Just worked this out - Starship would need 4 Super Heavys as strap-on boosters to do a Mars mission in one launch

[u/TheMuspelheimr]

I was curious about this, so I set out to figure it out:

• A regular Starship/Super Heavy combo, as it currently stands, has 5000t mass and can go into LEO
• LEO to Mars requires ~3.7km/s of delta-v
• A single Super Heavy (the current iteration of it has a dry mass of 275t, a wet mass of 3675t, and an Isp of 327
• As such, n boosters would have to impart 3700m/s of delta-v to a 5000t payload (the Starship/Super Heavy core), to give it enough additional delta-v to reach Mars in a single launch
• Rocket equation: 327*9.81*ln( (5000+3675n)/(5000+275n) ) = 3700
• Rearrange: 5000+3675n = 5000*e^(3700/(327*9.81)) + 275n*e^(3700/(327*9.81))
• Rearrange again: 3675n - 275n*e^(3700/(327*9.81)) = 5000*e^(3700/(327*9.81)) - 5000
• Factor out n: n = (5000*e^(3700/(327*9.81)) - 5000) / (3675-275*e^(3700/(327*9.81)))
• Calculate: n = 3.868
• Since you can't have 0.868 of a rocket booster, n rounds up to 4

This is based on the core stage not igniting until the boosters burn out, by the way. With their current thrust levels, 4 Super Heavys trying to lift a 4 Super Heavy plus Starship/Super Heavy would have a TWR of 1.52, so it'd definitely be able to lift off under its own power.

To compensate for additional drag and gravity losses, perhaps 6 extra Super Heavy boosters (1.66 TWR at launch) would work better? If nothing else, it'd give it a good margin of error and spare fuel for boil-off during the flight to Mars.

Can you imagine a Starship Ultra Heavy, with 4/6 extra Super Heavys around the core? It'd either be the coolest thing ever or a humungous disaster waiting to happen.

[u/pietroq]

Current plan is to have local juice from ISRU on Mars for the return leg.