The reason it is difficult to send something from Earth orbit is simple; we are falling around the Sun very, very quickly; almost 30,000 meters per second. By comparison, the speed of sound at sea level is about 340 m/s. (Solar escape speed at Earth orbit is about 11 km/s; almost a factor of three less than the change in velocity to fly into the Sun.) In order to fall into the Sun, we have to get rid of all of that speed; otherwise, we just fly around the Sun. Just pointing our spacecraft at the Sun doesn’t help; even as we go forward, we slip “sideways” in orbit, and we just end up with even more speed orbital speed, and our orbit becomes more elliptical, and in fact, we’ll end up escaping the solar system before we can hit the Sun. The only way to fly into the Sun is to completely kill all of that orbital speed, and the best way to do that is to go outward where orbital speed is lower and negate it there, either by a planetary swing-by, or by directly thrusting into our path. At the orbit of Jupiter, orbital speed is about 13 km/s–less than half of what it is at Earth orbit–and with a judicious selection of trajectory and a fair amount of patience, it takes only a very modest amount of delta-V to get there.
Send it out to Jupiter for a fly-by that kills its horizontal momentum and let it just fall into the sun… oops, something got in the way… earth! Now you have a city-sized Necronomicon crater spewing forth Jupiter demons. Great job!
Ooh, that’s an interesting side-question… if the aforementioned rectangular object were stopped (effectively) dead in space at Jupiter orbit and then proceeded to fall straight-ish towards the sun and that pesky Earth got in the way, how big a boom are we talking about here? I figure it’s going to be more than if a fella dropped a phone book off the top of the Empire State building, particularly since this book isn’t going to burn up on re-entry.
I had never really thought about this before. So what you are saying is that it is harder to fall into a black hole than I previously thought. (Somehow I feel so much safer now.)
On a related note, there must be some orbital radius around the sun where it takes an equal amount of energy to escape the solar system as it does to fall into the sun. Is there any significance to this radius? Is it ever likely for orbiting bodies to have stable orbits within that radius for example?
Actually there isn’t. Escape velocity is sqrt(2 G M / r), and orbital speed (for a circular orbit) is sqrt(G M / r). Here M is the Sun’s mass, and r is whatever radius you’re at.
So if you’re already in circular orbit, you’d need to change your velocity by sqrt(G M / r) to stop (and then fall into the Sun). To escape, you’d need to add (sqrt(2) - 1) * sqrt(G M / r) to your velocity.
That’s looking at it from your initial reference frame. If you look at it from the Sun’s frame of reference, since kinetic energy goes like velocity squared you double your kinetic energy to reach escape velocity, and of course bring it to zero to stop in orbit. So from that point of view, it’s true at every radius.
Probably not as much as you think. If it just starts “falling” back toward the Earth from Jupiter’s orbit (or anywhere else), the maximum velocity falling in is going to be roughly the same as the escape velocity getting out, or about five miles per second. I wouldn’t want to be in the way of it, but it would probably mostly burn up.
Fast rocket with fast launch initiation, with accuracy of launch timing to the 1/10,000th sec. Globe spinning at 30k m/sec. Calculate lead time to where the centroid of the sun will be in position factoring in the velocity (travel time) from Earth to sun, the time it will take for the rocket to “shake off” the orbital and gravitational pull of the earth, the time to negotiate the gravitational vicissitudes of the sun. Wait until rotational point of launch site satisfies the above. Blastoff.
The Solar Probe Plus is ~600 kg of instruments, heat shields, structure, etc. Obviously we just want to dump 5 kg directly into the sun, and aren’t interested in any of that “science” nonsense. How much closer to the sun could we get if we got rid of that heavy probe and replaced it with a ~600 kg upper stage?
This could only be true if you were initially orbiting the black hole, which in turn won’t necessarily be true. Orbital velocity is the entire problem with getting something from the earth to the sun. Without any orbital velocity, it’s trivially easy: just wait, and you’ll fall right in.
Earth is rotating at about 7.3X10[SUP]-5[/SUP] rad/s, which works out to about 465 m/s at the equator. If the Earth were spinning at 30,000 m/s at the equator, nothing would stay stuck to the surface and the centrifugal loads would tear it apart. However, setting all of this aside, you would not want to fire your craft into the Sun but rather back into the orbit of the Earth. You are also going to have to add additional impulse to make up for what is lost during the period of ascent (so-called “gravity drag”) and to escaping Earth’s sphere of influence.
It depends upon the propulsive capability of the stage, but I guarantee that a 600 kg stage using any kind of chemical propulsion will not provide nearly enough impulse.
