The Things I Think About When I’m Half Awake

I woke up this morning with a bit of an epiphany. I’ve been working on a post discussing selling points for the Mars NOW mission architecture, but that’s been postponed for the time being. One of the points that I was considering for that discussion is why I can get to Mars before SpaceX can get there with the Starship. This line of questioning brought me to my semi-conscious realization this morning.

The current plan for SpaceX to go to Mars is to send a cargo mission in 2022 and then a manned mission in 2024, both utilizing the Starship vehicle that is currently in development. This is a great plan, and if anyone can pull it off it’s SpaceX. That being said, there’s a really good reason that it makes more sense to send just one person in either the 2022 or 2024 launch windows.

One of the things that I learned at the Mars Society Conference last month is that not all Hohmann transfer windows are created equally. Because Mars has an elliptical orbit that is much more eccentric than Earth’s, the energy required to go from Earth to Mars varies depending on where the transfer orbit intersects Mars’ orbit. To illustrate this idea, this is what a normal Hohmann transfer between Earth and Mars would look like if both planets had a circular orbit.

Hohmann transfer with circular orbits

The green orbit is Earth, the red orbit is Mars, and the blue orbit is the Hohmann transfer from Earth to Mars (funny, the whole thing looks a little like my Mars NOW logo). This is the lowest energy transfer between the two planets because it is just tangential to both of the planets’ orbits. Because Mars orbits the sun more slowly than the Earth, the transfer orbit needs to be initiated when Mars is slightly ahead of Earth in its orbit. Since the transfer orbit captures Mars on the opposite side of the solar system from where it was initiated, the journey essentially takes half of a year (that’s a little oversimplified, but call it 6-8 months). This example is great for understanding the basic principle of the Hohmann transfer window, but the eccentricity of Mars’ elliptical orbit complicates the picture.

Hohmann transfer with intersection at perigee

This is a more realistic depiction (within the limits of my artistic skills) of what the transfer would look like taking into account the eccentricity of Mars’ orbit. This particular example depicts a transfer window at perigee. Sorry, that’s not the tasty Russian dumplings- that would be pierogi. Perigee refers to the point of an elliptical orbit that is closest to the Earth, and for the transfer to Mars this is the best case/lowest energy scenario. Unfortunately because Mars orbits the sun more slowly than the Earth, this ideal arrangement only occurs every 15-17 years. Last year was the most recent occurrence, and this alignment won’t happen again until 2033.

Hohmann transfer with intersection at apogee

This last illustration depicts what we’re looking at for a 2022 transfer window. Mars is at apogee- the opposite of perigee- meaning that it is at its furthest distance from Earth’s orbit. Because of the larger elliptical transfer orbit, it requires more energy than would be required during more ideal transfer windows. The transfer energy in 2022 is approximately 55% higher than it would be in 2028, which results in higher fuel requirements. Since it requires greater force (and more fuel) to accelerate a larger mass to the velocity associated with a particular energy level, minimizing mass reduces thrust requirements to establish a transfer orbit. In addition, since velocity has to be dissipated to capture Mars’ orbit on arrival, the fuel penalty for increased mass is basically doubled in comparison to a lighter vehicle.

These considerations underscore the eficiency of the Mars NOW concept as compared to Starship. Applying the 55% increase in energy requirements to the lower payload mass results in a much smaller performance penalty than if the same increase were applied to Starship. That’s not to say that it can’t be done or even that it shouldn’t be done, but it’s worth considering using a light efficient platform now and waiting until a less energy intensive window to send the larger vehicle.

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