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View Full Version : Query for mathematicians
Tony Mead 03-30-04, 02:34 AM If you launched a spsce craft and it travelled at 600 miles per hour but sat on it were 4 other crafts that the next one launched, travelled at 600 miles per hour, would they be travelling at 1200 miles per hour to an observer on the Earth or 3600 miles per hour, if the later by the time you launched the 5 craft it would be travelling at 160,000 miles per second, I was intreged if this is the correct answer, if a craft were invented to travel at light speed then launch a second at light speed would it travel at 22,000 times the speed of light speed?. I'm not volunteering for that mission. :eek:
mathman 03-30-04, 04:34 PM Your description of the various 600 mph crafts is confusing.
As for the second part, nothing material can go at light speed, although in theory you can get as close as you want. If a craft was travelling close to light speed and launched a second close to light speed relative to the first, the second craft would appear only slightly faster than the first as viewed by the original observer. The specific formula for addition of velocities is:
z=(x+y)/(1+(xy/c^2))
where x is the speed of the first craft, y is the speed of the second craft relative to the first, and z is the speed of the second relative to the observer.
Jaredster 03-30-04, 07:28 PM wow gj mathman.
Starthane Xyzth 03-31-04, 12:18 AM One cannot add velocity to that of light; if a spacecraft somehow could travel at lightspeed (i.e. if it were composed of pure energy, like the holoship in "Red Dwarf"), no smaller craft launched from it would go any faster. Also, if the second ship were launched directly astern, it would travel at the speed of light in the opposite direction - relative to a stationery observer. I suppose, relative to the first holoship, it would be receding at TWICE lightspeed, just as photons emitted from a bulb in opposite directions will separate from each other.
First. One does not add velocity in that fashion. The "classic" way is wrong; it's merely tolerated as a good enough approximation for when speeds are low. The Einsteinian method must be used if you're getting up to speeds comparable to that of light.
Second. No spacecraft ever built can go the speed of light or even close to it in any way that would let its velocity be measured to be going at or above the speed of light relative to a stationary observer outside it. Nothing goes faster than the speed of light, barring crackpot nonexistent theories about tachyons.
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Tony Mead 04-02-04, 04:16 AM Your description of the various 600 mph crafts is confusing.
As for the second part, nothing material can go at light speed, although in theory you can get as close as you want. If a craft was travelling close to light speed and launched a second close to light speed relative to the first, the second craft would appear only slightly faster than the first as viewed by the original observer. The specific formula for addition of velocities is:
z=(x+y)/(1+(xy/c^2))
where x is the speed of the first craft, y is the speed of the second craft relative to the first, and z is the speed of the second relative to the observer.
Thanks for your help, I could not understand what C^2 is could you expand, to clear up the confusion I meant each vehicle leaves the last one each time the last one reaches 600 miles per hour, this process repeating five times, in fact you would need 5 more vehicles to slow down and stop and five more to return very complex way to get around.
c<sup>2</sup> is the velocity of light in vacuo, c, squared.
mathman 04-02-04, 06:51 PM c is the velocity of light, NOT c*c!
Rappaccini 04-02-04, 08:50 PM He didn't write that, mathdude.
Fraggle Rocker 04-02-04, 11:03 PM If you launched a spsce craft and it travelled at 600 miles per hour but sat on it were 4 other crafts that the next one launched, travelled at 600 miles per hour, would they be travelling at 1200 miles per hour to an observer on the Earth or 3600 miles per hour, if the later by the time you launched the 5 craft it would be travelling at 160,000 miles per second, I was intreged if this is the correct answer.No, the key to understanding this is that this is not the correct answer. To say that you launch a spacecraft "and it travelled at 600 mph" omits the important details of how it attained that velocity. It must accelerate from zero (relative to the launch site) and it requires consumption of energy to reach any arbitrary speed.
Relativity says that if you have a string of ships and each one appears to be going 600 mph faster than the next one in line (from the perspective of either of the two ships), nonetheless the aggregate velocity differential between the two ships at the ends of the string is not linear.
The observed speed of any object compared to any other object can never be greater than c.
things travel faster than the speed of light.
http://radio.weblogs.com/0105910/2003/05/23.html
http://news.bbc.co.uk/1/hi/sci/tech/781199.stm
eburacum45 04-03-04, 04:15 AM Bah; those are only pulses superimposed on a beam of light which is itself travelling at light speed; nothing actually travels faster than light.
It is possible for shadows to exceed light speed, in the Hubble variable nebula, for instance; but of course shadows have no sustance.
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Starthane Xyzth 04-03-04, 10:44 AM The "footprint" of a laser pointed at the Moon can be switched from one edge to the other by moving the projector only 0.5 degrees: the point of light may apparently cross the Lunar disc faster than the speed of light, but it can convey no information from one location to the other. The beam itself, of course, always moves at c.
c is the velocity of light, NOT c*c!
If you are addressing me, Mathman, I know this. And it is stated in my post that this is so. Just pay careful attention to the punctuation.
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