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[10ebbor10]

Scoops would be magnetic.

[UXLZ]

Yes, p=mv. And kinetic energy = mv²/2. So if you only have momentum, you have no way to compute kinetc energy.

In that case then I see what you mean. You'd need either m or v so you'd get either

KE=¹/₂Pv
or
KE=¹/₂(P/m)²

*edit* Nope, that last one is wrong. It would just be P²/m
I think that may be right.

I might be screwing something up though.

[Urist Tilaturist]

No spacecraft captain would only have momentum, since measuring momentum usually involves multiplying mass by velocity. If he knew his momentum, he would also know his mass and velocity, and therefore his kinetic energy.

Is there a situation where a captain could measure momentum without knowing mass or velocity?

[~Neri]

If he had a reference point purrhaps? I don't know?

[TheDarkStar]

No spacecraft captain would only have momentum, since measuring momentum usually involves multiplying mass by velocity. If he knew his momentum, he would also know his mass and velocity, and therefore his kinetic energy.

Is there a situation where a captain could measure momentum without knowing mass or velocity?

If he hits something really fast? He could figure out the momentum, but he'd only get mass as a function of velocity and vice versa.

[Urist Tilaturist]

If he hits something really fast, he will not be measuring anything on account of being almost certainly dead.

I would expect that he would have instruments to measure his velocity, and know his mass, though of course that would change near light speed.

[wierd]

There's also the problem that is inherent to magnetic fields, which is that they extend to infinity with a falloff of interaction strength. This means that they can be interacted with by other strong magnetic forces.  Flying near a magnetar or other strongly magnetic object with the scoop on would be bad mojo.

[wierd]

this is not quite true. One can use a combination of a standard candle star, and positional parallax to compute one's velocity relative to the frame of the (2 or more) stars used to compute the parallax. Doing this for 3 reference vectors will constrain a nearly straight vector of motion.

granted, the degree of parallax is going to be very small, so you will need very sensitive equipment, but it should be possible with existing image processing tech.

[Urist Tilaturist]

He could measure his velocity from his acceleration if he knew his starting velocity.

[BurnedToast]

There's also the problem that is inherent to magnetic fields, which is that they extend to infinity with a falloff of interaction strength. This means that they can be interacted with by other strong magnetic forces.  Flying near a magnetar or other strongly magnetic object with the scoop on would be bad mojo.

Magnetic force drops off nearly exponentially with distance, so this is not really much of a problem unless you're flying VERY VERY VERY close... at which point you've already messed up somewhere. Space is really, really big and really, really empty - it's not like the ship captain is suddenly going to ram into a stray magnetar like it's some kind of galactic pothole or something.

Or, to look at it another way, gravity also extends infinitely but you wouldn't consider a physical scoop to pose a special risk of sucking the ship into a black hole due to it's extra mass, would you?

[Urist Tilaturist]

The chance of a spacecraft hitting anything in space unless it is aiming for it is near 0. This is true even in asteroid belts.

[Urist Tilaturist]

Orbit is a special case, since the craft must be at a certain speed to stay in that particular orbit and is constantly accelerating around the object (changing the direction of velocity and possibly the magnitude if the orbit is eccentric). Collision is only likely in that case if the planet has rings like Saturn's or if its low orbits are full of space junk. Even then, it is far more likely that for any reasonable length of time the craft stays in orbit, it suffers no major collisions.

[Sergarr]

A relativistic speed spacecraft can easily determine its own velocity by using http://en.wikipedia.org/wiki/Redshift#Doppler_effect
this.

No parallax needed.

[10ebbor10]

Uhm, not really. You just examine the Doppler shifting of the emission spectra. Since those emission spectra are known, deriving your speed from that is easy.

[wierd]

There's also the problem that is inherent to magnetic fields, which is that they extend to infinity with a falloff of interaction strength. This means that they can be interacted with by other strong magnetic forces.  Flying near a magnetar or other strongly magnetic object with the scoop on would be bad mojo.

Magnetic force drops off nearly exponentially with distance, so this is not really much of a problem unless you're flying VERY VERY VERY close... at which point you've already messed up somewhere. Space is really, really big and really, really empty - it's not like the ship captain is suddenly going to ram into a stray magnetar like it's some kind of galactic pothole or something.

Or, to look at it another way, gravity also extends infinitely but you wouldn't consider a physical scoop to pose a special risk of sucking the ship into a black hole due to it's extra mass, would you?

No, but I wouldnt have to worry about the very large scoop accelerating iron based micrometeorites or pockets of cold plasma (Or even the nuke plasma behind the vessel!) toward the scoop, and thus toward the ship either.  A magnetic scoop has its own series of hassles associated with it, and a big honking physical one stuck on the prow has its own as well.

In this case, since you are on course to a very distant (a few dozen to a few hundred light years) destination, any alteration of your course from even a slight tugging can be quite significant. Gravitational bodies would indeed present a hassle, even if they are not anywhere near strong enough to cause immediately noticable effects. It would be sufficient to throw you off course.

10ebbor10: That wont work, because you are not assuming that your reference frame is "stationary".  When we measure the doppler shift of receding galaxies and stars, we are assuming that the earth's reference frame is stationary, or can be treated as stationary. However, if the vessel is moving at a significant fraction of C, then what if the star you are measuring is moving towards the ship, while you are moving toward the start? The blueshift will be higher. Unless you know the velocity and vector of the reference body, you cant use it with the doppler shift calculation to get a discrete value for velocity. There is a significant variable that you are not accounting for.