Is it true that you could get to Mars in 1 day at an acceleration (and deceleration) of 1g?

Question

I find this a rather startling fact, but apparently if you accelerate at 1g for half the distance and decelerate at 1g for the other half then you can get to Mars in 1 day. Is this right? How much reaction mass would you need, assuming you could chuck it out the back at a significant proportion of C? How much would you need to go the 4 light years to the nearest star? Is it conceivable that a spacecraft could generate enough power to maintain this kind of acceleration over a long period of time?

darkpheonix262: Fascinating, I will look into this, many thanks.

I'm very impressed with all your answers - Thanks!

Answer 1

Not quite!

Assuming that sufficient energy were available for constant acceleration, the distances covered over a given amount of time can be easily calculated with the following equation:

d = 0.5gt^2

...where g is the level of acceleration and t is the time involved using the same units. Solving for t, we get:

t = sqrt( d / (0.5g) )

Now, given the average orbital radius of both Earth and Mars, we have an approximate distance of 7.8x10^7m at closest approach. To traverse half this distance with a constant acceleration of 9.8m/s^2 would require:

t = sqrt( (7.8x10^10 / 2) / (0.5 * 9.8) ) = 89,214s

...or about 24.8 hours. Double this, and you get a total travel time of 49.6 hours. Still a very, very fast trip (considering current conventional methods would require many months or even years to reach Mars), but just a tad over 2 days instead of just a single day.

At Mars' furthest, it is about 3.8x10^11 meters away. Assuming the sun were not in the way, this distance would require:

t = sqrt( (3.8x10^11 / 2) / (0.5 * 9.8) ) = 196,915s

...or about 54.7 hours, for a total travel time of 109.4 hours.
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To answer the second part of your question would require knowledge of what portion of c your reaction mass could be ejected. As this speed v approaches c, the required mass would approach zero. But then, of course, the energy required to accelerate the mass to that kind of speed would approach infinity.

Obviously, no current technology can achieve such energy levels.

Answer 2

No. Distance covered at constant acceleration, starting at 0, is a*t^2/2. When Mars was at its closest approach back in 2003, it would have taken a little over 59 hours.

If your propellant speed is a sufficiently large proportion of c, half a kilo will do it. The force on your ship is mdot * v/sqrt(1-(v/c)^2), where mdot is the mass flow rate, and v is the speed at which matter is ejected. Divide the force by the mass of the ship to get acceleration. No need to correct relativistically for the speed of the ship, as your propellant mass will increase in the same proportion.

No current technology can provide that sort of sustained power.

Edit --off by a factor of sqrt(2) up there - more like 42 hours.

Answer 3

Yes, it's true, you could get to Mars in about a day with continuous acceleration and deceleration of 1 g. You can get by with a reaction mass as small as you like if you accelerate it to a high enough velocity. If you can think of a way to scoop up enough interplanetary dust and gas, say with a magnetic field extending from your spacecraft, you wouldn't need to carry the reaction mass with you. Back in the 1970s the British Interplanetary Society proposed an unmanned space probe to Barnard's Star, about 5 light years away. It would accelerate continuously for 5 years by ejecting pea-sized pellets of frozen deuterium-tritium mix and zapping them with electron beams. The resulting mini-thermonuclear blasts would accelerate it to about 60 000 km/sec, and the trip would take 50 years. It wouldn't decelerate at the other end, just fly past. Even with today's technology we could possibly build a continuous acceleration rocket by using a fission reactor and obtaining a few thousand tonnes of reaction mass from the asteroid belt.

Answer 4

The math is not difficult, but the science is.

Nobody has pointed out to this person that though it sounds easy to accelerate 1g (a good sports car will do it), nobody has come near to divising a ship that could carry enough fuel to accelerate it more than a miniscule fraction of the distance to the planets.

The fact is, all our planetary space shots use the orbital speed of the Earth (30 km/sec) to give them a start, and all have to rely on gravitational properties to swing them around from planet to planet.

Basically, ships have to spiral from one orbit to another to get anywhere in the Solar System, which is why they travel 100s millions of kms just to go to the nearest planets.

Nothing can travel straight A to B in the Solar System without expending masses and masses of energy fighting Solar gravity. You have to use the sun's gravity to get anywhere, and only use engine power briefly to spiral into a new orbit, or use a planet's gravity to get you into a new orbit.

Answer 5

No i do not think that acceleration at 1g could get you to Mars in one day, not even close. In order to visit other stars we will have to invent a type of propulsion system that does not use a lot of fuel as we still have to escape Earth's gravity. We would have to accelerate all of our mass to 7 miles per second to achieve escape velocity.

Answer 6

the truth is that in order to reach far away astrol bodies (planets, stars) matter based fuel will simply not do, reason, weight, and size os containment.
the solution, ZERO POINT ENERGY. it a long topic and complicated but go to these site to lean about it. and ZPE is real, achieving it on the other have is, for now, tricky

www.calphysics.org/zpe.
www.zpenergy.com
en.wikipedia.org/wiki/Zero_point

or the only other viable means is antimatter, which only a very very small emount has been made in the last decade or so, and for long term high scale star travel, that just wont do, hope this helps

Answer 7

Constant accelleration/decelleration covers distances suprisingly fast, but I was on a centrifuge ride at Space Camp when I was a kid, and the narration said that at constant accelleration and decelleration of 3Gs you could get to mars in some number of days. But even at 3Gs it was more than a day. Don't remember what the number is exactly, but I'm almost positive it was more than a day, and that was at 3Gs...