Two spaceships with unlimited ability to accelerate at 1 g leave space dock, the 2nd exactly 1 second after the first. They both accelerate in the same direction. What is the maximum distance the two ships will be separated by.
2006-11-16 01:51:58 · 9 answers · asked by Cirric 7 in Science & Mathematics ➔ Astronomy & Space
well the velocity difference will not continue to grow to infinity, but it will grow until light speed, or near it is reached. That means the greatest possible difference between the two should be 186,000 miles
2006-11-16 04:35:54 · answer #1 · answered by SteveA8 6 · 2⤊ 1⤋
Looking at it without getting too technical:
Acceleration: constant
Velocity: linear growth
Distance: parabolic growth.
Since the limit for velocity is c, asuming the spacecrafts can reach this speed, the velocity will eventually become constant and acceleration become 0, so eventually the two spacecrafts will travel at c, some distance apart. The distance apart will be constant. Therefore there is a max distance, it won't be infinite. Since I don't have paper/pencil/calculator/time/mood to solve this, I'll leave it to somebody else to solve it.
I think you have to do it as the sum of a series, since every second the velocity of each craft increases by 9.8 m/s starting from rest until they reach c.
2006-11-16 04:43:51 · answer #2 · answered by Anonymous · 0⤊ 0⤋
By sheer luck, I could be right.
Distance is given by g time t^2 divided by two. Time span is one second. The distance at a given time between the two is
g/2 (t^2 - (t-1)^2) = g/2 (2t - 1).
Distance grows at the gt rate. t is growing and g is constant.
The longer the time, the bigger the distance is in newtonian universe. In einsteinian, hi Lorentz, how are you doing ?
The answer will be finite but from our referential. The transform will be a delicate derivative because relativistic influences are speed dependant and they are different. Time is also speed dependant. I'm no match.
2006-11-16 02:13:56 · answer #3 · answered by S2ndreal 4 · 0⤊ 0⤋
Im going to say 32 feet
Reason, acceleration of 1g is 32 fps per second.. and they only leave one second apart and they both accelerate exactly the same until they reach C..
Actually they will never reach C but .99999 the speed of C because their mass will approach infinity as they approach the speed of light
2006-11-16 01:57:23 · answer #4 · answered by Jonny B 5 · 1⤊ 0⤋
Since velocity = da/dt and distance = dv/dt the delay of even one second would cause the spaceships to have an ever increasing velocity difference, and hence, ever increasing distance.
That is, as time approached infinity, the distance between the spaceships would approach infinity.
Hope I'm correct!
2006-11-16 01:58:47 · answer #5 · answered by cfpops 5 · 1⤊ 0⤋
The first spaceship will always be going faster than the second. The distance between them will therefore continue to grow.
2006-11-16 02:05:45 · answer #6 · answered by ICH 4 · 1⤊ 0⤋
Infinity... since the first ship has an acc RELATIVE to the second by 1 g. So they will continue to get further and further from each other at the rate of 1g ....
2006-11-16 02:17:34 · answer #7 · answered by pitamm 2 · 1⤊ 0⤋
This totally depends on how long both space ships have been accelerating.
2006-11-16 05:46:45 · answer #8 · answered by Anonymous · 0⤊ 1⤋
given enough time, the width of the known universe
2006-11-16 03:23:22 · answer #9 · answered by Anonymous · 0⤊ 1⤋