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This is totally not based off the Lost Cosmonauts Theory, what are you talking about??

I am working on this horror-scifi story based on the lost cosmonauts theory, where the Judica-Cordiglia brothers detected an SOS from a manned probe veering off into space before Yuri Gagarin ahem... I didn't say that.

Basically, a team of astronauts are sent by an private space research agency (Definitely not SpaceX, lmao) in a manned capsule to explore the outer solar system, especially between the orbits of Saturn and Uranus, for well... ^plot reasons^

The astronauts then spot a weird metallic spiky "asteroid" floating around in space. They come up close, and actually discover that it is not a "asteroid", but a really old probe. After docking with the probe, they discover to their horror, that there are several paper pages lying on the floor of the probe, and more unsettling, the preserved corpse of a dead cosmo astronaut.

The astronauts read the paper pages. It seems to be a sort of rant written down by the (dead) astronaut, about how he got lost in space.

Apparently, he was the first man to be launched into space, as the result of a space race between two global powers, whom we shall call A and B. The astronaut was launched by A, into orbit, to study cosmic radiation and stuff. However, as soon as he was scheduled to land on Earth, his retrorockets misfired in the wrong direction. Unfortunately, the controls were jammed due to some reason, so the astronaut had to watch in sheer terror, as he watched Earth getting smaller and smaller through the window. He knew his probe was on an escape trajectory and veering into deep space. He sent an SOS, in a last attempt, and eventually commited s****de by opening the hatchlock and suffocating in the vacuum.

Now of course, I may be experienced at Astronomy and stuff, but absolutely suck at aerospace engineering. (I don't think if retrorockets even have buttons to control them). So here are some dumb attempts at drawing a parallel between this situation and known rockets.

The rocket that fired A's astronaut into space can be comparable to the Saturn V. And the rocket engines were Bell nozzles, similar to what the Space Shuttle used.

As far as I have heard, retrorockets don't even use liquid fuels, let alone LH2 (Wasn't it something like, I dunno, a nitro- compound or smth?). But again, this is interesting for the plot, because maybe they were trying to experiment with different fuels?

But anyways, considering the real story:

The amount of fuel to get on an escape trajectory is astounding. It takes like 3 million pounds of fuel for launching something like the Space shuttle to LEO, forget escape trajectory. And the probe, was well, found drifting between the orbits of Saturn and Uranus, about a billion miles away, last time I checked.

Considering that the astronaut in the story was sent into a escape trajectory from LEO to about 1 billion miles away, I am sure it would have taken a B*ttload of liquid hydrogen for the retrorockets to actually misfire that bad. This brings me to my question:

How much liquid hydrogen is required as fuel to veer a manned probe off course into an escape trajectory?

Some additional info:

  • The probe, in question was found orbiting between the orbits of Uranus and Saturn, which suggests that it may have slowed down due to the gravitational force of the two planets, and settled into a orbit.
  • After doing some research, I found out that the velocity of the rocket must not have been greater than 13.6 km/s or 9.6 km/s.
  • The fuel being used by the retro-rockets is liquid hydrogen, with liquid oxygen being used as oxidizer.
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    $\begingroup$ Why the downvote? If there is something wrong with my question, please point it out. $\endgroup$
    – Furious Arcturus
    Nov 4 at 14:46
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    $\begingroup$ Liquid hydrogen is a complete non-starter for retrothrusters due to its propensity to boil off. For a launch to orbit, where you can keep pumping in propellant up until the last minutes before launch, this isn't so bad, but retrorocket propellant needs to stay in the tank until fired. You'd need to carry (complex, very heavy) cryogenic equipment to keep it in its liquid state all the way to orbit. An aside: the nitrogen compound you're thinking of is probably hydrazine, possibly UDMH + nitric acid. $\endgroup$
    – Cadence
    Nov 4 at 18:32
  • $\begingroup$ I say this is better asked on Astronomy.SE, yet I've heard that there's more people in here that could answer such questions than there. Yet you're really into very high delta-V ranges with this, perhaps an easy answer won't do. $\endgroup$
    – Vesper
    Nov 5 at 15:11
  • $\begingroup$ Why are you censoring "suicide"? I'm not sure how worldbuilding.se could be mistaken for tiktok. $\endgroup$
    – Starfish Prime
    Nov 8 at 14:58
  • $\begingroup$ @StarfishPrime If you hang around Spam-Central (charcoal) long enough, you'll see all sorts. Automatic filters would seem necessary to you, I'm sure. Never seen invitations or advice on the "S" word, but it probably seemed like a good idea at the time the word was added to the trigger list. $\endgroup$
    – Escaped dental patient.
    Nov 8 at 18:30

