Quantum Footprints in the Cosmos: The Calculus of Space Exploration
Quantum Footprints in the Cosmos: The Calculus of Space Exploration
Quantum mechanics governs the behaviour of particles at microscopic scales. But space, with its vacuum, high radiation, and zero-gravity conditions, reveals phenomena that only quantum physics can explain. From precision in navigation systems to understanding black holes, quantum mechanics enables us to interpret and engineer…
In the future, humans will explore the stars. This may happen in a few decades or centuries, but it is inevitable. The long time period is due to the fact that stars are incredibly distant, beyond what we can imagine. Our current technology is not advanced enough to travel through interstellar space. However, as we advance in our understanding of physics and technology, it is likely that we will…
NEXT-C electric propulsion engine poised for production
NEXT-C electric propulsion engine poised for production
Photo Credit: NASA
The NEXT-C ion propulsion engine has successfully completed a Critical Design Review conducted by NASA and is planned for use on the agency’s 2021 DART (Double Asteroid Redirection Test) mission. With the CDR finished, the next step in the process should be the production of actual flight units. (more…)
To make sure that the chemical rocket from last week isn’t a giant waste of effort and fuel, I’m going to do a quick and dirty estimate of what a solar-electric propulsion system would have to look like for my 55 or so ton wooden framed spaceship.
Here you go:
For starters, for this version of the Myrtle it’s very important that the ship spend its time parked at the Earth-Moon L2 Lagrange point.
(pulled from Wikepedia, here)
The Lagrange points all orbit Earth at the same angular velocity as the moon, so they all take about 27.3 days to complete one orbit.
L3 through L5 are about the same distance from Earth as the moon, so the effect of the moon on their orbit means that there are hardly any neat gravity tricks that can be done from those locations.
L1 is about ⅚ the distance from Earth as the moon, so anything located there is going ⅚ as fast as it should be for a circular orbit at that location and anything there that slips off it’s hill toward Earth will fall into a deep ellipse with a periapsis that nearly brushes Earth’s atmosphere, making it a useful point for staging chemical rockets that can leverage the Oberth Effect.
L2 is about 7/6 the distance from Earth as the moon, so anything that falls off L2 away from the moon will, I believe, actually find itself hurled clear out of Earth’s Hill Sphere and into orbit around the Sun. Depending on the exact timing, it might find itself pulled back into an Earth flyby, dropped into an orbit that dips towards Venus, or tossed up into an orbit that rises towards Mars. Leaving L2 around the full moon ought to get us leaving Earth and started on our way to Venus for essentially no fuel. This is ideal for an electric thruster, as even the best can only manage a thousandth or so of a g in acceleration and if we were parked in low earth orbit, we’d need to spend months building up the 7+ kilometers per second of velocity it would take to get out of the Hill Sphere without using the Oberth Effect.
So if we’re leaving Earth for free, the question is how much more work will it take to get us to Venus?
Well, Earth has an orbital velocity of about 30 km/s and Venus has a velocity of about 35 km/s, so as a first pass we could say that we need 5 km/s of delta-v to go from Earth orbit to Venus orbit. Unfortunately this is not, in any sense, how you do that calculation. In the real world, neither is what I’m about to do, by my method is fairly accurate for how physics is approximated in Kerbal Space Program.
What you’re actually doing when you apply delta-v is changing your orbital energy, which is essentially a combination of velocity and elevation, so both velocity and elevation need to be considered.
At L2, velocity is about 1.2 km/s and distance from Earth is about 450,000 kilometers. So relative to Earth, Myrtle starts out with 720,000 m2/s2 (or joules per kilogram) of specific kinetic energy and -890,000 J/kg of specific potential energy. That means that if the sun didn’t exist, there would be a total of -170,000 J/kg of net specific energy keeping Myrtle in orbit. It also means, more importantly, that at the the 1.5 million km boundary of Earth’s hill sphere Myrtle should still have a velocity of over 400 meters per second relative to Earth. If we time things right, at the Hill Sphere boundary that 400 meters per second should be more or less directly retrograde to Earth’s orbit about the Sun and we should exit Earth’s gravity nearly 1.5 million kilometers sunward of Earth travelling 400 meters per second slower than Earth relative to the sun.
