## General Considerations for a Mission to Mars

The mean distance between the Earth and Mars is approximately of 78,300,000 km., that is, roughly half the distance from the Earth to the Sun. As compared to the Moon, our boldest step in manned exploration so far, which is some 380,000 km away, Mars is at more or less 200 times the distance.

This obviously implies that the design of a Mars bound trajectory will be completely different from the "point and shoot" concept used in the Apollo missions.

The following table shows some orbital parameters of the Earth, Mars and Venus :

## Orbital Comparison

: Mars Venus Earth
Distance to Sun: 1.52 AU 0.72 AU 1.00 AU
Mean: 227,900,000 km 108,200,000 km 149,600,000 km
Max: 250,000,000 km 109,000,000 km 152,200,000 km
Min: 206,500,000 km 107,400,000 km 147,100,000 km
Eccentricity: 0.093 0.007 0.017
Period: 686.98 days 224.70 days 365.26 days
Inclination: 1.8x 3.4x 0.0x

Several important conclusions can be drawn from the above table:

Celestial bodies that will influence the trajectory: The orbital mechanics of the mission will be influenced gravitationally by the nearby celestial bodies. In the case of an Earth-Mars mission, the Earth, Mars and the Sun will be primary factors due to mass (in the case of the Sun) and proximity (Earth and Mars) As it can be seen from the table, Venus is sufficiently near to exert its influence. Probably many of the trajectories to be considered will lie very close to Venus and thus be greatly influenced by its gravitational field.

Eccentricity: According to Kepler's Laws , the planets revolve in elliptical orbits in which the Sun is at one of its foci. These elliptical orbits are described by their eccentricity, that is, how much different from a circular orbit they are.
In the case of the three planets that influence the trajectory (Earth, Mars, Venus) the values are reduced (maximum value is 0.093 for Mars). Based on that, we can admit as a first simplification to our model that the planets move in circular orbits around the Sun. Corrections for this difference will be applied in successive refinements of the model.

The same can be said with respect to the inclination of the orbital plane of both the orbits of Mars and Venus with respect to the plane of the terrestrial orbit. We will also suppose that due to the reduced value of the angle of inclination of these planes that they lie on the same plane as the terrestrial orbit.

Relative angular speeds of the Earth and Mars : The Martian year is roughly twice as long as the terrestrial year. This means that Mars' angular speed is half that of the Earth. The relative angular speeds of the Earth and Mars are very important factors to be taken into account in the determination of the trajectory. When launching from the Earth to Mars, ideally Earth should be much behind in the orbit to allow the spacecraft starting with the Earth's orbital velocity to catch up with the slower Mars. When returning from Earth to Mars the our home planet should ideally also be behind to be able to intercept the Mars bound spacecraft in the inner orbit.