Tuesday 18 August 2020

orbital motion - Why are planets in unstable equilibrium in a stable orbit?



It is well known that a planet in stable orbit is in unstable equilibrium. If e.g. the moon was just a few m/s slower in velocity, or a few m closer to the earth than it is, the gravity would constantly be more than the centripetal force and over millions of years, it would be pulled towards the earth. As it moved towards the earth, the gravity would increase still further, causing it to crash to earth even faster. THERE WOULD BE NO POINT WHERE THE GRAVITY WOULD BECOME EQUAL TO THE CENTRIPETAL FORCE AGAIN, ALLOWING IT TO ENTER A STABLE EQUILIBRIUM. Similarly, if it was a little faster or a little further away, it would fly off in space, and never return to equilibrium.


It is also well-known that systems not in equilibrium cannot exist in practice, e.g. for a pencil standing on its point, where it would fall if tipped slightly, we would not expect millions of such pencils standing on their point routinely existing in nature. Similarly, if evaporation of water in a closed vessel were to cause more evaporation, then all the water would be evaporated and the vapor would never be in equilibrium with the liquid.


Yet, we see millions of planets and moons in stable orbits yet in unstable equilibrium in nature. How is this possible?


When each planet (with respect to its star) and each moon was first created, or first passed by one another, how did they come to be at the very exact velocity and very exact distance from each other so that they could get trapped in a stable orbit, so that if the velocity or distance was just a little bit more or less, the orbit would have decayed and would never be stable? How did this very rare coincidence happen billions of times so that there are billions of planets and moons in stable orbits?




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