A speed beyond light question ^^

Read the damn book, Brandon, exact reference was posted above. Sober up enough to learn basic Newtonian gravity (infinite GRAVITY propagation speed MUST apply IF angular momentum is to be conserved, and the conservation of angular momentum wasn't doubted by Newton!) first, though.

I really don't see where you add value to this discussion if you can't even grasp complete BASICS. Sorry I'm not going to waste any more time until you start showing at least SOME grasp of basic concepts, never mind relativistic gravity field equations.

Although Newtonian mechanics has been superseded by relativistic mechanics, and, therefore, is not relevant here, I am willing to respond to this post of yours. Neither of us can add value unless he understands the basics. With two physics degrees, I think I do. Do you? I'll ask you an elementary question about gravity and circular motion in Newtonian mechanics, which anyone who completed a high school physics class with good grades could work out in 10 or 15 minutes. If you can answer, we can continue the discussion. If not, I'll give the solution in detail, and you can stop talking about physics.

Your post was number 3519687. I'll use that number. A satellite has a circular orbit around the Earth at a height of 3519 miles. What is its speed and kinetic energy? Give your units, and show your work.

For the kinetic energy question, you can assume that the satellite weighs 10 pounds, or else keep your equations in symbolic form.

I really don't see where you add value to this discussion if you can't even grasp complete BASICS.

And you, Brandon, are demonstrating a terminal lack of capacity to understand simple mathematics, not to mention basic English.

Never once did I say anything other than I'm a mathematician. You are evidently not one, nor have you made the least effort to work your way through the Lorentz transformations - which have many applications in physics, as even we mathematicians have heard...

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Certainly a great expert on Newtonian mechanics and satellite orbits like yourself ....

Sorry, I need parentheses:

x' = (x + vt) / SQRT(1 - v^2 / c^2)
y' = y
z' = z
t' = (t + vx/c^2) / SQRT(1 - v^2 / c^2)

for a frame F' moving at speed v in the x direction relative to frame F.

A similar path to the same goal could also be taken in those manifolds in which the line element is expressed in a less simple way, e.g., by a fourth root of a differential expression of the fourth degree…

Similarly for the super-light cones (or spheres), there would be a single state of motion with respect to which all of those null surfaces would be spherically symmetrical. Only the accumulation shell, i.e., the actual light-cone itself, would be spherically symmetrical with respect to all states of motion.

Brandon9000 wrote:

Sorry, I need parentheses:

x' = (x + vt) / SQRT(1 - v^2 / c^2)
y' = y
z' = z
t' = (t + vx/c^2) / SQRT(1 - v^2 / c^2)

for a frame F' moving at speed v in the x direction relative to frame F.

Brandon - the problems with your equations exceed lack of parentheses: specifically, you left out an additional term. The extra term (which, if you had remembered, you would have preceded by SQRT, which is conventionally written as {^1/2}, when, as on this website, mathematical notation is unavailable) is:

[1-(v/c)^2]^1/2

.....

The transformations apply to a four-dimensional coordinate system, with three spatial coordinates (x, y, & z) and one time coordinate (t). The new coordinates are denoted with an apostrophe, pronounced "prime," such that x' is pronounced x-prime. In the example below, the velocity is in the xx' direction, with velocity u:

x' = ( x - ut ) / sqrt ( 1 - u2 / c2 )
y' = y
z' = z
t' = { t - ( u / c2 ) x } / sqrt ( 1 - u2 / c2 )

This system of specifying positions is quite stable, but not perfect. Around 150 BC the Greek astronomer Hipparchus carefully compared his own observations of certain stars with observations of the same stars recorded by Timocharis 169 years earlier (and with some even earlier measurements from the Babylonians), and noted a slight but systematic difference in the longitudes. Of course, these were all referenced to the supposedly fixed direction of the line of intersection between the Earth's rotational and orbital planes, but Hipparchus was led to the conclusion that this direction is not perfectly stationary, i.e., that the direction of the Sun at the equinoxes is not constant with respect to the fixed stars, but precesses by about 0.0127 degrees each year. This is a remarkably good estimate, considering the limited quality of the observations that were available to Hipparchus. The accepted modern value for the precession of the equinoxes is 0.01396 degrees per year, which implies that the line of the equinoxes actually rotates completely around 360 degrees over a period of about 26,000 years.