Re: Gravity and the Sun

From: JM Albuquerque (jm.aREMOV.E_at_sapo.pt)
Date: 08/18/04 

Date: Wed, 18 Aug 2004 22:08:24 +0100

"Old Man" <nomail@nomail.net> wrote:
>
> "JM Albuquerque" <jm.aREMOV.E@sapo.pt> wrote in message
> news:2of9t7Fa9vo1U1@uni-berlin.de...
> >
> > The big question is:
> > How do you get GM / r^2 = 0.006 m/s^2 ???
>
> From http://nssdc.gsfc.nasa.gov/planetary/fact***/sunfact.html
>
> Sun: GM = 1.3 x 10^20 m^3 / s^2
>
> From http://nssdc.gsfc.nasa.gov/planetary/fact***/earthfact.html
>
> Earth's orbit: R = 1.5 x 10^11 m
>
> Thus a = - GM / R^2 = - 0.006 m / s^2
>
> > No value of M and r seams to satisfy your above statement.
> > Can you explain please?
>
> JM must explain it. He has made numerous arithmetic errors.

You are right Old Man, now I made a stupid arithmetic error with
the sign of the distance between Earth and Sun, as you have
pointed out.

Now I get the picture.
You have assumed that the Earth is free falling around the Sun
with an acceleration of 0.006 m/s^2.
Apparently it doesn't matter what is Earth mass, since that all the
objects fall at the same rate in a gravity field.

The problem is that Earth speed is a fundamental parameter
in order that Earth orbit be stable.
An object stopped at Earth distance from the Sun will fall to the
Sun along a straight line and will not have a "circular" orbit.
Earth mass and its kinetic energy is fundamental.
Without the right mass and the right speed the Earth will not
orbit the Sun, but will either go away or fall straight to the Sun.

At this point it is clear that if the Sun gravity is switched off
during a given period of time the Earth will go away and when
the Sun gravity is switched on again the new orbit is no longer
a stable orbit. The new orbit will have excess radius, or else
a speed deficit.

Angular momentum must be conserved.
So, when gravity is switched on again we have already seen
that Earth speed remains the same, but with a longer radius,
so that the usual balance between the "gravity force" and the
"centrifugal force" doesn't balance anymore.

I know that gravity force and centrifugal force are apparent
according to the recent physics philosophy, but I'm old and
I like them very much.

If this experiment could be done in reality we will know once
and for all if inertia and centrifugal force exists, or else if the
Earth orbit radius (or Earth absolute speed) will adjust to obey
the mathematical formula of the equivalence principle.

I bet that if the Earth is at a bigger orbit radius with the same
speed (same angular momentum), when the gravity of the
Sun is switched on again it must...

What's your bet ?
1 - It will spiral inside up to the previous position (the initial orbit).
2 - It will spiral away and forever.

I found this to be a difficult question.
Need to draw a picture on a computer graphic software.

Applying the angular momentum conservation Law, my bet
is that Earth will go away due to the inverse square term on
the radius, which means that inertia really exists, being the
central force (in the centrifugal force direction) always bigger
then the central gravity force.

Motion do cares on inertia, not on the equivalence principle
written on a paper (a mathematical formula).

The fact is that unbalanced satellites will fall, or will go away.
Satellites don't care about the mathematical formula.
Satellites must have the right speed at the right distance,
or else they will fall or will go away.
The same with the Earth.

"Old Man" <nomail@nomail.net> wrote:
>
> Old Man gave an expression for delta_R, the difference
> in radial distance between the circular orbit with gravity
> turned-on and the straight-line orbit with gravity turned-
> off. GM / R^2 is the acceleration for the initial circular
> orbit with gravity turned-on. It is assumed that
> delta_R << R and that v*delta_t << R.
>
> Except for the sign of delta_R, the order of events makes
> no difference. Gravity can either be turned on or off for
> one second. The only difference is in the sign of delta_R.

The order of the events is fundamental.
Your vision must be wrong due to what I've explained above
and I resume below.
- The Earth will spiral away forever because the angular
momentum is conserved (same inertia), but the force of
gravity decreases inversely proportional to distance.