This is not true, but depending on the relative position of the Earth and Mars, the amount of fuel required for the flight may vary significantly. About once in a year and a half, the most optimal conditions arise for a flight to Mars, and these optimal conditions are so much better than all others that any other time for sending spacecraft to Mars is simply not considered.
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There are several possible flight paths for the Earth-Mars route and not each of these flight paths implies a start from the Earth when the Earth and Mars are relatively close to each other.
However, returning missions to Mars are a matter of the future. Now, the probes and rovers are sent to Mars one way. For such a flight, a launch should take place when Mars and Earth are pretty close.
Mars and Earth achieve their closest convergence in moments called opposition of Mars. However, spacecraft are not launched precisely at times of confrontation.
They try to send the spacecraft along the trajectory requiring the least possible amount of fuel called Hohmann transfer orbit. This orbit works as follows: the spacecraft starts from the Earth’s orbit at the pericenter when the first impulse of the engine’s operation occurs. The purpose of this impulse is to increase the aphelion of the orbit so that it is at a point in the orbit of Mars on the other side of the Sun with respect to the starting point.
So, our goal is for Mars to be at the same point as our spacecraft. The period of the Hohmann orbit is 520 days, but since the spacecraft overcomes only half the orbit, this means that the path to Mars will have to take 260 days. The orbital period of Mars is 687 days, i.e. in 260 days, Mars will pass an angular distance of 136 degrees, while our device – 180 degrees. This means that in order for the spacecraft and Mars to meet, the launch must take place when Mars is 44 degrees ahead of the Earth (180-136 = 44). In practice, this means that we must launch a rocket with a spacecraft about 3 months before Mars and Earth are in opposition.
The reasoning given above refers to ideal conditions that do not always arise. Firstly, the spacecraft rarely moves along a clean Hohmann trajectory, since the orbital planes of the Earth and Mars are inclined at an angle of 1.85 degrees, which requires additional maneuvers.
Besides, there is a three-pulse scheme for launching vehicles to other planets of the solar system called MEGA (Moon and Earth Gravity Assist).
The essence of this scheme is that the spacecraft is launched into a geostationary orbit, where the engines make an impulse that increases the apogee of the spacecraft’s orbit and sends it to a point beyond the moon. At the apogee, the impulse again directs the directing apparatus back to Earth in such a way that it performs gravitational maneuvers near the Moon and the Earth and picks up additional speed. Finally, at the perigee of the orbit, the engines make the third impulse of the guiding apparatus on the transitional trajectory to Mars or another planet.
This approach was used during the launch of the Japanese Nozomi probe to Mars. Unfortunately, the gravitational maneuver near the Earth did not go as the Japanese scientists expected and as a result, the probe was almost lost.