Thread "Space Travel (a physics question)" in forum "Comic Talk and General Discussion *"

Posted at 7:01AM, Jan. 30, 2010

therealtj, you made a big mistake there, that distance is already HALF the distance to Mars. You're halving it again.

Whoops >_>

I guess I missed that part of your post.

Posted at 7:01AM, Jan. 30, 2010

Oh and by the way, just to pick at this old scab a little bit more, I'm still getting about a two-day travel time, and so did that German physics student friend of mine at the other site. Depending on what distance I plug in I get either a 42-hour or 49-hour flight time. The discrepancy seems to be that I'm ending up with a higher final velocity than 330,000 m/s. I keep getting 731,865 m/s.

2x9.81x2.73E10 = 5.356E11
SQRT(5.356E11) = 731864.74

So I guess the right answer comes down to which is the correct vF. Of course this really isn't important now that I've gone a different direction with the story but I'm sure it's still interesting just for its own sake. Or not.

Posted at 9:01AM, Jan. 31, 2010

OK, Mars at its closest to us (theoretically) is 54.6 million km. Half of that is 27.3.
The equations of motion are (according to my old highschool physics book):

s = 1/2(u+v)t
s = ut + 1/2 at^2
s = vt -1/2 at^2
v = u + at
v^2 = u^2 +2as

Acceleration is:
a = (v - u) / t

v is end velocity
u is initial velocity
t is time
s is distance
^2= squared…

You know u = 0
You know a = 9.8 ms^2
You know s = 27,300,000,000 meters

Given that, it shouldn't be too tricky to work out… shouldn't it? :(

I came up with 82.97 days half way (rounded), which is 165.94 days for the full journey. But I am SHITE at algebra and physics, so I don't trust that figure for a second.

If you did this, your rocket would never leave the atmosphere, let alone the ground. Since you're trying to break from Earth's gravity, your acceleration would have to be greater than 9.8 m/s^2 (being equal to that results in a net force of 0). Also, you wouldn't be spending half your trip accelerating through space, since the majority of fuel used for thrust is used to just break through the atmosphere. In reality, all you need to do is find a way to make it into the exosphere and out of Earth's gravitational pull. Remember, space has virtually no friction, so your ship doesn't need to accelerate anymore. All you need is to pick a speed at which your craft will be moving until you reach your destination.

Take a look at this graph:

Notice after the Saturn V's final stage the acceleration drops to zero. Also, keep in mind that your rocket should be optimizing the fuel it's using to lift itself. The sudden dips and rises in the graph are the points at which the rocket detaches one of it's stages making it weigh less and allowing the remainder of fuel to launch it faster than it would otherwise.

Essentially, the time of your trip varies greatly depending on two main factors:
1. Your rocket
2. Your fuel supply

Posted at 1:01PM, Jan. 31, 2010

If you did this, your rocket would never leave the atmosphere, let alone the ground. Since you're trying to break from Earth's gravity, your acceleration would have to be greater than 9.8 m/s^2 (being equal to that results in a net force of 0). Also, you wouldn't be spending half your trip accelerating through space, since the majority of fuel used for thrust is used to just break through the atmosphere. In reality, all you need to do is find a way to make it into the exosphere and out of Earth's gravitational pull. Remember, space has virtually no friction, so your ship doesn't need to accelerate anymore. All you need is to pick a speed at which your craft will be moving until you reach your destination.

Take a look at this graph:

Notice after the Saturn V's final stage the acceleration drops to zero. Also, keep in mind that your rocket should be optimizing the fuel it's using to lift itself. The sudden dips and rises in the graph are the points at which the rocket detaches one of it's stages making it weigh less and allowing the remainder of fuel to launch it faster than it would otherwise.

Essentially, the time of your trip varies greatly depending on two main factors:
1. Your rocket
2. Your fuel supply

That's broadly true, but it wasn't the question. We can basically assume that the craft in Wl Cid's question has already escaped earth's gravity well in some way. This is mostly a simple A-B situation. :)
The reason for the 9.8ms^2 acceleration isn't speed, it's for the effect on the crew. It's a roughly human scale measure to work around for a fictitious story from which you can extract a realistic time based on the maths.