Dealing with Creationism in Astronomy: Geocentrism vs. Inertial ...

Anyone who's flown on a plane knows that once the aircraft reaching its cruising speed (roughly constant) and altitude, for the most part, you can walk around the cabin just as you would if you were on the ground.? Your leg muscles apply force in the same way as if you were walking on the ground.? You need to do nothing special to account for the fact that you are moving 600+ miles per hour relative to the Earth.? If the aircraft is accelerating, changing altitude or speed, whether by turbulence or intent, you must expend more effort, but accelerated frames are a topic for another time.

Similarly, any child knows that if the car (or van) is traveling at a constant speed on straight and level highway, you can toss your ball up from your lap and it will fall back to your lap, same as if you were sitting in a chair at home, even though the van you are in might be moving 50+ miles per hour relative to the Earth.? You get a similar experience traveling on a train or subway.

The reason for this is that Newton's Laws are the same in inertial reference frames.? Inertial frames are defined as non-accelerating, or moving at a constant velocity.? A consequence of this fact is that Newton's Laws DO NOT DISTINGUISH ANY PREFERRED INERTIAL FRAME.

Why is this?

By Newton's Second Law (wikipedia):

F = m*a

where 'F' is the applied force, 'm' is the mass of the object to which the force is being applied, and 'a' is the acceleration, or rate of change of velocity, 'v' (velocity is the rate of change of position).? Mathematically, these are written using derivative (wikipedia) notation:

a = dv/dt = d^2x/dt^2

and the acceleration is the second derivative of position, x, with respect to time.

If the force, 'F', and mass, 'm', are constants, the most general solutions to this equation is, for some future time, t>0, for velocity, v:

v = dx/dt = B + (F/m)*t

and for position, x:

x = A + B*t + (1/2)*(F/m)*t^2

where 'A' & 'B' are called 'arbitrary constants' in the mathematical sense.?? In practice, these constants are determined from initial conditions (wikipedia) of the system under consideration. ? Beyond that, these constants are truly arbitrary - you can choose them with any origin, or zero point, that is convenient for your problem - the corner of your house, the center of the city, the center of the Earth, the center of Mars, or even the center of the Galaxy, or the center of a galaxy a million light-years away.

Note that the variable 'B' represents a velocity, so in addition to Newton's Laws being the same regardless of your POSITION in space, the laws also do not require a favored VELOCITY in space.
Note that if F = 0, the equation reduces to the spatial component of the Galilean transformation (wikipedia):

x = A + B*t

This equation solves the problem in one spatial dimension, but you can expand the case to three-dimensions by writing similar equations for the y and z directions, which are perpendicular to the x-direction, and each other.

Engineering Implications
Newton's Laws, and their invariant properties under coordinate transformations, have been experimentally tested for over three hundred years and have huge practical implications.? They get tested with the construction of probably every mechanical device.?

The most important of these practical applications is that in inertial frames, we can build devices that will work exactly the same if they are moved (accelerated) to another inertial frame.? We can test a rover robot on the surface of the Earth, then transport it to Mars, and the forces required for it to move are fundamentally the same (adjusting for the different surface gravity, ground texture, etc.) - the torque driving the wheels moving it forward does not need to consider that the rover is on a planet moving many kilometers per second relative to the Earth.? Similarly, thrusters adjusting the course of spacecraft moving very fast in the distant solar system (wikipedia: New Horizons) impart the same accelerations to the satellite as if it were in Earth orbit.

If the Earth were physically preferred reference frame, as claimed by Geocentrists, we would expect these principles to function differently when moving relative to the Earth, or at great distance from the Earth.? The fact that these devices function according to the same physical laws we've discovered on the Earth is evidence that the Earth is NOT a physically preferred reference frame.? A scientist on Mars will derive the exact same physical laws as a scientist on the Earth.

If Geocentrists want to claim that certain devices work in these other remote locations because we've designed them to work that way, the statement carries with it the implied assumption that somehow human technology violates the laws of physics.? That is utter nonsense.? The technological progress human society has enjoyed over the past three hundred years is an outgrowth of our ability to understand those physical laws and work within their constraints. ?

Additional References:
Frames of Reference and Newton?s Laws
by Michael Fowler

Source: http://dealingwithcreationisminastronomy.blogspot.com/2012/02/geocentrism-vs-inertial-frames.html

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