ORBITS, OR GOING ROUND AND ROUND,
JUMP UP! For a short time you were in orbit. REALLY! Unfortunately the orbit you were in intersected the surface of the Earth so you crashed after a short time. Let me explain. As the earth rotates we on the surface have a certain velocity. At the equator it's about 1000 MPH. That's your orbital velocity at apogee, the high point of your orbit. All objects in orbit about the Earth see the mass of the Earth as a single point, at the center of the Earth. If the Earth were to suddenly shrink to a small black hole, the Moon would continue to orbit exactly as it does now. So, when you jumped up, you were in an orbit about a point located at the center of the Earth. You crashed because the ground got in the way.
The parameters of an orbit are described by Newton's Universal Law of Gravitation, and there is an excellent discussion on how to calculate orbits in "The Space Handbook" a text printed for Air Force officers. (see the reading list on my web page, http://web.wt.net/~markgoll/) I calculated it out just for fun, and the perigee or low point of our "jump in the air orbit" is 3948 miles underground, or about 50,000 ft from the center of the earth.
Now if we want an orbit that avoids the prospect of hitting the earth, we'll have to gain a little more orbital velocity. An additional 16,500 miles per hour more or less, or 17,500 MPH total. Unfortunately the atmosphere that keeps us all alive makes that a bit difficult, there's just to much drag. The solution is to go above the atmosphere. Of course on the Moon you could orbit at ground level if you went fast enough, but watch out for the railroad crossings.
There are three types of orbits. Circular, always keeping a constant distance from the center of the planet. Elliptical, keeping a constant distance from two points, one of which is at the center of the planet. And hyperbolic, leaving the gravity of a planet and never returning.
The rocket is the only means by which we can get into space, and into orbit. Most rockets deliver their payloads into a "parking" orbit at an altitude of about 100 miles. That's just above the atmosphere. When the rocket releases the payload it is usually in an elliptical orbit with the low point, perigee, at the release point, and the high point, apogee, 180 degrees around on the other side of the planet. The apogee and perigee are always on opposite sides of the planet. (I always keep them separated by thinking that A=Apart=Aopgee) A short apogee burn is used to raise the perigee to create a more circular orbit. If the perigee is too low, atmospheric drag will cause the orbit to decay and the satellite will reenter the atmosphere.
Now for the rules of the game of orbital billiards. If you are at perigee, the low point, and you add energy, you raise the apogee. If you are at apogee, the high point, and you add energy, you raise the perigee. All bodies approaching from outside the gravitational field are on hyperbolic paths that will pass by the planet, and leave the gravitational field at the SAME VELOCITY. To convert a hyperbolic orbit to an elliptical one you remove energy. To convert an elliptical orbit to a hyperbolic one you add energy. You don't go anywhere with out energy.
The Hohmann transfer (Walter Hohmann, 1920's) is how you go from one circular orbit to another circular orbit. We'll go to a higher orbit. First you add energy, that raises the apogee on the other side of the planet to the height of the new circular orbit. When we get to the apogee, we add energy again to raise the perigee up to circularize the orbit. Until the early 70's the Hohmann transfer was the only way to get around in space, then somebody figured out the gravity assist, the orbital equivalent of a bank shot. When a satellite approaches a planet at a crossing angle to the planet's orbital path it will pass by the planet on a hyperbolic course. If the satellite's hyperbolic course leaves the planet along the planet's orbital path, it will have added the planet's orbital velocity to it's own. The satellite approaches and leaves the planet at the same relative velocity, but it's ANGLE with respect to the sun has changed. That's where the added energy comes from. The planet slows down slightly to balance the energy. Gravity assist can be used to speedup, slowdown, or simply change the course of a satellite.