1) What would happen if artificial satellites in various orbits above the earth exploded? Where would the fragments go? 2) How do constituents of asteroid belts stay in their orbit? Why don't they change orbits? Why that particular distance? Thanks
That depends on the type of explosion.Some may continue orbiting the earth or fall to earth(depending on the circumstances
In what way is this any different than asking Why does the Earth stay in its orbit (around the sun) ? Why that particular distance? Why does the moon stay in its orbit (around the Earth) ? Why that particular distance?
short answer: they do 'change orbits'...but it's a slow process....like the earth and moon separating..... http://en.wikipedia.org/wiki/Asteroid_belt
Imagine a satellite in a perfectly circular orbit. The debris from the explosion is accelerated away from the initial position of the satellite. This causes ALL of the debris to enter elliptical orbits. The debris ejected in a direction opposite of the orbital direction is decelerated with respect to the Earth and enters an orbit with less energy and a smaller semi-major axis. Debris ejected forwards, in the direction of the initial orbit, will enter a higher energy orbit with a larger semi-major axis, as the explosion accelerates it and gives it the necessary energy to reach this orbit. Given enough energy from the explosion, the debris could either be ejected completely out of orbit of the Earth or its orbital velocity could be decelerated so much that it simply falls back into the atmosphere. Changing orbits requires that something add or subtract energy from the object. With satellites and spaceships we use rocket engines to do this. Asteroids and other orbital bodies have, for the most part, been occupying about the same orbit for billions of years since there has been nothing to change their orbits. The formation of the solar system was a very chaotic place and it's likely that a great number of changes occured, but since everything settled down about 4 billion years ago there have been few major changes.
My original questions come from my perception that certain conditions are necessary for an object to remain in orbit. I presumed the conditions to include altitude above the body they are orbiting. Is there a certain altitude which, above it, an object placed there will orbit, for every reasonably close altitude above it?
The only condition is that the orbiting object be moving fast enough to not fall into the body it orbits. The smaller the orbit, the greater the speed needs to be since the attraction of gravity is stronger. For example, the Moon is an average of 384,000 km away from the Earth and orbits at a velocity of about 1 km/s. Geosynchronous satellites orbit at about 36,000 km and have a velocity of about 3 km/s. The International Space Station orbits at about 420 km with a velocity of about 7.6 km/s.
In the early days of the space program, several orbital missions above the Earth were devised to practice docking the manned capsule with an unmanned craft, both of which were put into the same (or nearly the same orbit). When the astronauts first approached their target docking, they found that there was a difference in vertical separation, w.r.t. the view of the astronauts in the manned capsule. The astronauts tried using attitude thrusters to bring the two craft into alignment. This maneuver failed, and the problem was not resolved until someone on the ground realized that only by changing the speed of the manned capsule (faster or slower, depending on the relative positions) could the vertical separation of the manned and unmanned vehicles be eliminated.
Not true. It is true that all debris leaves the initial circular orbit, because all debris is accelerated in some direction. True assuming the speed to which they are accelerated is small. And given that the orbit is either high enough in the first case, or low enough in the second case. No. It requires that something alter the momentum of the object. It is possible to leave the energy unaltered if the original speed, added speed and new speed are the sides of an equilateral triangle. Which is possible if the added speed is less than twice the original speed. If the new speed happens to be horizontal like the old speed was, then the new orbit is also circular, and with the same semimajor axis, only plane differs. If the new speed is the same as the old speed, but no longer horizontal, then the new orbit is elliptical but has the same semimajor axis.
The same explosion in different orbits and even in different positions if eccentric orbits would give different results. You can check different equations here to see the posibilities: http://en.wikipedia.org/wiki/Orbital_speed
The general problems of orbital rendezvous have been understood for a long time. For objects which are close together, the immediate effect of thrusters is as intuitively expected, but the complications are related to time scales which are a significant fraction of the orbital period, which for low earth orbit is around 90 minutes. This means that relative velocities can change significantly over a few minutes just as a result of orbital effects. For example, if you have two objects in a similar circular orbit, and one fires thrusters to move upwards, that will have the effect of making its orbit elliptical, first going higher then going lower than the original orbit. Paradoxically, if you boost forward in orbit, that has the effect of raising the orbit which increases its period, so over a whole orbit you will drop back relative to something ahead of you in the original orbit, and vice versa. If you look at the relative motion as a pair of objects move around an orbit, a forward boosted object will soon start to change towards upwards motion, then into backwards motion, then downwards in a loop, ending up coming round to forwards again at the original altitude but further back in the orbit. Similar looping motions apply for other small differences of velocity. In Newtonian mechanics, a particle which passes through a particular point in an orbit around a static spherical object and is in free fall will pass through the same point on its next orbit, if there is a next orbit (that is, unless it escapes completely or hits the atmosphere). The "same point" in this sense ignores the rotation of the Earth, so it will not necessarily occur above the same location on the Earth, and the time taken to get back to that point depends on the energy of the orbit, so particles given different energy by the same explosion will pass through the same point later (if they have not hit the atmosphere) but at different times.