Al -Amal , Tianwen -1 , Perseverance . What do these vehicles sent to Mars have in common? All of them have arrived this year, and all of them departed Earth in late July 2020. That buildup in launch times was no accident. To reach the neighboring planet, space probes take advantage of a window of opportunity that opens only every 26 months. But why that window? And what trajectory do the ships that want to reach the red planet follow? A tour of the basic laws of mechanics allows us to answer these questions.
How can we modify the trajectory of an object that, in principle, would only obey the gravitational attraction of the Sun and the planets? Naturally, for this we must exert a force. However, in the vacuum of space there is no ground to walk on, no water to float on, and no air to propel us. If we exclude sunlight (the resource on which solar sails are based ), the only possibility left to us is the principle of action and reaction.
When a physical system expels a mass backwards, the conservation of momentum (the product of mass times velocity) implies that the rest of the system will be propelled forward. In practice, and for rocket engines, the resulting propulsive force is given by the ejected mass flux (mass per unit time) multiplied by the ejection velocity. This has two consequences.
On the one hand, said force does not depend on the speed that the rocket has already acquired. That is, unlike what happens with a car, accelerating does not become more and more difficult. On the other hand, the chemical combustion engines used in interplanetary probes cannot run continuously. This limitation is due to the small amounts of fuel that can be loaded on board, as well as the high mass flow required to achieve the required accelerations. As a consequence, once the probe is freed from Earth’s gravity, it is as if the motors run only for brief moments, causing instant changes in speed. To achieve their goal, such variations have to take place at very specific points in the trajectory.
Optimize the trajectory
To simplify the calculations, once the probe has left Earth, let’s forget about the gravitational attraction exerted by Earth, Mars and the other planets and imagine that the spacecraft follows the same orbit as Earth. That means that we start with a nearly circular path around the Sun, moving along at a respectable speed of 29.8 kilometers per second (km/s).