From Newsgroup: sci.physics


I have asked an AI-bot the following questions, and got
the following answers:

Q1:
A satellite is orbiting Earth with constant speed.
Is the orbit necessarily a circle?

A1:
Yes, a satellite in a circular orbit around Earth has
a constant gravitational potential energy.

Q2:
Is the geoid at the same gravitational potential?

A2:
Yes, the geoid is an equipotential surface, meaning it
has the same gravitational potential.

Q3:
Is the geoid at longitude 0 a circle?

A3:
No, the geoid at longitude 0 is not a circle.

Q4:
You have stated:
"No, the geoid at longitude 0 is not a circle."
and
"Yes, the geoid is an equipotential surface"
and
"Yes, a satellite in a circular orbit around Earth has
a constant gravitational potential."
Comment?

A4:
"The geoid is an equipotential surface of the Earth's
gravitational field, meaning it is a surface on which
the gravitational potential is constant.
. . .
Therefore, the geoid at any longitude, including longitude 0,
is not a circle because it reflects the complex, non-uniform
gravitational field of the Earth.
. . .
A satellite in a circular orbit around Earth does not have
a constant gravitational potential. While the satellite's
orbit is circular, the gravitational potential varies slightly
due to the Earth's non-uniform mass distribution."

My comment:
This is correct. If the orbit is circular, the gravitational
potential isn't necessarily constant due to "Earth's non-uniform
mass distribution." (The quadrupole momentum.)


Q5:
You have stated:
"Yes, a satellite in a circular orbit around Earth has
a constant gravitational potential"
and
"A satellite in a circular orbit around Earth does not
have a constant gravitational potential."
Comment?

A5:
"The apparent contradiction rCo stating both that a satellite
in a circular orbit has constant gravitational potential
energy and does not have constant gravitational potential
energy rCo arises from a misunderstanding or misstatement.
The correct physical principle is:
A satellite in a circular orbit around Earth
has constant gravitational potential energy.
Therefore, the statement "A satellite in a circular orbit
around Earth does not have a constant gravitational potential"
is incorrect if referring to a stable, unchanging circular
orbit.

My comment:
Read this answer carefully, and you will se that it is nonsense.
The point is that the "physical principle":
"A satellite in a circular orbit around Earth
has constant gravitational potential energy."
is wrong!
Due to the quadrupole momentum of Earth an orbit at constant
gravitational potential is not necessarily a circle.
It will be circular if it is in the equatorial plane,
and very close to circular for high orbits like GPS.
But for satellites in low orbit it will be a difference.
An orbit right above the geoid would be at the same
altitude above the ground.

I re-asked question 1:
Note that if the speed of the satellite is constant,
the satellite will be at constant gravitational potential.

Q6:
A satellite is orbiting Earth with constant speed.
Is the orbit necessarily a circle?

A7:
A satellite orbiting Earth with constant speed does not
necessarily have a circular orbit.

While a circular orbit involves constant speed, the reverse
is not always true. An object in a circular orbit maintains
a constant speed because the radius and gravitational force
are constant, resulting in uniform circular motion.

However, in elliptical orbits, the speed of a satellite variesrCo
faster at perigee (closest point to Earth) and slower at apogee
(farthest point). But there are specific cases, such as circular
orbits, where speed is constant.


My comment:
Now the confusion is complete! :-D
Compare the first and last statement in the answer.
--
Paul

https://paulba.no/

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From Newsgroup: sci.physics

"Paul.B.Andersen" <relativity@paulba.no> wrote or quoted:

Compare the first and last statement in the answer.

I'm not really surprised by chatbot contradictions, because I deal
with them constantly, and I know a chatbot's fed with conflicting
info too.

The Earth can be modeled in different ways, like a sphere with
constant mass density, or a rotation ellipsoid with constant density,
or as precisely as all known details allow. Depending on how you mod-
el it, you get different conclusions, and in your chat with the bot,
you've probably mixed multiple models.

To make the whole thing a bit more consistent, you could start
by agreeing with the bot on one specific model. But even then, it'll
probably mess up sometimes.


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