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Interplanetary Mission Design and Analysis

To launch a spacecraft from Earth to an outer planet such as Mars using the least propellant possible, first consider that the spacecraft is already in solar orbit as it sits on the launch pad. This existing solar orbit must be adjusted to cause it to take the spacecraft to Mars. The desired orbit’s perihelion will beat the distance of earth’s orbit, and the aphelion will be at the distance of Mars orbit. This is calledHohmann transfer orbit. The portion of the solar orbit takes the spacecraft from Earth to Mars is calledthe trajectory. Well, the spacecraft is already at periapsis. So, the spacecraft lifts off the launch pad,rises above the Earth’s atmosphere, and uses its rocket to accelerate in the direction of Earth’s revolutionaround the sun to the extent that the energy added here at periapsis will cause its new orbit to havean aphelion equal to Mars’ orbit. The acceleration is tangential to the existing orbit. After this briefacceleration away from the Earth, the spacecraft has achieved its new orbit, and it simply coasts the rest ofthe way. Getting to the planet Mars, rather than just to its orbit, requires that the spacecraft be insertedinto its interplanetary trajectory at the correct time so it will arrive at the Martian orbit when Mars willbe there. By using Lambert’s theorem to compute the porkchop plot, which gives the launch windowanalysis for launching spacecraft fro interplanetary missions, we come up with a launch arrival date pairthat gives a single, unique trajectory solution for getting into. The opportunity to launch a spacecrafton a transfer orbit to Mars occurs about every 26 months. To be captured into a Martian orbit, thespacecraft must then decelerate relative to Mars using a retrograde rocket burn or some other means. Toland on Mars, the spacecraft must decelerate even further using a retrograde burn to the extent that thelowest point of its Martian orbit will intercept the surface of Mars. Since Mars has an atmosphere, finaldeceleration may also be performed by aerodynamic braking direct from the interplanetary trajectory,and/or a parachute, and/or further retrograde burns.