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by T-A 535 days ago
m_ISS ~ 4.5e5 kg [1]

Rocket equation [2]:

m_0 = m_f exp(v_delta / v_e)

where

m_f = final mass, i.e. mass of ISS and the boosters

m_0 = m_f + propellant mass

v_delta = velocity change

v_e = effective exhaust velocity of the boosters

Let's try a high-thrust transfer from LEO to the Lunar Gateway's orbit via TLI (Trans-Lunar Injection) [3]:

v_delta = 3.20 + 0.43 = 3.63 km/s

For boosters, let's use the dual-engine Centaur III (because Wikipedia has mass and v_e data for it) [4]:

m_dry = 2462 kg

m_propellant = 20830 kg

v_e = 4.418 km/s

The idea is to attach n of these to the ISS. The rocket equation becomes

m_ISS + n (m_dry + m_propellant) = (m_ISS + n m_dry) exp(v_delta / v_e)

Solve for n:

n = m_ISS (exp(v_delta / v_e) - 1) / (m_propellant + m_dry (1 - exp(v_delta / v_e)) )

Plug in numbers and find

n ~ 32.4

So we need 33 Centaur III (and some way to attach them, which I optimistically assume won't add significantly to the ISS mass).

Total Centaur III + propellant mass: 33 * (2462 + 20830) = 768636 kg

Planned Starship payload capacity to LEO is 2e5 kg [5], so assuming that a way can be found to fit 7 Centaur III in its payload bay, we can get all 33 boosters to LEO with five Starship launches.

Why not use Starship itself? Its Raptor Vacuum engines have lower v_e (~3.7 km/s) [6], and if you want it back, you need to add fuel for the return trip to m_f. Exercise for the reader!

[1] https://en.wikipedia.org/wiki/International_Space_Station

[2] https://en.wikipedia.org/wiki/Tsiolkovsky_rocket_equation

[3] https://en.wikipedia.org/wiki/Delta-v_budget#Earth_Lunar_Gat...

[4] https://en.wikipedia.org/wiki/Centaur_(rocket_stage)

[5] https://en.wikipedia.org/wiki/SpaceX_Starship_(spacecraft)

[6] https://en.wikipedia.org/wiki/SpaceX_Raptor#Raptor_Vacuum

1 comments

Thanks for the numbers. I think it's still possible to create gists with .ipynb Jupyter notebooks which have can have latex math and code with test assertions; symbolic algebra with sympy, astropy, GIZMO-public, spiceypy

> and some way to attach them

Because of my love for old kitchens on the Moon.

(The cost then to put all of that into orbit, in today's dollars)

So, orbitally refuelling Starship(s) would be less efficient than 33 of the cited capability all at once.

This list is pretty short:

Template:Engine_thrust_to_weight_table: https://en.wikipedia.org/wiki/Template:Engine_thrust_to_weig...

What about solar; could any solar-powered thrusters - given an unlimited amount of time - shove the ISS into a dangerous orbit towards the moon instead of the ocean?

> and some way to attach them

There's a laser welding in space spec and grants FWIU.

Can any space program do robotic spacecraft hull repair in orbit, like R2D2? With laser welding?

Or do we need to find more people like Col. McBride in brad pitt space movie, more astronauts?

> sympy, astropy, GIZMO-public, spiceypy

poliastro

Is the task to fabricate a 3d mount to attach a gradual thrust mechanism to a NEO?