Would it be feasible for a possible mars mission earth departure spacecraft to stay in earth orbit for a period of time prior to departure and gradually build up speed so that the journey would be faster and cheaper? and if there was any problem during the time they are accelerating they are just in orbit and not halfway between earth and their destination. The trip home would be alot longer but doing ths might reduce some of the risk involved.
Similar trajectories have even been suggested for lunar missions... It's POSSIBLE but has a LOT of downsides. As you accelerate, your orbit gradually rises higher and higher, which before too long puts you smack dab in the middle of the Van Allen Radiation Belts (all those charged particles from the solar wind whipped around the Earth by the Earth's magnetic fields, which generate a lot of radiation.) Such radiation plays heck with electronics over time and is downright dangerous to human life. About the only upside is that you can use low-thrust high-efficiency boosters like Solar Thermal rockets, VASIMIR, or solar electric rockets (plasma/ion engines) which have PHENOMENAL ISP (fuel efficiency) generally speaking, but have VERY low thrust levels, and so can only accelerate payloads over a period of weeks or months at a very low rate.
There have been some folks advocating a solar-electric space tug equipped with solar electric propulsion or VASIMIR engines that would slowly 'spiral out' an unmanned lunar lander to the vacinity of the moon... eventually your orbit is SO vast that it 'intersects' the moon's orbit, but then you have to reverse your thruster's direction and 'spiral in' to lunar orbit. Such a system, depending on the size of it's solar panels and number/power of it's ion thrusters, would take anywhere from a month to several months to get from LEO to LLO (low earth orbit to low lunar orbit).
For a Mars trip, it would basically require the switch to a nuclear thermal rocket or nuclear electric propulsion. Nuclear thermal rockets were designed and tested back in the 60's (NERVA, etc.) but were never developed and soon cancelled due to budget and environmental concerns, and possible treaty problems with orbiting nuclear powered equipment, etc. A nuclear electric propulsion system would use a nuclear reactor to generate electricity that would be used in an ion engine to provide propulsion, but the efficiency is not too good because most of the energy released by nuclear reactors is thermal, or heat energy, and conversion to electricity is both heavy, bulky, and not very efficient from a loss standpoint. Coupled with the very low thrust levels of ion propulsion, despite the high propellant gas efficiency of the rocket engine, it would be a very slow and expensive propulsion method, compared to nuclear thermal. Solar electric isn't really feasible for Mars missions because of the nature of the propulsion systems-- for low-thrust systems like this 'spiralling' out to their destinations, you start slow, and gradually over a long period of time accelerate to pretty high velocities, BUT then you have to reverse your thrusters in the middle of the flight and start slowing down so you're going slow enough when you get to the destination to brake into orbit. The intensity of solar power is about 1/2 what it is at Earth out at Mars, so you'd need TWICE as big a solar array to provide the same power as you'd need at Earth, all of which has to be accelerated by the low thrust engine and braked by the engine down to speeds low enough for a Mars Orbit Insertion (MOI).
So, while feasible, the problems are daunting, and there are VERY SUBSTANTIAL development programs required and a lot of hurdles both real and imaginary to overcome. Ion propulsion has been proven on Deep Space One and is being used on some other probes, but it's in it's infancy as a space propulsion system. Solar power is feasible for a power source for the engines, but it's low density and rapid falloff as you go away from the sun means it requires heavy, large, easily damaged solar panels, and even larger ones as you go toward the outer planets (that's why all the outer solar system probes beyond Mars are powered by NTG's-- nuclear thermal generators, which are essentially take the heat of plutonium decay and use that to drive a thermocouple to generate electricity, but the power density is VERY low (unsuitable to power anything much beyond instrumentation, certainly not enough for a viable Ion engine). Nuclear would also have to overcome all the resistance from Greenpeace types that are convinced launching a nuclear powered rocket, even one with an unactivated reactor in a 'safed' condition that wouldn't be activated until it's in orbit, would somehow lead to a global Armageddon if it went awry... plus possible diplomatic resistance related to the Space Treaty banning certain types of nuclear stuff in space. Then there's the budgetary problems, as to how to pay for it all, which is the largest and most fundamental problem.
Project Prometheus was going to revive nuclear thermal propulsion for a Mars trip by Constellation; it was cancelled almost before the ink was dry on the VSE...
Later! OL JR