A Mars cycler (or Earth–Mars cycler) is a kind of cycler, a spacecraft with a trajectory that encounters Earth and Mars regularly. The Aldrin cycler is an example of a Mars cycler. Cyclers are potentially useful for transporting people or materials between those bodies using minimal propellant (relying on gravity-assist flybys for most trajectory changes) and can carry heavy radiation shielding to protect people in transit from cosmic rays and solar storms.
Earth–Mars cyclers A cycler is a trajectory that encounters two or more bodies regularly. Once the orbit is established, no propulsion is required to shuttle between the two, although some minor corrections may be necessary due to small perturbations in the orbit. The use of cyclers was considered in 1969 by Walter M. Hollister, who examined the case of an Earth–Venus cycler. Hollister did not have any particular mission in mind, but posited their use for both regular communication between two planets, and for multi-planet flyby missions. A Martian year is 1.8808 Earth years, so Mars makes eight orbits of the Sun in about the same time as Earth makes 15. Cycler trajectories between Earth and Mars occur in whole-number multiples of the synodic period between the two planets, which is about 2.135 Earth years. In 1985, Buzz Aldrin presented an extension of his earlier Lunar cycler work which identified a Mars cycler corresponding to a single synodic period. The Aldrin cycler (as it is now known) makes a single eccentric loop around the Sun. It travels from Earth to Mars in 146 days (4.8 months), spends the next 16 months beyond the orbit of Mars, and takes another 146 days going from the orbit of Mars back to the first crossing of Earth's orbit. The existence of the now-eponymous Aldrin cycler was calculated and confirmed by scientists at Jet Propulsion Laboratory later that year, along with the VISIT-1 and VISIT-2 cyclers proposed by John Niehoff in 1985. For each Earth–Mars cycler that is not a multiple of seven synodic periods, an outbound cycler intersects Mars on the way out from Earth while an inbound cycler intersects Mars on the way in to Earth. The only difference in these trajectories is the date in the synodic period in which the vehicle is launched from Earth. Earth–Mars cyclers with a multiple of seven synodic periods return to Earth at nearly the same point in its orbit and may encounter Earth and/or Mars multiple times during each cycle. VISIT-1 encounters Earth three times and Mars four times in 15 years. VISIT-2 encounters Earth five times and Mars two times in 15 years. Some possible Earth–Mars cyclers include the following:
A detailed survey of Earth–Mars cycler trajectories was conducted by Ryan Russell and Cesar Ocampo from the University of Texas at Austin, Texas. They identified 24 Earth-Mars cyclers with periods of two to four synodic periods, and 92 cyclers with periods of five or six synodic periods. They also found hundreds of non-ballistic cyclers, ones which would require some powered maneuvers.
Physics
Earth orbits the Sun in one Earth year, Mars in 1.881. Neither orbit is perfectly circular; Earth has an orbital eccentricity of 0.0168, and Mars of 0.0934. The two orbits are not quite coplanar either, as the orbit of Mars is inclined by 1.85 degrees to that of Earth. The effect of the gravity of Mars on the cycler orbits is almost negligible, but that of the far more massive Earth needs to be considered. If we ignore these factors, and approximate Mars's orbital period as 1.875 Earth years, then 15 Earth years is 8 Martian years. In the diagram above, a spacecraft in an Aldrin cycler orbit that starts from Earth at point E1 will encounter Mars at M1. When it gets back to E1 just over two Earth years later, Earth will no longer be there, but it will encounter Earth again at E2, which is 51.4 ∘ {\displaystyle 51.4^{\circ }} , 1⁄7 of an Earth orbit, further round. The shape of the cycler orbit can be obtained from the conic equation:
r = a 1 − ϵ 2 1 + ϵ cos θ {\displaystyle r=a{\frac {1-\epsilon ^{2}}{1+\epsilon \cos \theta }}}
where r {\displaystyle r} is 1 astronomical unit, a {\displaystyle a} is the semi-major axis, ϵ {\displaystyle \epsilon } is the orbital eccentricity and θ = − 25.7 ∘ {\displaystyle \theta =-25.7^{\circ }} (half of − 51.4 ∘ {\displaystyle -51.4^{\circ }} ). We can obtain a {\displaystyle a} by solving Lambert's problem with 51.4 ∘ {\displaystyle 51.4^{\circ }} as the initial and final transfer angle. This gives:
a = 1.60 {\displaystyle a=1.60}
Solving the quadratic equation gives:
ϵ = 0.393 {\displaystyle \epsilon =0.393}
with an orbital period of 2.02 years. The angle at which the spacecraft flies past Earth, γ {\displaystyle \gamma } , is given by:
tan γ = ϵ r sin θ a ( 1 − ϵ 2 ) {\displaystyle \tan \gamma ={\frac {\epsilon r\sin \theta }{a(1-\epsilon ^{2})}}}
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