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 The Direction of the Rotation of Planets

## Background

One of the most remarkable features of our solar system is that nearly all of the revolutions and rotations are in the same direction. From a point high above the north pole of the solar system the planets are revolving about the sun and rotating about their axes in a counterclockwise direction. This holds true also for the asteroids. If the planets and asteroids were formed from merely random accretions the would be an even mixture of the directions of revolution and rotation. The sun itself also rotates in a counterclockwise direction. The satellites of the planets also generally revolve and rotate in a counterclockwise direction. Of the thirty something satellites only six do not do so; they are said to have retrograde motion. Of the six exceptions five are outer satellites likely to be captured asteroids. More information will be given later about these exceptions.

## An Explanation for Planets Having the Same Direction of Rotation as Their Direction of Revolution

Consider the sun at some incredibly ancient time surrounded with a planetary disk much as Saturn is now surrounded by rings. The disk would have some direction of spin, say counterclockwise as shown below.

The disk would be spinning but not turning as a whole. The equilibrium distribution would have the tangential velocity proportional to the reciprocal of the square root of the disance from the sun. This follows from Kepler's Law as is shown in Orbital Velocities of the Planets.

#### v = α/r1/2 thus v2 = v1/(r2/r1)1/2

The red horizontal lines in the above diagrams represent the tangential velocities at different distances from the center of the sun.

When a center of agglomeration forms it draws in material. Some of this material comes a place more distant from the sun than the center of aggomeration. When this material moves toward the sun its tangential velocity increases to preserve angular momentum. Likewise the material that comes from places closer to the sun. As it moves out its velocity decreases to preserve angular momentum.

#### angular momentum per unit mass = v1r1 = v2r2thus v2 = v1/(r2/r1)

If the Earth's center is 93.5 million miles from the sun and it travels in a circular orbit then it travels 67,018 miles per hour. Material at 94 million miles from the sun would be traveling at a speed of 67,018/(94/93.5)1/2=66,839 mph. Material at 93 million miles would be traveling at a speed of 67,018/(93/93.5)1/2=67,198 mph. If the material at 94 million miles moved to 93.5 million millions its speed would increase to 66,839(94/93.5)=67,196. If material at 93 million miles moved out to 93.5 million miles its speed would decrease to 66,839 mph. Thus the material from 0.5 million farther out would be traveling (67,196-66,839)=357 miles per hour faster than the material 0.5 millions farther in. This would give a body composed of material farther out with material farther in a spin in the same direction as the spin of the planetary disk; in this case counterclockwise. This is shown in the diagram below.

In the case of Earth the points on the equator are traveling at about 1,000 mph. This might seem that some points area moving forward while points on the opposite side are moving backward, but this is not the case. The points on one side are moving forward at 67+1 thousand miles per hour and points on the opposite side are moving forward at 67-1 thousand miles per hour.

## The Exceptions

Venus and possibly Uranus are the exceptions to the counterclockwise rotations of the planets. Venus travels around the sun once every 225 Earth days but it rotates clockwise once every 243 days. This pecular combination gives it a day with respect to the sun of 117 Earth days. Uranus is tilted on its side about 90° so its direction of rotation is ambiguous. Its angle of inclination is usually given as 98° which would mean that its direction of rotation is not retrograde. If its direction of rotation is presumed retrograde then its angle of inclination would be 82°.