Okay… we have an elecrically-powered pork-product projector on the earth’s surface, which fires indestructible (i.e. perfect) pound-sized pork pieces into orbit. We have to supply energy to reach earth escape velocity, plus additional energy to compensate for the drag of the atmosphere, plus some additional amount to take us from earth orbit to the asteroid belt. I had an image of the pork piece coasting upwards, away from the earth and sun through the solar system, and moving slower and slower until at the centre of the asteroid belt, it comes to a halt for an instant, then slowly starts to fall backwards. It would probably fall back to land in the sun and lend a hint of pork flavour to the solar wind for a moment.
Is it possible to do this with one well-aimed shot? What if we wanted the pork to take up orbit in the belt, rather than just pausing there?
No, the bacon will likely end up in orbit around Jupiter or Mars or one of the bigger asteroids. Each body has a region of space where it is the dominant gravitational well, called the Hill Sphere. I suppose it might be possible to time your shot so that you can slingshot around but if it stops in the asteroid belt, it’s going to stay near there.
Yes it’s possible. Do I know the precise mathematical numbers involved, no. But, keep in mind that its probably just launched into orbit around the sun, so actually hitting the sun on the return trip is a bit tricky. You’d have to aim it close enough to another object, like Ceres, that the interaction would slow the bacon down and alter the trajectory to hit the sun.
Ditto, for settling into orbit in the asteroid belt.
Possible, yes. Easy, even to a rocket scientist, no. I don’t know any nasa engineers that would want to try it without the possibility of correction thrusters.
Actually, after you get to the asteroid belt you’ll have put the bacon into an elliptical orbit. It’ll come back, cross the earth’s orbit, and drop down to a minimum somewhere (I’d have to figure it out, and I ain’t got the time right now – probably still further out than Venus’ orbit) before going back up towards the asteroid belt. It’s not going to end up around Jupiter or Mars anytime soon.
Incidentally, there are ways to shoot a small package up into space without benefit of a rocket. The Laser Propulsion project I worked on for a few years was meant to do precisely that – getting small packages into orbit, with only an outer shell and a block of Reaction Mass. Leik Myrabo’s Apollo Lightship was supposed to do the same thing, but without the reaction mass – he concentrated the light on the surrounding atmosphere.
If technology has progressed enough that we have batteries nearly an order of magnitude better (actually, not nearly as technologically crazy as the auto-adjusting wheels on the skateboard), then we can just put the bacon on the Space Elevator, then catapult/railgun it out to the asteroids. Avoids atmosphere issues, and requires only the energy to counteract the gravity well (although the pre-cooking no longer happens)
Actually, it does. That’s the whole definition of escape velocity.
Steps:
Derive the equation for gravitational force on 1 lbm of bacon as a function of distance from earth’s center.
Integrate from the earth’s surface to a distance of infinity; this gives the total gravitational potential energy of the bacon after it has been moved infinitely far from the earth’s surface. This is the amount of kinetic energy that must be imparted to the bacon, at the earth’s surface, for it to keep moving away from the earth forever.
No matter what your object - porcine or otherwise - if you neglect atmospheric effects, escape velocity from the earth’s surface is in the neighborhood of 25,000 MPH. Bacon launched with this initial velocity will continuously decelerate as it moves away from the earth, but barring interference from other celestial objects, it will indeed continue moving away from the earth forever.
So, as you move farther and farther from the centre of the earth, the escape velocity at that point gets less and less? I’m imagining the bacon coasting slower and slower, but never quite stopping and falling back. This is in a universe where the bacon and the earth are the only two objects.
For going from the earth to the asteroid belt, would there also be calcualtion for the escape velocity from the sun, starting at the distance of the earth’s orbit? And if we don’t actually want to escape, but just go to the asteroid belt, we don’t need to supply as much velocity?
Cool! It turns out that you need much more energy to go from earth’s oerbit to the asteroid belt than you need to only escape from the earth. Interesting.
So you’re saying that if I manage to shoot a bb at 25,000 mph (defined as escape velocity earlier in the thread) from my back yard - it will leave earths gravity well. Even, when atmopheric drag reduces its speed to 24,999 after a small distance?
Think about what you’re saying when you say what I said wasn’t true.
You’re saying that a satellite orbiting at orbital speed, that accidentally hits the wrong thruster and accelerates to 25000, then corrects itself back to orbital speed is screwed and cannot possibly return to orbit - no matter what amount of thrusting manuvers it undertakes.
Ayup, that’s pretty much it. Like rolling up a hill whose slope gets more and more gentle as you approach the summit.
A lonely, but oh-so-delicious universe.
The sun would affect things. How much is hard to say without doing the math. I looked up the earth’s orbital velocity around the sun, and figured out that the centripetal acceleration (and therefore the sun’s gravitational acceleration at the earth’s orbital radius) is about 0.006 meters per second, just a tiny fraction of earth’s surface gravity. I’m too lazy to calculate solar escape velocity from the earth’s orbital distance, but I’ll WAG it doesn’t add much to the 25K MPH we’re already imparting to the bacon.
the bacon will probably fry on the way up. Atmospheric drag will heat the bacon, and the fat/grease will bubble up and be blown away in the wind.
