Can planet Earthtoo put a Tooian in orbit too?

Question

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?

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Use the following values:

radius of planet:   12740 km
rotation period:    24 hours
launch location:    equator
surface gravity:    19.6 m/s^2
atmosphere density 
    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
    (derived)
orbit inclination:  0 degrees

(*) remember to use 9.8 and NOT 19.6 if you convert Isp to effective thrust velocity!

Answer 1

Pettit's article doesn't mention the advantage of staging at all. All he's actually saying is that a hydrogen fueled single-stage-to-orbit launcher can't work on a planet 50% larger than Earth. Staging doesn't invalidate the Tsiolkovsky equation but it does work around the need to attain extreme propellant mass fractions in a single stage.

As Hohmannfan notes, the Isp and mass ratio assumptions in the question as written are pretty unrealistic, but I think the Tooians can do this with Apollo-era technology and a 4-stage rocket 4 times the size of a Saturn V.

I think the gravity losses are a bigger concern, so I aimed for 20km/s of total ∆v.

Stages:

• Payload: Stripped Mercury, 1 t
• Stage 4: Basically a shortened Centaur, 2 RL10-A3, 13t, 6038 m/s
• Stage 3: 3x J-2, 135t, 5535 m/s
• Stage 2: 5x M-1, 1500t, 5462 m/s
• Stage 1: 40x F-1, 9500t, 3261 m/s

Total 11149 tons -- Saturn V is about 3000.

The fuel fractions on the stages are 80%-84%, since I assume the larger structure and higher gravity are concerns. Generally it needs twice as much engine per mass as Terran rockets, which also contributes to dry mass. Here's my worksheet:

The three upper stages are smaller than the three stages of the Saturn V launcher; there's no question that these could be built. The M-1 engine was never completed and flown but got well into development, and there's no reason to think it wouldn't have been successful. It could be replaced on a 6:1 basis with J-2s if not. The first stage is certainly hefty. Simply finding enough stage-base area to mount so many engines requires that the stages be short and squat (or perhaps conical, like the Russian N-1 design); this means that drag will be of greater relative concern than on Earth.

The max accel values assume that each stage continues burning at full thrust until fuel is expended. Saturn V shut down center engines partway through the burns on the first two stages in order to reduce g-force on the crew, peaking at about 4g. I assume Tooians are a little tougher, but if necessary, this rocket can do something similar. Obviously the first stage needs better than 2g initial acceleration (=1:1 TWR) for liftoff. The initial acceleration of the other stages may seem low, but note that Saturn V second stage lights up at only 0.8g and third stage about 0.55g, while the Tooian rocket maintains better than 1:1 TWR at all points until the last stage.

Answer 2

First, we need to find what additional $\Delta v$ the rocket needs to achieve orbit. Earth LEO velocity is for instance 7.8 km/s, but the real $\Delta v$ needed is somewhere around 9-9.5km/s because of drag and gravity losses. That is an additional 1.5km/s. The first thing I notice is that Earthtoo has a denser atmosphere, but that the scale height is lower. Here is a plot comparing the atmosphere to ours:

After just a few kilometres, the density is in fact lower. Drag is more important when the velocity starts to get high, so I will say that an Earthtoo rocket looses less $\Delta v$ due to it. That should compensate a little for the higher gravity losses. I want more thrust too, so I chose larger engines to compensate for the rest, increasing my dry mass share to 0.05. For a worst case scenario, I then design my rocket for a $\Delta v$ of 18 km/s.

Here is my design:

I have 3 stages, each of them 3 times more massive than all the mass they carry.

Payload:    1000kg
3rd stage:  4000kg ( 200kg dry mass)
2nd stage: 15000kg ( 750kg dry mass)
1st stage: 60000kg (3000kg dry mass)
Total:     80000kg

The idea is that the mass ratio for each expended stage is then $\frac{1+3}{1+3 \cdot 0.05} = 3.48$.

The $\Delta v$ added for each of the three stages is then:

$$\Delta v = \ln{3.48} \cdot 500s \cdot 9.81m/s^2 = 6120 m/s$$

That is 18360m/s in total, slightly more than needed.

I can not see the need to run this in a sophisticated spaceflight simulator, as some of the given parameters are highly unlikely. For instance, a performance of 500s independent of ambient pressure is extremely optimistic, as most launchers $I_{sp}$ at sea level is around 300s, and an atmosphere twice as dense does not help at all. Secondly, complete rocket stages seldom have a better total-to-dry mass ratio than about 15. (0.067), so even the more conservative figure I used (20 instead of 25) is fiction.