Euroluna expects to put a landing craft (ROMIT) on the Moon in accordance with the X-prize rules.

But in addition to the standard constraints, we have a few more...

• Low Cost
• Reliable Design
• Optimize our design efforts (do what we are good at)

We therefore expect to go to LEO on a piggyback ride.

We will make a very light combination spacecraft-rover.

We will choose a route that requires as little energy as possible.

My job is to make the software that is used to calculate the trajectory to the Moon. The goal of course is to design the best possible route taking lots of factors into account:

Low expenditure of fuel.
Reasonable transfer time.
Land on the right side of the Moon and in sunshine.
As few rocket burns as possible.

Going to the Moon means going up a gravity well E = GM/RMoonDist - GM/REarth . This energy is approximately equal to a v of 11 km/sec. By starting from LEO (800 km above Earth) we get 8.9 km/sec of potential and kinetic energy, which means that we have to provide 2.1 km/sec. In addition we have to brake to get safely down to the moon’s surface, which is at least another 1.5 km/sec, or a total of about 3.6 km/sec.

This calculation assumes that we don’t have to spend energy to change our velocity on the way.

In practice we would like to go into a nearly circular orbit around the moon before landing in order to get time to find a suitable landing spot and in order to measure our exact velocity differential. This way we will know how much energy we have to remove in order to land safely (with a speed below 5 m/sec).

We carry fuel for about 5 km/sec.

Therefore we are looking for ways to get free v. We are looking at two:

1. Using the Sun’s attraction.
2. Using the Moon’s attraction.

The Sun’s attraction is used when we move in the direction of the Sun to give a little extra acceleration. It also helps bend our trajectory to a shape that fits better with the moon’s orbit.

The Moon’s gravity is used as the band in a sling shot to accelerate ROMIT. In order to get maximum effect, this requires us to pass very close to the Moon where the gravity is strongest.

But if we are already close to the Moon, why not just land?

There are two reasons:

• The speed would be too high.
• We would be landing either in darkness or on the side of the Moon that faces away from Earth.

We need to change the trajectory so that we approach the Moon with a difference in velocity that is only slightly larger than 0.

More to follow

Tor Foss Mortensen