Listen Now Download as mp3 from the show The Milky Way's local black hole QuestionJack Stott asked: Dear Dr Chris.
I have plucked up the courage to write to you with a question from a colleague of mine which I can't answer.
I have no idea why he wants to know this ( I think he reads too many science fiction comics or watches too much 'Star Treck' ) but here goes :
If an object of negligible size & mass is launched from a standing start in a vacuum, and is subjected to an acceleration force of 1 G  how long will it take to reach the speed of light.
Hope you are able to provide an answer, or even a formula to calculate an approximate result when and if you have the time.
Best Regards
Jack Stott BSc(Hon) Elec Eng Science Multimedia
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CommentsIt will never reach the speed of light. It would take an infinite amount of energy. This results from Einstein's theory of Special Relativity. However, from the perspective of anyone travelling on this craft, they will experience a contraction in the distances in their direction of travel. So although they can never get to 186,000 miles per second they can (theoretically), nonetheless, achieve a speed such that they can travel a distance that they may initially have measured (before accelerating) as 186,000 miles in less that 1 second as measured on their clocks. If I remember correctly this turns out to be the same time (to get to this speed) as would be calculated by Newtonian mechanics  I would need to check this with some maths to be sure. There are some unfortunate consequences of travelling this fast resulting from time dilation so that should return at some point you would find the earth you left having aged considerably compared to yourself. graham.d, Wed, 1st May 2013 There are many unfortunate consequences of travelling near the speed of light, microscopic specks of dust would be like express trains when you hit them and the CMBR would be blue shifted up to Gamma rays. syhprum, Wed, 1st May 2013 Yes. Forward Shields to maximum please Mr Scott :) graham.d, Wed, 1st May 2013
Given a proper acceleration "a" (the acceleration felt by the astronaut inside his ship) and denoted with "T" the proper time (the time measured by the astronaut's wristwatch), the spaceship' speed u, as measured from Earth, is given by: As stated above a particle subjected to uniform accleration as measured in its own frame of reference wil never travel at the speed of light. It will only come closer and closer to it. On the other hand its impossible to force a particle to accelerate at a constant coordinate acceleration, i.e. as measured in a particular inertial frame of reference. E.g. place a charged particle in a uniform electric field then the force on the charge would be constant but its acceleration would decrease with time. You can think of this as the (inertial/relativistic) mass increasing with speed and thus with time. Very nice Pete. yor_on, Thu, 2nd May 2013 All that relativity garbage is just that. Garbage. As you aproach the speed of light nothing changes. It doesn't take any longer to accelerate the last half of the way to the speed of light as it does the first half. When you acheive the speed of light nothing happens , nothing changes. If you keep accelerating at 1G twice as long as that then you will be going twice the speed of light. Specks of dust should be destroying the space station by now because for all we know the solar system and the entire galaxy could be moving away or toward one another at 100s of times the speed of light. Unless your Christopher Colombuses Queen of Spain and you beleive the ocean continues on to infinity and where your sitting is the center of the universe, the sun goes around the earth and this is ground zero and you are perfectly still. Did you measure our speed in the universe by the warehouse walls at the edge morons? What I want to know is where these idioitic concepts like Vaporizing or going back in time come from? Since you haven't invented a spacecraft that can accelerate constantly at a 1G acceleration you automatically asume from some erouneous candle light and horse era mathimatical scribble that you will vaporize at the speed of light which if you recall they also tried to sell us about breaking the SOUND barrier before it was possible. Why do you mathematical types persist at this nonsense. It takes 380 something days to accelerate to and PAST the speed of light as closely as I had calculated at one time but I cannot ever get a straight answer on this very pertinent question because of all the geeknoid scientific daydreaming about these infinite forces barring coming near the speed of light GETTING IN THE WAY. Shut up all ready you have no proof for all that hogwash. John B, Thu, 27th Jun 2013 Not worded quite correctly the post meant to compare the solar system and this galaxy moving toward or away from other galaxies (not within our own)at possibly 100s of times the speed of light. John B, Thu, 27th Jun 2013
There is some extra weirdness that happens close to the speed of light. I read an article recently about two ships traveling close to the speed of light attached by a rope....does it break or no. Length contraction and other effects.
