Can a Slower Spacecraft Overtake a Faster One in Relativistic Travel?

[robertbogdon]

I've run into a scenario in a sci-fi rpg that I'm running and I haven't been able to come up with a satisfactory answer on my own. Assuming a ship traveling at .9999c, would it be possible for another ship traveling from the same origin to the same destination, but launched later, to arrive first, either by traveling slightly faster, or (and this hurts my brain) traveling slower?

 

[curiousphoton]

I've run into a scenario in a sci-fi rpg that I'm running and I haven't been able to come up with a satisfactory answer on my own. Assuming a ship traveling at .9999c, would it be possible for another ship traveling from the same origin to the same destination, but launched later, to arrive first, either by traveling slightly faster, or (and this hurts my brain) traveling slower?

Well, it depends. If your first ship traveling at .9999c left Earth and headed to the moon at Time A, and your second ship traveling slightly faster (.99999999c) left at Time B (1*10^-8 after...let's say) later, then the second ship would arrive at the moon before the first.

As for slower, you didn't say they take the same path, so technically the slower ship could arrive before the faster one if it's path was enough shorter. If they traveled in the same direction, the ship leaving later and traveling slower would always arrive after the first ship.

 

[robertbogdon]

Well, it depends. If your first ship traveling at .9999c left Earth and headed to the moon at Time A, and your second ship traveling slightly faster (.99999999c) left at Time B (1*10^-8 after...let's say) later, then the second ship would arrive at the moon before the first.

As for slower, you didn't say they take the same path, so technically the slower ship could arrive before the faster one if it's path was enough shorter. If they traveled in the same direction, the ship leaving later and traveling slower would always arrive after the first ship.

In general I'm assuming the same path, or at least close enough that it probably doesn't make a significant difference when traveling at those speeds. I guess the thing that still confuses me is how all of the works out from the point of view of an observer on Earth. My understanding, which could be wrong, is that from the point of view of someone on Earth, a ship traveling slower could reach the destination and return before the faster ship reaches the destination.

 

[curiousphoton]

My understanding, which could be wrong, is that from the point of view of someone on Earth, a ship traveling slower could reach the destination and return before the faster ship reaches the destination.

What makes you think that?

 

[robertbogdon]

What makes you think that?

In this case, the distance is about 17 light years. Really rough numbers, it's about 17 years from the point of view of the ship traveling at .9999c, and about 1200 years from the point of view of someone on Earth. Now a second ship traveling at .5c, it's 34 years from their point of view, but 39 years from the point of view of someone on Earth. Of course, that assumes I got all the math right.

At the very least, that leaves me with trying to figure out which ship would actually get there first. It certainly makes sense that the faster ship would get there first, but I have to say I'm still very confused. At this point I'm mostly trying to figure it out for my own benefit, it's a sci-fi game, physics works however I say it does, but I'd still like it to be as close to the real world as possible, ignoring some of the glaring errors I've already made.

 

[curiousphoton]

In this case, the distance is about 17 light years.

In what case? If it's the case I gave in my example (ship traveling from Earth to moon) than I assure you the distance is not 17 light years. When doing any type of calculation in life, ALWAYS ask yourself "Does my answer make sense?"

It didn't take Apollo 11 (17) light years to reach the moon in 1969. It didn't take them 17 years, or even 17 days.

 

[IcedEcliptic]

You have to consider the expansion of space as well, and the period during which the ship must brake, which would take a long time. I don't think you've given enough information to accurately answer you.

 

[Nabeshin]

In this case, the distance is about 17 light years. Really rough numbers, it's about 17 years from the point of view of the ship traveling at .9999c, and about 1200 years from the point of view of someone on Earth. Now a second ship traveling at .5c, it's 34 years from their point of view, but 39 years from the point of view of someone on Earth. Of course, that assumes I got all the math right.

At the very least, that leaves me with trying to figure out which ship would actually get there first. It certainly makes sense that the faster ship would get there first, but I have to say I'm still very confused. At this point I'm mostly trying to figure it out for my own benefit, it's a sci-fi game, physics works however I say it does, but I'd still like it to be as close to the real world as possible, ignoring some of the glaring errors I've already made.

Eerh... no. Okay let's do the example with two ships going a distance of 17ly. One moves at .9999c and the other at .5c.

We on Earth see the following:
.9999c: For all intents and purposes this is measured as c to those of us on earth. So we view the ship as taking 17 years to arrive at its destination (17ly/speed of light).
.5c: 17ly/(.5*c) is 34 ly. So we one Earth see this ship take twice as long as the first ship to arrive. Nothing tricky here.

On board the spaceships:
.9999c: The 17ly distance is shrunk to look like .24ly. So it takes them about .24 years, or ~3 months to get there from their perspective.
.5c: The 17ly distance is shrunk to look like 14.7ly, so it takes them about 29.4 years.

Now that we have correct numbers, what exactly is your question?