On September 29, 2013, SpaceX performed the first supersonic retropropulsion (SRP) maneuver to decelerate the reentry of the first stage of their Falcon 9 rocket.
NASA asked if their EDL (entry, descent, and landing) engineers could watch and study SpaceX’s data, and SpaceX agreed. Beginning in 2014, NASA and SpaceX worked together for three years. They SRP analyzed SpaceX Falcon 9s for the NASA Propulsive Descent Technology (PDT) project. The F9 boosters were outfitted with special instruments to collect data specifically on portions of the entry burn which fell within the range of Mach numbers and dynamic pressures expected at Mars. Additionally, there were visual and infrared imagery campaigns, flight reconstruction, and fluid dynamics analysis.
There is a lot of fuel management issues for a SpaceX Mars landing. This is reviewed in the video below. If there was a fuel depot created on Deimos (Mars Moon) then it would become far easier and safer to land on Mars.
Mars’ thin atmosphere (1% of Earth) provides challenges not found on Earth or the Moon. A large, heavy spacecraft streaking through Mars’ thin, volatile atmosphere only has just a few minutes to slow from incoming interplanetary speeds to under Mach 1, and then quickly transition to a lander to slow to be able to touch down gently.
Using thrusters creates a shock front ‘bubble’ created around the vehicle by firing the engines somehow insulates the spacecraft from any buffeting, as well as from some of the heating.
EDL engineers now believe that SRP is the only Mars entry, descent and landing technology that is intrinsically scalable across a wide range and size of missions to shed enough velocity during atmospheric flight to enable safe landings. Alongside aerobraking, this is one of the leading means of landing heavy equipment, habitats and even humans on Mars.
There are still multiple unknowns for landing a spaceX Starship on Mars.
How a big ship such as SpaceX’s Starship would be steered and flown through Mars’ atmosphere?
Can fins be used hypersonically or will the plasma thermal environment melt them?
The amount of debris kicked up by large engines on human-sized ship could be fatal, especially for the engines you’d like to reuse for returning to orbit or to Earth, so how do you protect the engines and the ship?
Mars can be quite windy, so what happens if you encounter wind shears or a dust storm during landing?
What kind of landing legs will work for a large ship on Mars’ rocky surface?

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I’d add that Starship, having wings to allow aerodynamic control, is a lot better positioned to control an aerobraking or capture trajectory than your average space probe, which can only control it’s trajectory by expending fuel prior to hitting the atmosphere, and is then at mercy of the atmosphere.
“A large, heavy spacecraft streaking through Mars’ thin, volatile atmosphere only has just a few minutes to slow from incoming interplanetary speeds to under Mach 1, and then quickly transition to a lander to slow to be able to touch down gently.”
Generally speaking, it’s good enough to slow the ship down enough on the first pass to become gravitationally captured; As long as periapsis is inside the atmosphere, you will get another opportunity to finish the entry, and another, and another. This is called “aerobraking”. In practice this can take as many as a hundred passes, though you’d hardly want to do it that gradually for a manned craft.
If you do it in one pass it’s called “aerocapture”, and IS much more difficult. But I expect they’d do at least two passes for Mars, possibly 3.
https://en.wikipedia.org/wiki/Aerobraking
Why not add a fuel transfer near the moon orbit, to bring more fuel on the journey to mars ?
Because then you need to spend a lot of fuel getting the fuel and rocket to near the moon. Sure, you can reduce the fuel requirements to reach Mars by launching from lunar orbit instead of Earth orbit, but getting everything out there erases the advantage.
You might be able to do a gravity slingshot maneuver around the Moon on the way to Mars, and save maybe 1km/s worth of delta V, but it would narrow the launch window considerably.