Re: Gravity and the Sun

From: tadchem (tadchemNOSPAM_at_comcast.net)
Date: 08/19/04 

Date: Thu, 19 Aug 2004 00:48:57 -0400

"JM Albuquerque" <jm.aREMOV.E@sapo.pt> wrote in message
news:2ohuksFb04c0U1@uni-berlin.de...

<snip>

> The problem is that Earth speed is a fundamental parameter
> in order that Earth orbit be stable.

The exact speed of an orbiting body is not critical to maintaining a stable
orbit. As long as the speed is *less than* escape velocity for that
distance, it will not leave the system.
http://scienceworld.wolfram.com/physics/EscapeVelocity.html

The lower limit for a stable orbit is a bit more problematical. Given the
'present' distance from the sun as the apehelion, the kinetic energy of the
orbiting body must be great enough that the perihelion falls outside the
Roché limit:
http://scienceworld.wolfram.com/physics/RocheLimit.html

> 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.

We are not necessarily talking about a dead stop in its tracks for the
earth, but a momentary cessation of the force that curves its orbit towards
the sun.

> 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.

The "right speed" to maintain a 'stable' orbit turns out to have a wide
range. If v is the speed in a circular orbit (eccentricity = 0) at a given
distance, any other speed from less than 0.1*v to 1.414*v will also lead to
a stable elliptical orbit (eccentricity >0 and <1):
http://scienceworld.wolfram.com/physics/Eccentricity.html

Tom Davidson
Richmond, VA

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