To mars in one hour!

So it's 200 years in the future and propulsion has advanced to a degree impossible today. Mars needs this medicine to counteract a martian virus, they need it in one hour.

How many G's does the spacecraft pull and how close to c does it get.

Assume two part journey, each one 50 million miles, where you accelerate for 50 million miles and decelerate the other 50 million miles where Mars is 100,000,000 miles away.

Originally posted by sonhouse
So it's 200 years in the future and propulsion has advanced to a degree impossible today. Mars needs this medicine to counteract a martian virus, they need it in one hour.

How many G's does the spacecraft pull and how close to c does it get.

Assume two part journey, each one 50 million miles, where you accelerate for 50 million miles and decelerate the other 50 million miles where Mars is 100,000,000 miles away.

Why not use the tunneling effect? You can be there in an instant with normal G.

Originally posted by FabianFnas
Why not use the tunneling effect? You can be there in an instant with normal G.

I put it out just for the math problem. Do you know accel formulae?

I put up another one, to the moon in one hour, normal rockets.

I did the same thing for Mars and found out it is possible to get there in one hour with normal but very advanced rockets. Just was asking how many g's it takes to do that.

Getting to the moon in one hour took a fairly low # of g's, about 12, which may or may not be survivable by humans but I put the problem in terms of a fedex parts order, just a package.

One complication seems to be, if the speed gets near the speed of light, the relativistic affects of acceleration on speed. Presumably we are worrying about the time as perceived by an approximately stationary observer on the planet mars?

light travels at 670,616,629 miles per hour, so, to get 100,000,000 miles in one hour we have to get 50,000,000 miles in half an hour.

As d = vt+0.5at^2 we without relativity considerations we solve
0.5at^2 = 50,000,000 as t = 0.5 hours we have
a/4 = 100,000,000 so a = 400,000,000 miles per hour / per hour

as speed = at, the speed at half way is 200,000,000 miles per hour, we are travelling at about 1/3rd the speed of light at that point and relativity will have an effect.

Originally posted by iamatiger
One complication seems to be, if the speed gets near the speed of light, the relativistic affects of acceleration on speed. Presumably we are worrying about the time as perceived by an approximately stationary observer on the planet mars?

light travels at 670,616,629 miles per hour, so, to get 100,000,000 miles in one hour we have to get 50,000,000 mile ...[text shortened]... e travelling at about 1/3rd the speed of light at that point and relativity will have an effect.

So how many g's does the spacecraft pull? I gotaverage velocity of 27,777 miles per second and peak of 55,555 miles per second. At that kind of velocity there would not be much relativistic effect, maybe a few minutes but no matter what the relativistic effect, the package still takes an hour from the POV of Earth and Mars. The medicine might have a slightly longer shelf life but that would be about it as far as relativistic effects go.

When I started playing around with this, I was surprised you could get to Mars in one hour, given a propulsion system of sufficient power without violating known laws of physics.

Originally posted by sonhouse
I put it out just for the math problem. Do you know accel formulae?

I put up another one, to the moon in one hour, normal rockets.

I did the same thing for Mars and found out it is possible to get there in one hour with normal but very advanced rockets. Just was asking how many g's it takes to do that.

Getting to the moon in one hour took a fairl ...[text shortened]... t be survivable by humans but I put the problem in terms of a fedex parts order, just a package.

Relax. I wrote it as a joke, nothing more.
I'm sure that you know the math more than I do.

Originally posted by FabianFnas
Relax. I wrote it as a joke, nothing more.
I'm sure that you know the math more than I do.

I knew that! The math is simple, from S=(AT^2)/2 which is the distance covered accelerating at a certain rate and from that solving for T,
T= sqr root of 2S/A, so to get to someplace with zero relative velocity, you need to split that into two parts, one accelerating halfway so the S is half the total distance and then halfway you decelerate the rest of the way at the same rate so you arrive with not much needed in the way of delta V. In the case of Mars at 100,000,000 miles you go 50 million miles acel and 50 million miles decel and you reach a peak of 55,555 miles per second (about 0.3c) and an average of 27,777 miles per second (0.15c).

These are more or less non-relativistic velocities so the time difference for the rocket and Earth or Mars time would be about the same.

You need to do about 5000 G's to get to that velocity in 30 minutes. Kind of leaves humans out of the mix though....

The amount of energy needed for 5000 G's with say a 275 ton spacecraft, if the thrust was 100% efficient, would be about 160,000 hp. Of course with regular rockets you are lucky to 1/1000th of that so think 160 MILLION hp.

And you need to put out that much energy for an hour. Not an easy trick.

A mere 100 gigawatts. No big deal, eh.