View Full Version : near light speeds and accelerating in different directions

gannon

2007-Sep-11, 12:09 AM

Sorry if this is an easy question but I was wondering. For a set amount of thrust at near light speed you don't get the acceleration that you would get at slow speeds.

How does direction of the acceleration come into play? If you thrusted in the opposite direction you are going would it acceleration be the same as slow speeds? How about going at a 45/90/135 degree angle from the direction you are traveling?

grant hutchison

2007-Sep-11, 12:18 AM

Aboard your spacecraft, you find that you have the same thrust as usual.

It's only external observers, who are watching you zoom past at close to lightspeed, who will see an apparent reduction in your acceleration.

The relevant factor is called gamma (γ), and you can calculate it as 1/sqrt(1-v²/c²) where v is your velocity relative to the observer and c is the speed of light.

If you accelerate along the line of your direction of motion (either increasing or decreasing your velocity), your acceleration seems to be reduces by a factor of 1/γ³. Transverse acceleration goes as 1/γ². For angles between transverse and in-line, you need to add vectors to find out the apparent magnitude of the acceleration.

You can view the difference in acceleration as arising from time dilation and length contraction. To the outside observer, your length is contracted along the direction of travel by 1/γ, and your time runs slow by γ. When you accelerate transverse to the line of travel, your acceleration takes a double hit from the time dilation (1/γ²). When you accelerate in the line of travel, you get the double hit from time dilation and an additional one from length contraction (1/γ³).

Grant Hutchison

gannon

2007-Sep-11, 12:31 AM

another question along these lines would accelerating 90 degrees from your direction make it seem like to the outside observers that your velocity in the direction you where originally going is slowing down?

grant hutchison

2007-Sep-11, 12:40 AM

another question along these lines would accelerating 90 degrees from your direction make it seem like to the outside observers that your velocity in the direction you where originally going is slowing down?Not if you're accelerating cross-ways to your line of flight. If you kept that up (rotating the ship to keep your acceleration vector always at right angles to your velocity vector), you'd move in a circle at constant speed.

Grant Hutchison

gannon

2007-Sep-11, 12:50 AM

I mean not rotating the ship after you point it cross ways. Wouldn't you get in trouble due to your velocity getting up to near light speeds in both directions?

grant hutchison

2007-Sep-11, 01:00 AM

I mean not rotating the ship after you point it cross ways. Wouldn't you get in trouble due to your velocity getting up to near light speeds in both directions?In that case, your velocity would increase relative to our patient "stationary" observer. You'd follow a curved path, with your velocity vector gradually rotating towards your acceleration vector. To the stationary observer, your apparent acceleration would tail off, both as your velocity increased and as the acceleration and velocity vectors became more aligned (getting more of that cubed gamma effect). So you'd end up creeping towards lightspeed and never reaching it, in the usual fashion, except following a curved path.

Grant Hutchison

gannon

2007-Sep-11, 01:30 AM

If I understand you correctly it would seem that your velocity in the direction that you where going does slow down due to the acceleration and velocity becoming more aligned. Is this correct? What would the traveler experience?

I am asking these question just to make it clear to me because at slow speeds accelerating crossways to the original direction wouldn't effect the velocity you are going in the original direction.

grant hutchison

2007-Sep-11, 02:56 AM

If I understand you correctly it would seem that your velocity in the direction that you where going does slow down due to the acceleration and velocity becoming more aligned. Is this correct?

No. If the acceleration seen by the stationary observer is always transverse to the original velocity vector, then there can be no reduction in velocity along that direction. The acquired transverse velocity is just small, because the transverse acceleration starts out small and decays towards zero as the spaceship approaches lightspeed. So just as the relativistic spaceship can't increase its velocity very much by accelerating along its line of flight, it can't alter its velocity vector very much by accelerating transverse to its line of flight.

What would the traveler experience?The traveller would see a Universe increasingly shortened along her line of travel. Trying to keep her engine aimed at right angles to her original course, she'll find she has to point it more and more backwards along her current line of flight, because the foreshortening of the Universe is accentuating the angle between her current direction of travel and her previous direction. So she will feel that her present course diverges strongly from her previous course, while the outside Universe will see only a small angular deviation.

Grant Hutchison

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