What goes up?
By Tom Brown
Mon, 26 May 2014
Even with the most reliable masses of information knowledge and understanding of gravity, it really still stays an enigma, a mystery we can work with but a mystery still. From Classical Mechanics to General Relativity and Quantum Physics, from Newton to Einstein, Schrödinger and Heisenberg, CERN and particle accelerators.
The more questions we can answer, the more many new ones take their place. It’s like a child’s game.
Mommy I want to fly from the roof! “You can’t you’ll fall down!
Why can a Jumbo Jet fly? “It’s an aircraft.
Why don’t we fall up? “It is gravity pulling everybody down.
Why? “Everybody does.
The people on the other side don’t fall off? “No they don’t.
Why? “Because the earth is turning.
Ending with, Mommy why is the Earth round? “Because it’s not flat.
However we would like to explore gravity from a layman’s view and concerning everyday practical kind of things. The discussion is limited to ordinary good old solid Newtonian mechanics.
Falling objects and terminal velocity
Galileo Galilei demonstrated with experiments that all objects fall equally fast. Up until then it was commonly believed and accepted that that heavier objects fall faster. There was no quantitative concept of acceleration then. The experiment was to drop a heavy and a light ball from a height (high building) and it was seen that they both hit the ground at the same moment.
This is not really 100% accurate because of the effect of air friction as I will explain. If the experiment is done in absence of atmosphere, that is in vacuum, yes then it's completely true. In order to explain the idea of drag, air friction, and its effect I will explain what terminal velocity is and how it works.
When an object moves through air it experiences a type of frictional force which is small at small speeds but increases as it goes faster. When the speed is relatively small the drag force is negligible and may be ignored as in Galileo's experiment. When someone jumps from an aircraft without a parachute his speed increases and until reaching an eventual “terminal” value. (A pun?) The well known kinematic equations for linear motion do not apply at comparative speeds.
As the velocity becomes larger the acceleration becomes smaller and smaller until there is no further increase in velocity and it reaches this constant value. In free-fall it happens when the forces balance, the drag force equals the weight. The same applies for any object.
Drag force at a given speed depends entirely on the aerodynamics: geometry– size and shape etc. and not mass. Terminal velocity itself depends not only on the shape and size of the object but also its weight, indirectly, mass. So that at “high” speeds traditional everyday impressions could appear to be correct.
Anything orbiting the earth the sun or a planet etc. can be called a satellite. This would include artificial (man made) objects as well as moon/-s etc. One may ask why doesn't a satellite fall? Well yes a satellite is falling all the time but in such a way that it misses the earth all the time. The idea is very similar to those of ballistic projectiles. Nearer satellites orbit faster and ones further away slower.
(By the way it’s a good argument to remember should you ever be confronted with “The earth is flat. You can see it’s flat.”)
The geostationary satellites are especially interesting since they are seemingly just hanging there up in the sky never falling down on us, as if by some magic trick or sorcery. Well the same, they do fall and just like any satellite they are in orbit but the orbit is synchronised to the earth's rotation, they orbit the earth once each day. The orbit is called is called geosynchronous.
Such geostationary satellites very obviously have terrific advantages. Think for example of communication or surveillance. The orbit then is of course in a very narrow range. The distance from earth and the placing needs to be precise in order make the orbital period exactly the same as one day. I would imagine that in order for a satellite to in effect completely “stand still” it has to also be directly above the equator.
External balanced gravity fields
There is another but distinctly different type of “stationary” satellite where it in effect stays in a fixed position relative to the earth and sun. It remains static in the same geometrical orientation. This kind of stationary situation now has nothing to do with the earth’s rotation. It is positions in space geometry that exist with gravity in balance.
Lagrange points are found when one looks for extrema of multi-variable functions under given mathematical constraints. The method can be applied too when the function and its constraints are defined implicitly. In this case, in balance, I’d think you want the points where the resultant gravitational field is zero. I would imagine there are three main types of such points, which I would call a stable “attractor”, an unstable “repellor” as well as different kinds of neutral equilibrium.
One possibility for such a point is where the earth and sun’s gravity are equal, a point that lies between them and moving together in unison, circling the sun together with the earth. And similarly or the same, but on other sides of earth. All of this can be applied verbatim to the earth-moon system or any appropriate candidate.
In this case clearly placement anywhere on the earth’s orbit will work a for such a “stationary” body. The satellite then is simply on exactly the same orbit as earth. Nothing fancy here. A neutral equilibrium. It is not a point in space either, it’s a line, a curve rather.
One could theoretically put a man-made object at a suitable placement where it would permanently just hang there, relative to the earth, a companion so to speak. To be able to station a satellite in such a critical position must bring great opportunities for research in pure science and observational astronomy. There are obviously interesting new possibilities for uses amongst more in surveillance and communications. Of course, and sadly, there will always be abuses for very destructive purposes for instance military and in warfare.
As far as astronomy, astrophysics and space exploration goes we are certainly living in very exciting times.