1 Answer 1

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About 70.8 metric tons

To plot courses around the solar system, I find this chart handy:

delta-v map

Source: Slightly upgraded delta v map of the solar system

To get from one orbit to another, simply travel along the tree and add the delta-v at each step. An Earth-Uranus transfer looks to be about 8.4 km/s, assuming a start from LEO already at 9 km/s. If the spacecraft is to stay near Uranus, then a Uranus capture is an additional 510 m/s, bringing the total delta-v, $d_{v}$, to 8.9 km/s.

The Vostok 1 capsule had a launch mass of around 5000 kg, I'll assume that's our capsule mass. As a guestimate, I'll assume the fuel tank mass is 6000 kg. Because the tanks carry our fuel, we have to haul them the whole way to our destination, and so they factor into our final "dry" mass, or the mass of the spacecraft after all fuel is spent, $m_{dry}=m_{capsule}+m_{tanks}$, which totals to 11000 kg. I'll also assume our hydrolox engine has a specific impulse, $I_{sp}$, of 450 s, which is pretty good. With these figures we can calculate the propellent mass, $m_{prop}$:

$$v_{e}=9.98\cdot I_{sp} \text{ m/s}$$ $$R=\exp\left(\frac{d_{v}}{v_{e}}\right)$$ $$m_{wet}=R\cdot m_{dry} \text{ kg}$$ $$m_{prop}=m_{wet}-m_{dry} \text{ kg}$$

Propellant mass for Uranus insertion runs to 70.8 metric tons. To find the hydrogen and oxygen fuel masses independently, we rely on a fuel mass ratio. The stoichiometric ratio of LOX to LH is 8:1, but maximum specific impulse is at ~4.3:1 (though most engines run with less hydrogen, at ratios of 5-6:1). $$m_{LOX}=m_{prop}\left(\frac{4.3}{4.3+1}\right)$$ $$m_{LH}=m_{prop}\left(\frac{1}{4.3+1}\right)$$

Of our 70.8 metric tons of fuel, 57.4 are LOX and 13.4 are LH.

You'll want to cycle back to see whether your tank mass guestimate was a good one by looking at the tank mass fraction: $$\frac{m_{prop}}{m_{tanks}}$$

For LOX/LH, an optimistic tank mass ratio is probably ~10:1, and ours is in that ballpark.

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  • $\begingroup$ While this will get you out of an Earth-centric orbit into a Sun-centric orbit, you'll still be at around Earth's orbital distance from the Sun. You'd need to put in an extra ~5 km/s at least to get out between Saturn and Uranus's orbital distances. $\endgroup$
    – Cadence
    Nov 4 at 18:19
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    $\begingroup$ So... just a bit more than the retros would likely be carrying, then. $\endgroup$
    – Monty Wild ♦
    Nov 5 at 0:16
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    $\begingroup$ From BMF's reply it appears an unlikly amount of fuel would be required, butyou might be able to reduce that a bit if you allowed for some gravitational boosting as has been used to get probes to jupiter/saturn...pluto etc. It would require a very unlikely initial trajectory, but if the retro-rocket errror provided just enough energy to get to Mars or Venus, then it may be possible to ger past Saturn via a series of slingshots around the moon, mars, earth, venus, earth again, etc... Assuming time is not an issue, you may just need minimum fuel to reach Mars or Venus orbit. $\endgroup$
    – Penguino
    Nov 5 at 23:14
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    $\begingroup$ @Penguino Your reply reminded me that the orbit might not work at all. Spacecraft are usually launched in the direction of Earth's rotation, which is canted at an angle off from the ecliptic plane. You wouldn't reach anywhere near Uranus unless it was a deliberate act. $\endgroup$
    – BMF
    Nov 5 at 23:23
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    $\begingroup$ Which is true regardless. A random thruster burn will send you basically anywhere except a planet. But even more delta-v would be required for the plane change, or a gravity assist. $\endgroup$
    – BMF
    Nov 5 at 23:27

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