time. You would choose between /h or /s depending on how long it is traveling or how big a number you want to make it look. For example, the New Horizon probe to Pluto (fastest ship to date) left Earth at 58,000 kph, which is about 16 km/s.
• interstellar cruising - could be the same as inside the stellar system, but probably will want it to be expressed in km/s because you're going to want to go way faster than even New Horizons. Hopefully you have some kind of continuous acceleration, and in that case, you'll be moving (relative from your departure place) a lot faster than even New Horizons.
• lightyears - without an advanced, non-Newtonian (i.e. "impossible") space drive, you will never need to measure velocity in light-years unless you're trying to be cute. e.g. "lightyears/century"
• Red/blue-shift or C - Mid-way through your decades/centuries long trips, you may find it convenient to use the red/blue-shift percentage of a set of "stellar beacons" or even your destination star, since your relative velocity could be a significant fraction of light speed... if you have a significant amount of acceleration the whole time. Or just use fractions or percentage of C (light speed) to simplify and make it more understandable to most people. E.g. 93% C or 0.93 C
• Distances could run the gamete from meters to kms to thousands or millions of kms to light-years (remember that light-year has nothing to do with measuring time, it's just the distance unit of how far light travels in one year, the same as a meter is how far light travels in a fraction of a millisecond)
• You would certainly want to measure distance between stars in light-years. It used to be common to use parsecs, but that's very Sol-centric.

• Acceleration - likely in meters per second squared for known technologies, or as is commonly expressed, maybe in "gravities" where 1 G = 9.8 m/s/s - the acceleration due to gravity at sea level on the equator on Earth. This would only be needed if your ships could accelerate very quickly though. Unprotected humans can only stand a few G's, maybe as much as 6 G's without injury.

• Note that if you are travelling within a relatively small interstellar area, you could create a frame of reference based on a set of "stellar beacon" objects (easily identified and stable stars, variable stars, pulsars, etc.), which could fulfill the role of a frame of reference and thus give you an pseudo-absolute velocity. Note that this would mean that the stars and planets would have their own pseudo-absolute velocities with that frame of reference, and you would have to then account for them into your ship's "absolute velocity". Nov 12 '15 at 17:31
• So departing a planet/orbit, you would already have some significant velocity, say 2000 km/s at 23 degrees right by 43 degrees up... and your ship will then have to match velocities of its destination in 4 dimensions (4 because you have to aim at where it will be when you get there). Maybe your arrival point has a velocity of 377120 km/s at 153 degrees right by 83 degrees down.... you can see that a relative velocity is much easier to deal with after all, and frankly, virtually none of your readers/players (?) will understand or care about the exact details anyway. Nov 12 '15 at 17:31

Special Relativity states that the relativistic mass of a object changes depending on your speed. If you were to measure the relativistic mass of an object on your ship you could calculate your velocity.

• But can you calculate that while actually on the ship? Or would your mass appear the same from your point of reference? Nov 11 '15 at 14:54
• @bowlturner If you were to vibrate the object along the axis of motion you could calculate the difference in mass while moving "with" the ship and "against" the ship. Nov 11 '15 at 15:03
• Welcome to Worldbuilding. Your answer sounds very promising! Would you ind elaborating a bit? Around here, we generally like more detailed answers better. Also, you may want to take the tour. Nov 11 '15 at 15:18
• I can't comment yet, so this is regarding hehe3301's answer and comment suggesting that you measure the relativistic mass (which changes with speed) of an object on your ship, such as by "vibrating an object along the axies of motion and calculating the difference when moving 'with' and 'against' the ship." It's a good idea, but Relativity conspires against you. Your measurements are tied to your reference frame. Measuring the difference in mass of an object moving in different directions will yield the same results regardless of whether Nov 11 '15 at 15:46
• @hehe3301: The mass only changes relative to the observer. From your frame of reference you wouldn't experience a change, and if you were to move an object back and forth it would appear to you to gain mass equally when moved in both directions. To an observer that's 'still' relative to you, the mass gain of the vibrating mass would differ, but from your point of view it wouldn't. Relativity is wonderfully weird sometimes. Nov 11 '15 at 16:49

This answer assumes that Newton's laws of motion are in effect:

In order to accelerate a vessel to some speed, including speeds greater than the speed of light, energy will be required to accelerate the vessel. If the approximate mass of the vessel is known, and the energy consumption of your propulsion system is known, and your efficiency is known, you can determine your acceleration, and thus current speed.

Modern car engine control systems can monitor the amount of fuel that goes into the engine, and we can determine approximate fuel efficiency with certain basic tests. Based on this, in certain vehicles, we can determine acceleration, and thus speed based on fuel consumption.

This has no basis in relativistic physics, and is based mostly in newtonian physics. This probably is a good thing, since if we assume we can break the speed of light by reasonable means, relativistic physics are questionable.

• No. How can you measure fuel efficiency without knowing your velocity? No car control systems use fuel flow to determine velocity or acceleration. Fuel consumption has nothing to do with it... A wheel speed sensor is the oldest method to measure velocity. From this you can calculate acceleration. Accelerometers can also measure acceleration directly, obviously. GPS, LIDAR, RADAR, and even optical flow sensors can also measure velocity and acceleration. From this you can calculate fuel efficiency, but you can't go the other direction. Nov 12 '15 at 2:26
• Even if we assume purely Newtonian physics, disregarding the work done by Einstein et.al. let alone hypothetical FTL drive, the forces that act on a spacecraft in interplanetary or interstellar space are quite different from the forces that act on a ground-based vehicle on a body with an atmosphere, such as a car on Earth. For the spacecraft, by doing things just right, you can make huge changes to your direction of travel and velocity with absolutely trivial propulsive maneuvers. See the article Space Friction on TV Tropes.
– user
Nov 12 '15 at 18:48