Planet Earthtoo saw that Earth could put a person in orbit, so they wanted to go to space too.
The planet Earthtoo is twice the diameter of Earth, with the same internal structure - the average density is the same as Earth so the total mass is 8 times that of Earth, and thus the surface gravity is twice that of earth.
LEtooO (Low Earthtoo Orbit) is lower than that on earth because even though the surface pressure is twice that of Earth, the scale height is half. However, Tooian scientists have decided that 200km is their target height for the first tootronaut to safely orbit.
Earthtoo also has a 24 hour day. They have no mountains, but a nice coastline on the equator from which to launch and take advantage of the rotation speed.
Tooian rocket scientists have perfected a conventional rocket engine with an Isp of 500 seconds independent of ambient pressure. They can be scaled in size.
Because of their deep admiration of Earth astronaut Don Pettit, they have studied his discussion of The Tyranny of gravity and worked and worked until they could build each stage of their rocket with 96% of its mass as propellant.
The mass of the orbiter with the tootronaut, life support, and substantial re-entry protection (twice the orbital velocity, twice the gravitational force) was an amazingly low 1000kg. They've been watching earth very carefully and took the best technologies. They sometimes call it the "Flying Tile" because of the substantial use of ceramic tile material.
Question: Based on the parameters below and situation described above, what is a rocket design that can put the tootronaut and orbiter into LEtooO? Please choose a widely accepted and recognized spaceflight simulator (Kerbal could be OK for example). Show enough of the answer that other people can independently run your design into orbit and verify that "yep, it works." How big is this rocket?
Use the following values:
radius of planet: 12740 km
rotation period: 24 hours
launch location: equator
surface gravity: 19.6 m/s^2
at surface: 2.4 kg/m^3
scale height: 3.8 km
mass of payload: 1000 kg
specific impulse*: 500 sec (any size engine, any ambient pressure)
stage dry mass: 0.04 of total mass when stage is fully fueled.
altitude of orbit: 200 km
orbital velocity: 15.8 km/s or thereabouts, for a circular orbit
orbit inclination: 0 degrees
(*) remember to use 9.8 and NOT 19.6 if you convert Isp to effective thrust velocity!