From: Ronald Wong (ronwong@inreach.com)
Date: Tue Nov 04 2003 - 02:24:51 PST
Message-Id: <l03102806bbca108cf85e@[209.209.18.69]> Date: Tue, 4 Nov 2003 02:24:51 -0800 From: Ronald Wong <ronwong@inreach.com> Subject: re: two questions
Recently, Mike brought up the following issues:
>...
>Another student asked whether an object moving in a gravitional field
>would accelerate indefinitely because there is no air resistance.
A. If the object is in orbit about a body, the answer is yes.
Unless the orbit is a perfect circle, the speed and
direction of the object would be constantly changing
forever (assuming we ignore air friction, the
gravitational influence of other bodies, tidal effects,
etc.).
B. If the object is moving towards a body, the answer is no.
It will ultimately crash into the body.
C. If the object is moving away from a body, then
1. If the velocity is less than the escape velocity at
the object's location, the answer is no. It will come
to rest at a certain distance from the body and then
turn into case B.
2. If the velocity is not less than the escape velocity,
then it will continue to accelerate as it heads out
to infinity.
>He wanted to know if an object could reach super high speeds because
>of this.
Referring to the above three cases:
A. In order to orbit a body, the object's maximum speed must
be less than the escape velocity. An object orbiting the
earth has a maximum speed of around 11 km/s for instance.
B. The final speed = 0 km/s.
C. 1. The final speed = 0 km/s
2. Since the object is moving away from the body, it's
kinetic energy is being converted into potential energy
The object is slowing down. It's acceleration is
negative and becomes less in size as the object gets
further away from the body.
The bottom line is that, for those objects that don't collide with the body
in whose gravitational field they are moving, the object's speed is finite
and less than the escape velocity.
>... or go into orbit around it, which would make it maintain a constant
>speed.
>Is this correct?
To maintain a constant speed, the orbit would have to be a perfect circle.
For a simple, two-body problem, the odds favor an elliptical orbit where
the speed and direction of the orbiting body are changing in a well defined
way. The circular orbit is a special case of an ellipse - one with an
eccentricity of zero.
Of the Sun's nine planets, two come close to a circular orbit: Venus and
Neptune with eccentricities a little smaller than 0.01 (the earth's is
around 0.02)
Cheers.
ron
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