Another thought experiment

[Robert TG]

There is a thought experiment of a person standing inside a stationary elevator on Earth and comparing this to another man standing inside an elevator in deep space that is accelerating at the rate of 1g. (1g is the acceration equal to the force of gravity.)
Both men would feel the same equivalent effect.

Now the acceleration required to equal earths gravity at sea level is as exactly 9.80665 m/s2 (approx. 32.174 ft/s2). This is equivalent to accelerating from 0 - 100 kph (62 mph) in 2.83 seconds. My car can’t do this but this accerleration is easily obtainable with modern engines and rockets.


So taking this a little further, let us imagine a man leaving Earth in the deep space elevator (space ship) has all the supplies and comforts that he requires to make a very long journey. To add to his comfort and supply him with artificial gravity his elevator accelerates at a constant rate of 1g. He lives in his 1g acceleration container traveling in one direction for a year.

Here are two questions that are easy to answer if you think about it.

Question one: At the end of one year approximately how fast will he be traveling?

Question two: How long (approximately) will be his entire trip for him to return to Earth safely?

The questions are not hard but the answers are interesting. :eartoear:

[Radar]

He would end up travelling at the speed of light after he had travelled for approx 105653 seconds?

I have no idea how long his trip woud take though. It must be some kind of trick question.

[Astro Dave]

Hmmm, this is a cranially challenging question. I'm enjoying sitting back and watching the results of these little quizzes we have going.

Does the winner get an MyAstroSpace.Com T-Shirt, key ring, mousepad or bumper sticker?

[Robert TG]

Radar, you are correct, our traveller will reach light speed by travelling in a spaceship accelerating at 1g.

I estimate that he would reach this speed in just under 354 days.

At this stage his ship would still be accelerating at 1g for the next 11 days to supply him with the artificial gravity and to complete the "one year" mission.

Our traveller would still be feeling comfortable as if he was in Earths gravity.

What I find really interesting about this is that it doesn't take incredible engine speeds to reach light speed, and that light speed could be reached comfortably in a year. From the point of view of the traveller, He is still accelerating for 11 days after he has reached what we have calculated as light speed.

Of course, with my understanding of relativity, our travellers clock has slowed down and stopped. From our point of view, he never makes it to a full year and never notices any difference.




The second question is not hard and not a trick question. After travelling for a year the process of turning around and returning home will take another three years. First year is the mission, second year would be to slow down to change direction at the same 1g rate, third year accelerating back to speed in the reverse direction and the forth year slowing down to land safely back on Earth.

What I think is interesting with this point is that we so often see Sci Fi films that have spaceships accelerate to light speed in an instant and turn quickly. Somehow the occupants are free from inertia, which would be a real problem to anyone changing course in space. Still you'd need good deflecting shields, as a collision with a piece of dust at these speeds would be catastrophic

[Robert TG]

Relativistic Rocket
A controller based on Earth is monitoring a space-ship moving away at a speed 0.8c. According to the theory of relativity he will observe a time dilation affecting the clocks on the ship and slowing them down by a factor of 0.6, even after he has taken into account the Doppler shift of signals coming from the space-ship. If he works out the distance moved by the ship divided by the time elapsed as measured by the on-board clocks, he will get an answer of 4/3 c. This means that the occupants of the ship are traversing the distances between stars at effective speeds greater than the speed of light when measured with their clocks. From the point of view of the occupants, it is the distance between the stars which is contracted by a factor of 0.6 and they also agree that they are covering the known distances between stars at 4/3 c.

This is a real effect which in principle could be used by space travellers to cover very large distances in their lifetimes. If they accelerate at a constant acceleration equal to the acceleration due to gravity on Earth, they would not only have a perfect artificial gravity on their ship, but would also be able to cross the galaxy in only about 12 years of their own proper time.

However, this is not true FTL travel. The effective speed calculated used the distance in one reference frame and the time in another. This is not the real speed. Only the occupants of the ship benefit from this effective speed. The controller will not see them travelling large distances in his lifetime.