Manned Trip to Mars and Back  

The distance between Earth and Mars when they are closest together, at opposition, varies between 100 million km and 57 million km, due mostly to the eccentricity of Mars’ orbit.  Any trip to and from Mars must take this into account.  The distance of 57 million km from M2 to the Earth’s orbit is indicated by a dotted line and the longer dotted line, to the right of E1, indicates 100 million km.

The launch from Earth must be so planned that the effective distance covered between Earth and Mars is as near to 57 million km as possible.  The closest opposition takes place every 15 years - the next in 2010 and the one after that in 2025.  This will be a good date to plan for - June 2025.

Diagram attached - Marsdgm

If the spaceship is launched when the Earth is at E1 in its orbit and Mars at M1, the spaceship will have the Earth’s velocity in its orbit of 30 km/sec, plus the shove from the rocket engines, to get it away from the Earth along the curve from E1 to M2.  The spaceship can then coast along until it meets Mars at M2 after about 200 days, when the Earth will be at E2 and Mars at M2.  The distance covered will be the length of the curved path from E1 to M2 i.e. approximately 550 million km. In effect, the spaceship will have  moved away from the Earth’s orbit by a distance of only 57 million km.  It is the same as using a long gentle slope against a steep hill, rather that a direct ascent to the top.

By the time Mars gets to M2 and the Earth to E2, 200 days would have elapsed.  From this moment onwards the Earth is rapidly pulling away from Mars so that when the Earth reaches E1 again, Mars will be languishing at M(x).  An immediate return trip cannot therefore be undertaken.  The tick marks on the two orbits indicate intervals of 10 days.

The explorers will therefore have to spend as much time on Mars as to allow for the planetary configuration to come into the correct relative positions to allow for an economic return journey.  This will come about when the Earth has passed through E1 twice and Mars will have gone once around its orbit.  Actually the best positions will be when the Earth is at E3 and Mars at M3 which happens after 2 years and 45 days have elapsed.  Since the journey from Mars has to overcome only the gravity of Mars, it will be more “downhill” than the outward journey, because the spaceship will be accelerated by the Sun’s gravity as well as the Earth’s gravity.  The return journey will only take about 130 days.

Note that when Mars is at its nearest to the Sun, its perihelion, at M(per) and the Earth is at its furthest from the Sun, its aphelion, at E(aph), the distance between the two planets is near  its minimum. Both the outward and return journeys would make use of  this fact, thus ensuring the most economical expenditure of fuel.
After about 1 ½ years, when the Earth is between E(4) and E(2), the Earth will be in the radio shadow of Mars, on the far side of the Sun, M(y) to M(z)..........There are no shortcuts in space travel.

The total time required for the outward journey, the time for exploration and the return journey will be about 910 days, or 2 years 6 months.  Astronaut Collins, who circled the moon in the command module while Armstrong and Aldrin landed on the moon, has worked out an itinerary requiring 2 years 7 months.  We beat him by one month if we follow the plan set out above.

Even if a mode of propulsion is discovered which will give considerably higher speeds to spaceships, the time required for the planetary alignment cannot thereby be affected.  Mars’ synodic period, opposition to opposition, is 780 days, which already comprises 2 years and 50 days!

Eben van Zyl