From: relativity@paulba.no   
      
   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 — stating both that a satellite   
      in a circular orbit has constant gravitational potential   
      energy and does not have constant gravitational potential   
      energy — 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 varies—   
   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/   
      
   --- SoupGate-DOS v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)