The Deliverator’s car has enough potential energy packed into its batteries to fire a pound of bacon into the Asteroid Belt.
A metaphor, like the decibel thing we discussed earlier? Maybe, maybe not. Let’s work it out and see.
The first thing to notice is that there’s several levels of complication involved depending on how much detail we want. Roughly speaking there’s two sources of gravity to overcome. There’s the earth and the sun. The bacon doesn’t have to go far to get away from the earth, but the force the earth exerts is pretty steep during that distance. The force of the sun is much smaller, but it’s not going to diminish all that much between the earth’s orbit and the asteroid belt. We could stop there by calculating the changes in potential energy associated with the translation up the gravity wells and we’d have a figure.
And it might even be mostly right, depending on how we interpret things. In reality you’re more than likely not just launching the bacon from a standstill radially away from the sun. The bacon is in orbit already because the bacon is on the earth and the earth is orbiting the sun. When it gets to the asteroid belt, it will still be orbiting though at a different orbital speed. So to calculate the total energy change you have to take into account the orbital kinetic energy.
That’s not all. The earth is itself rotating, and thus you can consider the bacon as starting off with that much speed. This is why the Space Shuttle is launched from Florida: the rotation of the earth is fastest near the equator and so NASA takes advantage of this free kinetic energy. I doubt an unmodified Shuttle could reach orbit from Anchorage, Alaska even if NASA wanted to.
That latter complication involving the rotation of the earth is dependent on both the latitude of the launch location and the direction of the orbit. As such I think we’ll ignore it. It’s a fairly good average assumption anyway, since some launch directions will help you out and some will make the launch more difficult (this is why no one launches their rockets westward – the earth is rotating in the other direction).
Now I’m also going to ignore the first complication, the orbital kinetic energy. This is because we’re not requiring the final orbit to be a circular orbit or any other particular kind of orbit. We don’t care what the bacon is doing when it gets to the asteroid belt. We only want it to get there, and if we add in energy equivalent to the change in potential, we can do it.
So what’s the equation for change in gravitational potential energy? It’s this:
I’ve finagled an overall minus sign so we can keep everything in positive territory. G is the universal gravitational constant, M is the mass of the earth (or sun when we get to that step), and m is the mass of the bacon.
For finding the potential energy due to the earth, we can drop the second term entirely. The distance to the asteroid belt will be so large compared to the radius of the earth that it might as well be zero. All told we end up with 26.4 MJ needed to get the bacon off the earth. Now repeat the process, replacing M with the mass of the sun, the initial r with the orbital distance of the earth, and the final r with a representative value for the orbital distance of the asteroid belt (say, 2.5 AU)*. I come up with about 241 MJ.
This gives us a total energy of 267 MJ. The energy content of the combustion of gasoline gives about 32 MJ per liter. All total, the energy we’re talking about is equivalent to… about seven liters of gasoline. Not so much. My car has enough energy in its tank to launch a pound of bacon into the asteroid belt, and my car is a little Nissan crackerbox. It’s entirely plausible for Hiro’s car batteries to have that much energy with no sweat.
Now in practice you can’t send pork products on interplanetary voyages with 2 gallons of gas. Energy efficiency is bad enough in a car engine. Energy efficiency in rockets is horrible. But strictly as a matter of energy with no reference to efficiency, the bacon delivery is not actually all that impressive.
*Though this happens to correspond to a thin gap in the belt due to a Kirkwood resonance.