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Name: Dileep
Status: teacher
Age: N/A
Location: N/A
Country: N/A
Date: Sunday, September 15, 2002


Question:
In a typical introductory course of physics, it is customary to assume that the gravitational force provides the centripetal force for the planetary motion and have the equation of velocity: V^2 = GM / r. The same approach is taken for finding the velocity of Earth's Moon also. In doing this, the direction of motion of, planet / moon, is ignored because: i) all planets are orbiting the Sun in the same direction - that is all planets of our solar system are prograde in nature and ii) as our Earth has only one moon and that too is prograde in nature. However, as we go to Jupiter the situation changes considerably because it has prograde as well as retrograde moons. This situation poses the question:

Can we use the same assumption for finding the velocity of a prograde as well as a retrograde moon of the Jupiter - without getting any problem in the comprehension of motion of these moons?


Replies:
Dileep,

The same formulas apply to either direction of rotation. There is nothing special about prograde motion except it happens to be the direction of the earth's orbit.

There is a theory as to why all planets in our solar system orbit in the same direction. It is possible that the sun was at one time much bigger than the solar system and much less compact. At the time, just a rotating glob of junk. The gravitational attraction pulls it in. Most of the matter collapses into a star. Some collapses into planets. The sun and planets rotate in the same direction.

Moons can come from the planet, from swirling debris around a planet, or from somewhere else. When a planet has moons orbiting in both directions, chances are that some of the moons are captured asteroids or meteors.

There is really nothing special about prograde vs. retrograde motion.

Dr. Ken Mellendorf
Physics Instructor
Illinois Central College


Yes, to an *excellent* approximation. Suppose the planet (or, more precisely, the center of mass of the planet/moon system) were moving in a straight line at constant velocity, instead of orbiting the sun. In that case, the formula for the moon's speed clearly would be unchanged, because physical laws address only relative motion. (Even if the formula were changed, there would still be no difference between prograde and retrograde motion in this case.)

Now what's the difference between a planet orbiting the sun and a planet moving in a straight line? Over the time required for one complete orbit of one of Jupiter's moons (seven days for Ganymede) Jupiter's motion takes it only about half of a degree of arc around the sun. (Jupiter's orbital period is ~12 years.) The difference between Jupiter's motion and a straight line, over the seven-day orbit of Ganymede, is negligible, and this means that the difference between prograde motion and retrograde motion is also negligible.

Tim Mooney



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