For comparison, the Delta Cryogenic Upper Stage has a dry mass of about 3,000 kg, with a wet mass of between 20,000 and 30,000 kg and a thrust of 110 kN for 1130 seconds. This is just barely enough to get something like a medium sized probe to escape Earth’s sphere of influence and into a minimum energy transplanetary injection orbit to Mars. While it might seem like there would be substantially more performance if we swap out a ~1000 kg probe for a 5 kg package, the fact remains that most of the energy expended during burn goes into pushing the stage and the unconsumed propellant (which decreases over burn).
Very true.
However, it isn’t just orbital velocity; if you approach a black hole with any significant lateral velocity you are very likely to go into a hyperbolic trajectory, where the black hole pulls you toward it and then bends you around it like a judo master. If you get close enough to a rotating black hole it may even twist your path back on itself in a trajectory that defies Euclidian geometry. This is why black holes do not consume all matter and energy in the universe, and why they can sit in the center of a galaxy like a campfire without sucking in all of the campers; they all start out with significant velocity relative to the mean field, and are rotating fast enough to kick a good portion of the pre-singularity mass back out in orbit or escape from it.
Put it on a ship piloted by a young serviceman on his last mission who has made it through the war without any injuries and is devoted to his pregnant wife. Launch the ship right after he calls his wife to tell her he loves her with all his heart and will be home soon.
The ship will head directly for the sun all on it’s own.
The science instruments make up less than 50 kg of that total mass. The rest of it is the spacecraft “bus” - structure, control computer, power system, communications system, navigational sensors, propulsion system (for course corrections), heat shield, etc.
If you’re just carrying a 5 kg inert payload (i.e. doesn’t require power), you still need a propulsion system and navigation sensors for course corrections, and a computer to control it, and a power source for these. And a communication system for remote access, even if it’s only for troubleshooting.
What if we were lucky and found an appropriate sun grazer comet. Could we smash the object into the comet? Would the differentials in energy alter the course of the comet? If so, could you selectively pick your sun grazer so that the course alteration directs it into the sun?
Yeah, actually, that would be an easier way to do it. The European Space Agency has a mission in place to land on a comet with a larger and more sensitive payload that you’re talking about. If you found a good comet that would impact the sun, or at least come close enough to allow the drag from the solar wind and corona to drag it into the Sun eventually, then you actually could save a lot of effort that way by hitching a ride. One caveat, though; appropriate comets are probably pretty rare. You’d need a comet that not only has an orbit that will put it into the Sun, but is also less than 30 km/s different in orbit from the Earth, otherwise it will actually take more energy to do this than to just shoot it into the sun anyway.
Paths through the ellipsiod ergosphere of a massive, rapidly spinning black hole can form what are called closed timelike curves (CLC) which can appear, from a non-accelerated observer to go back to a point in spacetime prior to the time of entry. However, in order to exit the ergosphere you have to follow the path back around past your point of entry. There are other solutions which may allow timelike curves with an arbitrary exit point, but the conditions to create them may be highly artificial and not physically realizable.
Wormholes and other manifold defects are seperate from this, although you can obviously end up with timelike paths through these defects as well. While there is nothing in the model of General Relativity that prevents the formation of these topological artifacts, we have no evidence at they can physically occur.
Actually, no. While the space and time coordinates within the ergosphere of a black hole will not behave the way a relativistically-naive observer would expect, they still don’t behave weirdly enough for the curves to actually close. You might be able to get that to happen inside the event horizon, but nobody cares about that, since it’s inside the event horizon.
And you can also get weird “hyperbolic” orbits even with a non-rotating hole. In Newtonian gravity, an unbound orbit will swing close to the central body, and then swoop back out after passing around it after turning something less than 180 degrees (potentially arbitrarily close to 180 degrees, but never more). That is to say, you could always draw a straight radial line out from the central object, in the plane of the orbit, that does not intersect the orbit.
In general relativity, however, this is no longer true. Given just the right trajectory, you could have an object fall in very close to a black hole, swoop around it an arbitrarily-large number of times, and then come back out, for an orbit that looks sort of like the spring in a clothespin.
Or failing that, if someone’s decommissioning a giant robot by auto-piloting it into the sun maybe you can ask them if they’ll let you send the book with it.
Or, I dunno, do some fancy portal-momentum transfers? The surface of the Moon is portal-able, I’m sure you can do interesting things with the distance between the Earth and the Moon so long as you don’t get sucked out into the vacuum of space.