Lorentz contraction in which frame of reference? Not in S, since "as measured in S they maintain the exact same distance apart". lightarrow, Thu, 4th Jul 2013
It does, as long as we give a 'inertial' preference to the ship under Pete. But what happens if we define the ship above as being 'inertial' too, at rest in a gravitational field? And if we assume the ship above to be at rest, with the ship under going for it at , ahem, full throttle (one constant uniform G acceleration) it becomes really intriguing :) Assuming a length contraction to be a symmetry in both directions (backward as well as forward of the ships motion) you can define them as being at rest, and that should make the best sense, possibly :) but you have a acceleration of matter to consider too, as well as the rope. A little like the (not infinitely) rigid pole you move, poking at the moon, with the 'motion propagating' in the rod at a approximate speed of sound, compressing and decompressing itself. Here you have particles of that matter constantly compressing (and decompressing?) relative each other as the 'force' of one G 'propagates in the matter, or should I assume that they are in a constant uniform state of compression? What I mean is that I find it tough to see that matter as being in a equilibrium as it is accelerated. yor_on, Thu, 4th Jul 2013
Think so :)
Ok Pete, I'll read it with interest. yor_on, Thu, 4th Jul 2013 Is this solution using two exactly equivalent ships Pete? Everything the exact same for both ships? As mass, acceleration, etc? If I assume them them being 'exact replicas' of each other in every aspect, accelerating equivalently, in a equivalently 'flat space', then they also should be able to be described as belonging to a same frame of reference I think? Wouldn't such a definition make their 'clockticks' equivalent too? And if they are, how do I from that get to different heights? yor_on, Thu, 4th Jul 2013
Ok, I think to have understood it now, thank you very much! I don't understand something. The way this article appears listed it seems as if lightarrow posted last in the thread. When I looked at it when I read the thread it no longer appears that way. What's going on here? Pmb, Sat, 6th Jul 2013
I'm not sure Pete, to me it boils down to if a Lorentz contraction is a complementary effect to a time dilation, depending on observer. If it's not complementary then you make eminent sense. If it is though, you still have to explain how a same frame of reference can give us different 'clock ticks'? Because that is how I read such a description, everything being 'equivalent', a 'flat space', 'exact replicas' of ships, etc. I would call it a same frame of reference, relative the ships involved? Like this possibly? One might assume the leading ship at each point of 'space' to present the exact same 'increasing acceleration' as the other 'trailing' ship have, in each moment, although later crossing that exact point having a further thrust than the first. (Considering as 'energy expended' now as they constantly accelerate.) Making the definition of one singular frame of reference for both wrong. And then we have 'simultaneity' too? So what it boils down too for me, is indeed, can I assume equivalent frames of reference to also share a same clock and ruler? If it can, then either this thought experiment fails to me as a idea, as it includes acceleration instead of uniform motion. Or, the string won't break as we now have moved from a acceleration, through (passing) SpaceTime points, instead using the 'eyes of a God', able to define two equivalently accelerating objects as being 'still', belonging to one same 'frame of reference'. It's the same question I asked myself. I wrote you twice an answer to your post, in which I was thanking you for your explanation of the problem, but it didn't appear. Let's see this time... under 4 days to reach 10% the speed of light. at 10meters per second^2 acceleration. here's my off the thumb calculation . light is 300 million meters per second speed. 10% of this is 3 million meters per second. gravity at 10 meters secone ^2 will get you to 3 million in 300,000 seconds. 1 hour is 3600 seconds. 300 000 / 3600 is 300/3.6 83.3 hours. which is 3 dyas 11.3 hours. againi used 10 instead of 9.8 for the speed of acceleration to make things simpler. to because the real acceleration is 2% slower. it's somewhere close. i would say under 4 days. if you wanna do the full calculation go for it. 10% the speed of light is fast as shit and very few celestial objects, as opposed to plasma winds, have been observed to move this fast. 3million meters per second is 3000 kilomters per second. the fastest asteroids appraoching earth, the few outliers beyond the 3 standard devitations are between 50 and 60 km/s . the vast majority 98% are between 30km/s and over 4km/s. 3000km/s is about 100 times faster the routinely fastest asteroids passing by earth. mercury, the fastest moving planet by far is 48km/s relative to revolving around the sun. mercuries orbit is influenced by relativistic effects due to the suns strong graviational field. and it's speed is only 48km/sec. the earth moves in the low 30's relative to the sun. the fastest object ever launched from earth was about 18 km/sec relative to earth and thus almost as fast as mercury relative to the sun. we are a LONG LONG way off getting to 3000/km/sec relative to the earth, or the sun. and remember, anytime you are launching in our solar system away from the sun. you are fighting the sun's gravity, which varies with distance of course. . guest, Thu, 8th May 2014 Ig = 9.8 m/sec/sec = 0.588 km/min/min = 35.28 km/hr/hr = 2116.8 km/day/day the speed of light is around 300,000 km/sec, so after 141 days you would be approaching the speed of light if you were constantly accelerating at 1 g. It's no big deal accelerating at 1 g, we are doing that all the time just lying in bed, but it would be a big deal if we accelerated away from the Earth at 1 g constantly because we would have to find a source of energy to do so. Richard, Sun, 5th Jun 2016 Over 3 years and dozens of replies and then finally someone who doesn't have their head stuck up their ..... finally answers the question. LOL. Artdodger, Fri, 24th Jun 2016 Yes, I lol'd as well. This topic got wayyyyyyyyy off track. YES you CAN break the speed of light, and NO you WOULD NOT instantly disintegrate NOR travel back in time. People sitting on earth watching you will never observe you break the speed of light, however you sitting on the ship accelerating at 1g constantly will break that speed like nothing ever happened, ...and when you flick on the lamp next to your bed on that ship in 141 days when you're traveling at the speed of light, the light from the lamp will move at the speed of light away from you like any lamp would on earth. (That's the speed of light^2 for you kids observing at home, however you'll never see it from your reference point, only the people on the ship will be able to see it. You'll end up just seeing a long stretched out line that is the ship). Robb1324, Tue, 30th Aug 2016 I suggest you read this article: https://en.wikipedia.org/wiki/Space_travel_using_constant_acceleration If you are thinking of things in a purely Newtonian way, the answer can be easily derived from the formula where time = the difference between the final velocity minus the initial velocity divided by acceleration. t=(vfvi)/a. It would take about a year given that vf is about 300,000,000 m/s and 1g acceleration is about 10 m/s. Doing the math, you get about 30 million seconds, or about 350 days. David Miller, Sat, 29th Oct 2016 The question isn't really valid in this universe. But to give an answer, you will NOT reach light speed, not from your reference frame or from any other. Sorry friends :( . 
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