So now, relative to the sun, Myrtle should have a velocity of 29.4 km/s and an altitude of 148.5 million kilometers instead of Earth’s 29.8 and 150 number respectively. Those numbers give Myrtle an orbital kinetic energy of 432 million J/kg and -875 million J/kg of potential energy for a total of -443 million J/kg. This corresponds to a heliocentric orbit with a semi-major axis of 147 million kilometers, and means that the far side of our orbit has a periapsis of 145.5 million kilometers, or nowhere near Venus’s average distance from the sun of 108 million kilometers.
To meet Venus, where we can aerobrake, we need to reduce our periapsis to below 108 million kilometers, which means we need to reduce our semi-major axis to about 128 million kilometers. That means changing our orbital energy to -508 million J/kg, which would involve dropping our velocity to 27 km/s or a burn of 2.4 km/s if we could apply all of it all at once. With electric propulsion, we can’t. So we’re going to need to pay a penalty. I’ll call it a 50% penalty, and furthermore say that we need to apply our thrust over the first 3 months of travel for reasons that I’m really not going to go into.
So, we need to have an engine that can apply 3.6 kilometers per second of acceleration to a 55 metric ton payload over a 3-month time period. That’s 3600 meters per second in 7776000 seconds, or 0.0005 meters per second squared of acceleration.
If we could ignore the mass of our engines and their power supply, that would mean we’d need a thrust of about 27.5 newtons (kilogram-meters per second squared). Off the Wikipedia shelf, that’s… oh something like 6 VASIMR engines that each need 200 kilowatts of power and weigh 620 kilograms. The paper referenced for the engine mass doesn’t seem to include the actual generation of power, so that’ll add something on the order of another 4 kilograms per kilowatt. All up, we’re looking at 8.5 tons of engines and panels. That bumps our total weight up to 63.5 tons and our force requirement above 30 so we need another VASIMR, even without including fuel. And fuel’s going to be 15% of total mass using the 3000 s specific impulse for VASIMR that corresponds to the highest thrust.
All up, it’ll actually take 8 VASIMRs, and raise our total mass to just over 76 metric tons. That’s a power requirement of 1600 kilowatts, and near earth orbit it’ll take a solar field of about 13,000 square meters thanks to the fact that lightweight solar panels are not very area efficient.
So we’ll wind up with that drawing from before the cut, and a ship that uses up about 12 tons of argon every trip.
Whether that’s a good idea or not depends on whether it’s easier to get 12 tons of argon into space or 20 tons of water.
I think it’s worth noting that there’s about 0.1 newtons of momentum available in the sunlight hitting the solar array for this thing. If you were wondering what a solar sail would look like for Myrtle, well that’s easy enough. Getting 30 N of force near Earth would require something like a 3-million square meter sail. At a density of about 10 grams per square meter for the sail and its supports, it would weigh about 30 tons and be about 1750 meters on a side if it were square.
That’s not actually big enough of a sail, considering that solar sails have limited control of what direction they’re thrusting in and we’re a bit overweight, but since the Myrtle is already essentially too small to see, I’ll leave it at that. The difference between 3 and 4 pixels across isn’t too important to me.
(One of these days I really need to sit down and figure out solar sail trajectories and work out things like a solar sail’s expected lifespan due to things like radiation weakening of polymer chains and micrometeorite impacts.)
Myrtle’s more or less done for the moment, and while I might be back with refinements and more detailed art, I might not as well.
Instead, next week I’ll give you a space post that touches on my aquaponics interests.
Aerojet Rocketdyne’s operation in Redmond, Wash., has won a $67 million contract from NASA to design and develop an advanced electric propulsion system that could power future trips to an asteroid and Mars. The goal of the 36-month project is to deliver an integrated system that could improve fuel efficiency by a factor of 10 over today’s chemical rocket propulsion systems, and double the thrust…
