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Is time the same throughout the galaxy?
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04-01-2017 5:11pm#1
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I wonder how extreme those effects can get?
It really does seem like making interstellar space travel a mundane type of travel like in sci-fi is going to be borderline impossible for a long time, and if people do leave it may be a one way trip where we say goodbye and don't really hear form them again.
Space is hard.
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If time dilation is affecting by the speed something is traveling at, could the way a person would experience time be different in different parts of the galaxy that would be traveling at different speeds?
Our star is flying through the galaxy at 70,000kph, if we went to another star traveling at a different speed would we be experiencing a significantly different rate of time?
Short answer: no.
Quick correction first -- you're missing a zero on your speed. We're doing a phenomenal 700,000 kph around the galactic centre, or 200 kilometres per second.
Unlike the Keplerian orbits of planets in the solar system where the orbital speed varies with the inverse square root of distance, the orbital speeds of stars in the galaxy don't change (much) with distance from the centre:
To account for this it is supposed that even though the density of luminous matter falls off with distance from the galactic centre, there must a substantial dark matter halo to account for the relatively constant rotation rate.
But even suppose we go to within a kiloparsec or so of the galactic centre where the orbital speed is only half of that at the Sun's distance. As the Sun overtakes such a star on the outside, the relative velocity of the two bodies is 100 kps. That's 0.03% of the speed of light. The time dilation is given by:
Plugging in our number:
So the time dilation is only half a part in ten million, on the order of about one second per year!0 -
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Closest Star is about 4.3 light years away so even if you could get close to the speed of light it's a decade long round trip.I wonder how extreme those effects can get?
It really does seem like making interstellar space travel a mundane type of travel like in sci-fi is going to be borderline impossible for a long time, and if people do leave it may be a one way trip where we say goodbye and don't really hear form them again.
Space is hard.
And if you look at the energetics we aren't going to get close to the speed of light, because that energy could be used to send loads of probes at half light speed.0 -
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Gentlemen, we really are playing/dreaming here, aren't we?
tac
Yes and no. Probably yes, because the EMDrive is likely a physical impossibility (and seems to violate the principle of conservation of energy). But if a propellantless drive is possible, there's a bit of a hole in this part of your argument:3. According to calculations based on the NASA prototype (which yielded a power estimate of 0.4 N/kilowatt), a spacecraft equipped with the EM drive could make the trip to Pluto in less than 18 months. That’s one-sixth the time it took for the New Horizons probe to get there, which was traveling at speeds of close to 58,000 km/h (36,000 mph).
Sounds promising, right?
Well, not really........
4. It would take a ship equipped with EM engines over 13,000 years for the vessel to make it to Proxima Centauri. Getting closer, but not quickly enough! and until such time that technology can be definitively proven to work, it doesn’t make much sense to put our eggs into this basket.
What you're ignoring here is that current chemical rockets are the 'hot air balloons' of space travel. A hot air balloon carries fuel, right? It's usually propane, but it's not used as a propellant. Its function is to get you up to higher altitudes where the winds can carry you somewhere useful (though only if they're blowing the direction you want to go). A few tanks of propane (plus lots of wind) can take you round the world.
An interplanetary chemical rocket is like that. The amount of fuel required to get to Pluto is so improbable that no chemical rocket is ever going to do it -- not in a straight line, anyway. We would need about a gigajoule of energy per kilogram of payload to get from Earth to Pluto. The problem is that the gigajoule must be provided by other fuel which itself adds to the weight. We end up with an exponential problem -- the well known rocket equation. When we put in the numbers, it turns out that for LOX + kerosene with an exhaust velocity of about 3 km/sec we need 1700 tonnes of fuel for every kilo of delivered payload, and it takes 20 years to get there. Want to get there in half the time? -- that'll be 4500 tonnes of fuel per kilo. Half the time again? -- well over 100,000 tonnes per kilo to get to Pluto in five years. Not happening!
That's not how we get to Pluto, of course. Our fuel mostly just gets us aloft (like a hot air balloon), from where we can use Earth's orbital energy around the Sun to point at our next target. After that it's a series of gravitational slingshots with a final kick from Jupiter to send us on our way. The beauty of the slingshot is that its effect is independent of the spacecraft mass, and provides the same acceleration regardless.
