Prograde and Retrograde Motion
Date: Sunday, September 15, 2002
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?
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
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
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
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.
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