Steps Towards Mars

Elon Musk has set an aggressive timetable to Mars which would aim to land men there by the end of the decade. How reasonable is it?

There have been many plans to send humans to Mars, and many timelines to do so. The latest projection from Elon Musk is not even his first. It was greeted by cynicism by his critics, and excitement by his fans. But the credibility or not of this is not a question determined by how you feel about the CEO of the SpaceX. It’s a question of engineering and physics, and can be answered objectively.

As I was writing this, Musk reiterated the goal with some specifics:

First, let’s break down the prediction. Musk intends for SpaceX to launch the first unmanned Starships in the 2026 window, then humans in what he calls the 2028 window (although it’s mostly in 2029 as we shall see). He acknowledges scope for slippage and so it may be that the human mission is delayed to the following window in 2031.

What is needed to do this? SpaceX must

• Recover the Superheavy booster and refly it, or be too constrained by engine production to achieve their goals.

• Get Starship to orbit

• Adapt Starship for interplanetary travel (e.g. power, radiation hardening, communications) and add landing legs.

• Rendezvous and transfer propellant between ships

• Increase the flight rate

Most of this is either in testing at the moment or well within the technical capability we have already seen from SpaceX.

Given that IFT-5 will likely attempt a catch of the booster this year, and they will keep doing it until they get it right through 2025, I will give them the benefit of the doubt that booster supply be sorted - and at least engines can be reflown if not whole boosters. Achieving actual orbit, rather than orbital speed but suborbital velocity as in flights 3 and 4, also seems close.

We don’t know to what extent SpaceX are working on adaptations for interplanetary travel and landing, but bearing in mind all the mentioned adaptations are needed for the Artemis Human Landing System contract, NASA would be quite unhappy if no work had been done on them. The notional target for that mission is also 2026, although it is likely to slip, so the work done on this ought to be aimed at being complete by that point anyway. Propellant transfer is set to be demoed next year as part of the HLS contract, and contrary to what some people seem to think I don’t think it will be a major difficulty once orbit has been achieved.

What is a more open question for me is if SpaceX will be able to fly a sufficient number of ships by 2026 to meet the initial goal.

The Next Three Windows

It is technically possible to fly from Earth to Mars at any point in time, but most of the time the required orbit would need a huge Δv to get there. The Mars window is when a transfer orbit connecting the two planets would have a lower Δv, and occurs for a few months every synodic cycle (the 26 month period between times when the Earth and Mars are in the same relative position). Here I calculate the transfer Δv starting from a 300km circular orbit with the same inclination as the transfer orbit.

At each departure date its possible to plot the cheapest transfer (with a travel time <250 days)

and from this we can see that each window has an optimal trajectory costing about 4,000m/s. This is measured from a circular LEO starting point. So for each of the following three windows, we know the Δv required and apply the rocket equation. For this, we should know something about the rocket.

The Landing

To land on Mars, Starship needs to perform a flip and burn. This entails slowing down from terminal velocity to zero when it is close to the surface. Terminal velocity is proportional to the square root of gravity, but inversely proportional to the square root of atmospheric density. With 38% of the gravity and 1% of the atmospheric density, this should make terminal velocity on Mars around 6 times higher than Earth.

Telemetry from the Starship flight 4 stream indicated terminal velocity was around 100m/s, so Starship will approach the ground at a spicy 600m/s - almost twice the speed of sound at Earth sea level. If we take the Raptor Isp in the near vacuum as 380 seconds, and the dry mass of the ship to be 100,000kg, then this would require roughly 17,000kg of propellant without carrying any payload.