So, in order to get a pound of bacon to the asteroid belt, you will need to start with quite a bit more bacon. How much? I dunno, but the fat content will be a variable in determining what the initial pile of bacon must weigh.
And, it might be what starts as bacon on the ground, won’t be bacon by the time it gets into space. Can you call a hunk of charred carbon bacon?
So, I contend you need some kind of shell to protect the bacon from thermal destruction during the first few minutes of launch. Possibly, with the right material, the shell might weight less than the initial bacon mass that would be needed for an unshielded launch.
And then, once it gets into space and is subjected to near absolute zero temperature and possibly cosmic ray bombardment, can it survive as bacon the remainder of the journey? I don’t know this either, but I am shocked that all you big brains haven’t considered this. So I contend it will need some kind of environmental support system to maintain its essential baconness. All of which will add a great deal of weight to the initial launch.
I also contend that the point of the whole exercise is to deliver edible bacon to the asteroid belt. Otherwise, you might as well ask what it takes to deliver a pound of mass to the asteroind belt.
Fortunately we have the technology. It’s called the Saturn V rocket.
Assuming you’re doing this the most efficient way, with a Hohmann transfer orbit, then the perihelion of the elliptical orbit will be exactly as far from the Sun as the Earth’s orbit.
And since the original quote said nothing about efficiency, and since there are ways to make energy loss from atmospheric drag arbitrarily small, I think we’re justified in ignoring the atmosphere.
Sure, but you still can’t really take air resistance into account without more information than we have. What shape is the bacon? If it’s a long, thin strand of bacon, then the air resistance might be very low (though it’d make it harder to fire it, but that’s an engineering problem). If it’s a roughly-spherical lump, or even something like a parachute shape, air resistance would be much greater.
Hi, physics grad student at your service. There are a lot of hidden assumptions going on here that are complicating the issue. I’m going to deal with the three different scenarios that have been intermixing themselves in this escape velocity side discussion.
An inert mass (such as bacon) is launched ballistically from Earth’s surface with an instantaneous initial velocity of 25,000 mph. There is no atmosphere.
In this simple scenario, the only relevant numbers are the bacon’s kinetic energy and its gravitational potential energy. Joe Frickin Friday’s post above explains why the bacon, assuming nothing else interferes, will never return to Earth.
An inert mass of bacon is launched ballistically from Earth’s surface with an instantaneous initial velocity of 25,000 mph. The Earth has its usual atmosphere.
Here, the atmosphere gives us velocity-dependent drag, which will reduce the bacon’s KE as it rises. This is not a problem, since the required KE for escape also reduces as the bacon rises. Offsetting it is a matter of using a higher initial velocity. This is your bb scenario, and 25k mph would be slightly insufficient to prevent it from falling back down.
An electronic satellite already in Low Earth Orbit misfires a thruster and reaches a speed of 25,000 mph.
This is a totally different scenario. As I pointed out above, escape velocity is not equal for all positions near Earth. An LEO satellite is already traveling at about 17k mph, so first of all it would have to be an accident exceeding the design specs of the satellite to bring it to 25k mph. Second, escape velocity for an LEO satellite is lower than 25k mph. Assuming an orbital altitude of 1,000 km, escape velocity is now about 23k mph.
Finally, and most importantly, a satellite with thrusters is not a ballistic object like the bacon was. If it does accidentally thrust itself into an escape trajectory, it can thrust itself back into orbit at the price of burning fuel. The word “ballistic” I keep using means that the object gets one impulse and then moves only under the influence of gravity. Any statement to the effect of “an object which reaches escape velocity never comes back” should be understood to apply only to ballistic objects.
To expand on what Spatial Rift 47 said, the whole idea of escape velocity is that it’s the initial velocity needed by an object to escape the gravitational well, without further impulse. Because it’s still affected by gravity, the object will obviously slow down as it escapes, but the point is that it won’t slow down enough to return to Earth (neglecting air resistance, of course).
In contrast, if we had a magic rocket that was able to provide a constant acceleration to exactly counter the gravitation of earth at any particular height above the surface, if I were to give it an upwards push of 1 m/s it would (again neglicting air resistance) eventually escape, even though it never reaches escape velocity, since there’s a constant thrust being provided. (Okay, eventually it’ll get far enough away to reach a point where the escape velocity is reduced to 1 m/s, but you get the picture.)
To go back to the original point of the thread, there’s a few things I’m wondering about. First, how much initial velocity could a car battery impart to a one-pound object, assuming all its potential energy were magically converted to kinetic energy of the bacon? How does this speed compare to escape velocity at the surface? Second, how much initial speed can be saved due to the fact that we only need to reach the asteroid belt before allowing the bacon to cease its outward journey? I mean, if we consider an isolated system with just the earth and a pound of bacon, shooting it at escape velocity will get it to an infinite distance from the earth eventually. However, we just need to get it to a distance of the astroid belt. This will take a smaller initial velocity, although I suspect it’ll turn out to be a miniscule difference. I would suppose the same holds true for moving the bacon within the sun’s potential well. Again, we don’t have to have it escape entirely, just get far enough to reach the asteroid belt. These savings might (and I emphasize “might”) be more substantial.
