Richard Campbell brought up an interesting idea in his recent Mars geek out show. Suppose you could travel to Mars accelerating at 1 g for the first half the trip, then decelerating at 1 g for the final half of the trip. Along the way you’d feel a force equal to the force of gravity you’re used to, and you’d get there quickly. How quickly? According to the show, just three days.
To verify this figure, we’ll do a very rough calculation. Accelerating at 1 g for time t covers a distance is g t2/2. Let d be the distance to Mars in meters, T the total of the trip in seconds, and g = 9.8 m/s2. In half the trip you cover half the distance, so 9.8 (T/2)2/2 = d/2. So T = 0.64 √d.
The hard part is picking a value for d. To keep things simple, assume you head straight to Mars, or rather straight toward where Mars will be by the time you get there. (In practice, you’d take more of a curved path.) Next, what do you want to use as your straight-line distance? The distance between Earth and Mars varies between about 55 million km and 400 million km. That gives you a time T between 1.7 and 4.7 days.
We don’t have the technology to accelerate for a day at 1 g. As Richard Campbell points out, spacecraft typically accelerate for maybe 20 minutes and coast for most of their journey. They may also pick up speed by slinging around a planet, but there are no planets between here and Mars.