Sure, given some provisos: 1) A high density, self sustaining fusion reaction, i.e., a contained plasma that has reached ignition temperature, which for deuterium-tritium occurs at about 100 million K, and has a fusion power output measured in TeraWatts (thousands of gigawatts.)
2) A thrust structure/magnetic containment system able to survive the incredible torrent of high energy neutrons that will be emitted by such a reaction. (Not to mention an efficient shielding system able to protect the passengers and cargo from such penetrating radiation!)
3) The ability to sustain such a reaction for days at a time enabling a vehicle to constantly accelerate at something near one g (even 1/5 g would be awesome!)
4) The ability to navigate in hyperbolic trajectories. The commanding officer of a fast moving ship will probably want to fly a modified or 'bent' hyperbolic trajectory that takes the vessel outside (above or below) the solar ecliptic--thus avoiding most dust lanes associated with comets and asteroid belts. Contact with even a 1 gram particle when moving at 1200 km/s will probably be instantly fatal to the ship as the relative kinetic energy is on the order of 720 MJ (or about the energy equivalent of 5 gallons of gasoline!)
We're still a long way technologically from such a vessel, however, given time, experience in space construction and operations and good ol' Frontier Innovation, I think that such a vessel ought to be possible in the future. Project Orion is the only thing that comes even close to these performance requisits, and a study of Orion gives a pretty good idea of just what can be done with current technology.
Is it just me, or are there others who think that to get "to Mars in 8-12 days" would require a lot more than 1g acceleration (and deceleration) ?? ....are we talking more like 10g to 20g ?
Presumably, with such a fast ship, one would take a more-or-less straight-line route at earth-mars conjunction (or thereabouts) ?
Anybody here savvy enough in orbital mechanics to be able to do a quick calculation ? (Thnx)
O.K., let's break this down. Assuming a straight line path (extremely energetic trajectories can be approximated by straight line paths. We will assume this to be the case.)
We will assume a constant 1 g acceleration to the half-way point, at which time the vessel does a "flip over" (which is arbitrarily assumed to be an instantaneous transition) and begins decelerating until the destination.
Relativistic effects are neglected.
The relation, Newtons Law of Motion for Uniformly accelerated motion D=1/2*(a*t^2) will be assumed to apply.
Mars' orbit is approximately 1.523 AU on average from the Sun. (CRC Handbook of Chem. & Phys. 2005.) Earth's is assumed to be 1 AU.
1 AU=149597870.691 km (taken from http://neo.jpl.nasa.gov/glossary/au.html)
Now d=1/2*(a*t^2) is our starting equation. Using algebra to rearrange terms to solve for t we get: t=sqrt(2*d/a) where d=distance to the half-way point (the flip-over point); a=sustained acceleration of vessel.
If we assume a Mars-Earth Conjunction, then we can expect that the mean distance between Mars and Earth at this point shall be about 0.523 AU, or about 78.24 million km.
The half distance is thus about 39.12 million km or about 3.912*10^10 m. Accelerating at 1 g or 9.80665 m/s^2 and plugging this into our equation gives us a "t" of about 8.932*10^4 seconds (or about 24.81 hours) Thus at conjunction, we can expect have our trip take about 49.62 hr (which is a little over an hour-and a half longer than two days!)
If the Sun were not an obstacle, and we could fly our ship on a straight line trajectory at opposition, the distance that need be covered is about 2.523 AU or about 377 million km. Thus the half distance (or 'flip over distance) will be about 1.262 AU or about 188.7 million km (or about 1.887 * 10^11 m.) Again plugging this into our Newtonian equation gives us a half-trip-time of about 1.962 * 10^5 seconds (which is about 54.5 hr) Thus total trip time could be about 109 hr or about 4.54 days. Incidentaly, the speed of the vessel at flipover will be about 1924 km/s!
If an avoidance menuver were incorporated into such a trip, so that our occupants did not have to take a suicidal dive into the sun (this would definately discourage frequent fliers!) then it does not seem unreasonable to assume that a trip of 5-8 days from Earth to Mars, even at Opposition, is not out of the question.
Very good ! ....I should have done that little calculation myself, before doubting the short flight time.
A couple of points about the opposition route : 1) a close fly-by of the Sun would provide a powerful slingshot acceleration (which would not be felt by the crew, in excess of the 1g spaceship acceleration), and 2) at opposition, the two planets are essentially going in opposite directions, with a big delta-V that would have to be made up by ship propulsion.
At conjunction the effect is not as drastic (the planets are moving in the same direction), but the earth is going quite a bit faster than Mars -- a significant delta-V that would have to be made up by ship propulsion.
True. The 'slingshot effect' as noted could be compensated for by bending the flight path above the plane of the ecliptic. As for the delta-v required for interception, for a ship accelerating at 1 g, whats a few tens of kilometers per second between friends?