Now, the thing about those NASA figures is that the speed given for the New Horizons spacecraft is the speed it left Earth on the way to Mars. New Horizons took a relatively direct route to Pluto, with just Mars and Jupiter flybys. It hit its maximum speed of 25 km/sec on the Jupiter slingshot, with the arrival speed at Pluto being the residual velocity after slowdown by the Sun's weakening gravity. The point is that the New Horizons flight time had relatively little to do with its own engines, and everything to do with the trajectory it took. A launch delay in 2006 nearly added four years to the flight time, as it would have had a more distant Jupiter encounter.
When NASA says an EMDrive craft would get to Pluto in 18 months, we are talking about a completely different beast. A chemical rocket coasts from planet to planet, stealing momentum in slingshots while all the time being dragged backward by the Sun. It can't be compared to a propellantless, and therefore constant mass, craft. The (improbable) EMDrive provides a small but constant acceleration. We can't just say that because it gets to Pluto six times faster that it will take one sixth of the New Horizons time to get to Proxima Centauri.
To do the sums right, we need to know what constant acceleration NASA was assuming for the EMDrive craft. (I think the force per kW is different from what you gave, but in any case we're only interested in the resulting acceleration on the whole craft). This turns out to be a quirky little integration problem, but I luv me sums, so here goes.
Let's call the constant acceleration. An EMDrive will never get us off the surface of the Earth, so we assume we've left Earth by other more conventional means and are now still in its vicinity climbing out the Sun's gravitational well. Our constant acceleration is offset by the Sun's pull in the opposite direction:
I've shown the total acceleration as a function of radial distance, r, since the Sun's gravitational pull depends on that. Now we recall some basic definitions from mechanics and do a little differential jiggery pokery:
Now we equate terms from the two previous equations and integrate both sides with respect to r:
Two things to note: the Earth's orbital velocity is of no concern to us. Without gravitational slingshots we are only interested in radial velocity, so we will set the constant of integrationto zero. We've taken the indefinite integral but since we are interested in the flight time from Earth to Pluto, we need a lower-bounded integral starting at the Sun-Earth distance,
:
Now that we have an expression for velocity as a function of radial distance, we do some more jiggery pokery to get the time as a function of distance:
So now we can just integrate over the distance from Earth to Pluto to get the time taken at acceleration
Now, as it happens, this integral does have an analytic solution. But it's frickin' scaldy!
Boiling the constant parts down to simple variables, Wolfram Alpha gives it as:
I don't think I have enough buttons on my calculator to work that one out. Sometimes it's easier to just write your own numerical integration, which is what I've done in this case. That allowed me to combine a goal-seeking algorithm to look for the value of
It turns out that the required acceleration is a measly 7 millimetres per second squared, less than a thousandth of a g on Earth. But this builds up relentlessly. It may get to Pluto six times faster than New Horizons but it flashes by Pluto at twenty times the speed, 280 km/sec. Now essentially free of the Sun and still accelerating it gets to Proxima Centauri not in 13,000 years but in 106! Admittedly you would flash by Proxima at a couple of tens of thousands of km/sec, which may not be exactly what you wanted.
But increase the acceleration by an order of magnitude -- still less than 1% of a g -- and you get there in 33 years. Even if you start decelerating half way to rendezvous with the star, you get there in a human lifetime. Suddenly we're talking proper space travel.
... pity the EMDrive is probably a delusion. :pac:0 -
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On the other hand, without time dilation the speed of light would be different in different reference frames, it would probably be possibly to violate causality, and the universe as we know it wouldn't exist. Compared to that, a few extra sums for the GPS seems a fair trade.Without time dilation, If we didn't have to make the corrections gps would just be easier to do. coordinates would not drift
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. An EMDrive will never get us off the surface of the Earth, so we assume we've left Earth by other more conventional means and are now still in its vicinity climbing out the Sun's gravitational well. Our constant acceleration is offset by the Sun's pull in the opposite direction:
to zero. We've taken the indefinite integral but since we are interested in the flight time from Earth to Pluto, we need a lower-bounded integral starting at the Sun-Earth distance, 
:
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