Moon Icon Launch! And Journey to Mars!

Homework!
Time to test your rocket science skills! With a launch of the Lunar Icon Aldrin Cycler!
Lunar Icon Initial mass 300,000mt
Using Vacuum Raptor 3s with a specific impulse of 380sec
and a Max Thrust 2.94MN
How many Raptors will we need if the thrust to weight ratio is 1.5?
What will be the propellant mass if we need 2,000m/s deltaV to get to LLO?
What if we use the RL-10-C3 hydrogen fueled engines instead?
With a Max Thrust of 106kN and a specific impulse of 461 seconds.
How many will we need and what will the propellant mass be?
And if we used advanced propulsion like the Neutron Star Systems superconducting applied field magnetoplasmadynamic thrusters with a specific impulse of 2,500sec, what will the propellant mass need to be, to accelerate at 2m/s^2 x 10 days? And what will the final velocity be?
Hint: Or what would the final mass of each version be, Raptor and RL-10,
if they just head to Mars the slow way by Hohmann transfer assuming:
deltaV fom Low Lunar Oribt to Low Mars Orbit is 1,298m/s
145 Moon escape
92 Earth escape
388 Mars transfer
673 Mars capture
------------------------------------
1298 TTL LLO-LMO dV

Видео Moon Icon Launch! And Journey to Mars! канала Terran Space Academy