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Table of Contents
Orbital Mechanics
Rendezvous With Mars
Transfer Orbits
1. Changing Orbit
It is not easy to reach Mars in a short period of time. The most energy efficient method of getting there is to launch oneself into an orbit whose aphelion reaches the orbit of Mars and whose perihelion is the orbit of the Earth.
Leaving the Earth (e) we fire the rocket engine on the spacecraft in the direction of the Earth's orbital motion. This manoeuvre is called orbital insertion because it inserts the spacecraft into a new orbit.
Orbital insertion launches the spacecraft into a new orbit which moves outwards, towards the orbit of Mars.
If we do not have a sufficient increase in the kinetic energy of the spacecraft during orbital insertion, we will not reach the orbit of Mars.
2. Minimum Energy
The mission to Mars requires that a spacecraft change its orbit, from one that is essentially the same as the Earth's orbit, to an orbit which just reaches the orbit of Mars.
This is known as a Hohmann Transfer Ellipse. It is the minimum energy orbit that allows one to send the biggest payload using the least amount of rocket energy.
The perihelion of this orbit is 1AU (the orbital radius of the Earth), and its aphelion is 1.5AU (the orbital radius of Mars).
The semi-major axis of the transfer ellipse is 1.25AU.
Using Kepler's Law we can calculate the orbital period of the transfer ellipse, which turns out to be 1.40 years (about 17 months). This means that the journey to Mars will take about 8.5 months - one way!
3. Minimum Time
The journey to Mars can be shortened by giving it more kinetic energy at the orbital insertion point. This gives a much larger transfer ellipse.
The high energy ellipse will intersect the orbit of Mars much sooner than a Hohmann transfer ellipse, but it uses far more energy (rocket fuel), and therefore compromises the size of the payload that can be delivered to Mars.
Note:
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The orbital insertion takes only a few minutes and then the spacecraft literally "coasts" for the entire journey to Mars, following an orbital trajectory determined by the Sun's gravity.
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The time of orbital insertion (called the "launch window"), must be selected so that the orbital motion of Mars and the spacecraft cause them to converge simultaneously.
