July 03 2004

Speed of Gravity Amendum


Previously I described gravity is a mechanical wave and as such doesnt not travel at the speed of light. I will now clairify that statement and state that it is not so much a wave as it is a shower of X particles down on a body that causes gravity. The particle(s) that is responsible for the downforce that we feel is not massless, therefore it is reasonable to assume that it does not travel at the speed of light. The photon is the only massless particle we know of and it does travel at the speed of light, the photon however because it is massless has no physical push to the object which absorbs it. So what is the speed of gravity?

The speed of gravity or downforce is exactly related and proportional to the mass and gemometry of bodies involved.

Example. A man weighs 170lbs on the surface of the Earth. That same man weighs 1/6 on the surface of the moon. That is because the speed of gravity, or rate of downforce, is 1/6 than that of the Earth. The moon has less mass therefore is less attrative.

The speed of gravity is relative.
-TDuncan

The relative speed of quantum gravity is known by the velocity of X particles being absorbed by a solar body.

Now even if you are still convinced somehow that gravity works as Einstien would state, a curvature of space, the speed of gravity as described by me can be related accordingly. The greater the "curvature of space", the greater the "inclination", thus the greater the speed at which you "roll" to center mass. In the same way although, the speed of gravity is still relative.

The confusion comes about as a result of field theory, trying to create a mediator particle, the graviton, that would mediate the gravity force. Now there is something to understand, the gravity force in this manner could be mediated at any speed including light (although that would suggest the graviton is massless), but the magnitude of attration could at the same time be weak, so that what you end up with is a constant attration at the speed of light but the velocity of the mass being affected is still related to the magnitude of this mechanism. In other words, if the magnitude of force is greater, the velocity of the mass will be greater regardless how fast the mediator particle travels. So really what that is saying is in field theory, the speed of gravity is declared by how fast the mediator particle travels, not the degree or magnitude of force felt, which most people would end up relating to speed of mass or the speed of gravity.

However in the absense of a field theory, because there is no independent mediator particle, what you need to calculate as the speed of gravity is the magnitude of force felt defined as a vector quantity, or 2, velocity of an object in a vaccum. Both with regard to being measured in a defined local or "gravitational field".

Now is the speed of gravity on Earth, the max speed at which an object freefalls - the terminal velocity? The answer is yes for all practial purposes. However that does not necessarily mean that is the speed of X particles inbound pushing on the mass as those may not feel a resistence equal to that of air resistence quantumly speaking. Right so, you can define the speed of gravity on the quantum scale and on the macro effect scale. On Earth, generally speaking, acceleration of a body due to gravity is 9.8m/s2. The gravitational acceleration decreases with the square of the distance from the center of the earth - an inverse square law. Note however while acceleration is a constant, velocity increases linearly and location increases quadratically.

Here is a table of calculated acceleration (meters per second squared), velocity (meters per second), and displacement (meters) at 1 second intervals.

Time = 0, Accel = 9.8, Velocity = 0.0, Distance = 0.0

Time = 1, Accel = 9.8, Velocity = 9.8, Distance = 4.9

Time = 2, Accel = 9.8, Velocity = 19.6, Distance = 19.6

Time = 3, Accel = 9.8, Velocity = 29.4, Distance = 44.1

Time = 4, Accel = 9.8, Velocity = 39.2, Distance = 78.4

Time = 5, Accel = 9.8, Velocity = 49.0, Distance = 122.5

Time = 6, Accel = 9.8, Velocity = 58.8, Distance = 176.4

Time = 7, Accel = 9.8, Velocity = 68.6, Distance = 240.1

Time = 8, Accel = 9.8, Velocity = 78.4, Distance = 313.6

- Terminal Velocity

The terminal velocity of a falling body occurs during free fall when a falling body experiences zero acceleration. This is because of the retarding force known as air resistance. Air resistance exists because air molecules collide into a falling body creating an upward force opposite gravity. This upward force will eventually balance the falling body's weight. It will continue to fall at constant velocity known as the terminal velocity.

The magnitude of terminal velocity depends on the weight and geometry(surface area) of the falling body. For a heavy object, the terminal velocity is generally greater than a light object. This is because air resistance is proportional to the falling body's velocity squared. For an object to experience terminal velocity, air resistance must balance weight. An example that shows this phenomenon was the classic illustration of a rock and a feather being dropped simultaneously. In a vacuum with zero air resistance, these two objects will experience the same acceleration. But on the earth this is not true. Air resistance will equal weight more quickly for the feather than it would for the rock. Thus the rock would accelerate longer and experience a terminal velocity greater than the feather.

The terminal velocity for a skydiver was found to be in a range from 53 m/s to 76 m/s. This value is variable since the weight and the orientation of the falling body play significant roles in determining terminal velocity.


Now to explain it in more technical terms. Mathmatical speaking, the weight of an object can be defined as the gravitational force. So an object which is falling through the atmosphere is subjected to two external forces. One force is the gravitational force, expressed as the weight of the object. The other force is the air resistance, or drag of the object. The motion of any object can be described by Newton's second law of motion, force F equals mass m times acceleration a: or F = m * a

which can be solved for the acceleration of the object in terms of the net external force and the mass of the object:
a = F / m

Weight and drag are forces which are vector quantities. The net external force F is then equal to the difference of the weight W and the drag D
F = W - D

The acceleration of a falling object then becomes:
a = (W - D) / m

The drag force depends on the square of the velocity. So as the body accelerates its velocity and the drag increase. It quickly reaches a point where the drag is exactly equal to the weight. When drag is equal to weight, there is no net external force on the object and the object falls at a constant velocity as described by Newton's first law of motion. The constant velocity is called the terminal velocity .

We can determine the value of the terminal velocity by doing a little algebra and using the drag equation. Drag depends on a drag coefficient, Cd the air density, r the square of the velocity V and some reference area A of the object:

D = Cd * r * V ^2 * A / 2

At terminal velocity, D = W. Solving for the velocity, we obtain the equation

V = sqrt ( (2 * W) / (Cd * r * A) )