San José State University

applet-magic.com
Thayer Watkins
Silicon Valley
USA

 An Explanation of the Slow Retrograde Rotation of Venus

The Solar System is a wonderously regular system. From a viewpoint high above the North Pole of the Sun the planet and their satellites are generally rotating and revolving about the Sun in a counterclockwise direction. Most of the planets of the Solar System formed near the resonance orbits; i.e., where the period of revolution about the Sun is one half or two-fifths of the period of the next planet beyond it. Most of the planet have periods of rotation between ten and twenty-four hours.

There are a few anomalies. Some satellites and the planet Venus rotate in the opposite direction. The period of rotation for Venus is 243 days. What is investigated here is a plausible explanation for the retrograde rotation of Venus and the enormously long period of rotation.

Consider the following scenario. Suppose in the region where Venus is now two planetoids formed; one near the 0.4 resonance orbit and one near the 0.5 resonance orbit. Here everything is measured relative to Earth's orbit radius and orbit period. (These are called Astronomical Units (A.U.).)

By Kepler's Law, R=T2/3, the radii corresponding to these orbit periods are 0.42/3=0.543 and 0.52/3=0.630 .

The tangential velocities of the two planetoids would then be 2π(0.543)/0.4=8.5294 and 2π(0.630)/0.5=7.9168. When the two planetoids were adjacent to each they would appear to be rotating in a clockwise direction with respect to their center of mass (C.M.). Clockwise rotation is retrograde.

The difference (0.6126) is their tantgential velocities would rate of rotation ω times the difference in their orbital radii (0.870).

Thus

#### ω = 0.6126/0.087 = 7.0414 radians per Earth year.

This means that it takes 2π/7.0414 Earth years to complete one rotation of the two planetoid system. This is 0.8923 of an Earth year or 326 days. The actual period of rotation of Venus is 243 days.

When the planetoids merge their surfaces are moving on opposite directions. It is a head-on collision of their surfaces. An enormous amount of energy must be dissipated as heat. The material of the planetoids would melt. The initial counterclockwise rotations of the planetoid would be cancelled. The collapsed system would be left with a clockswise rotation at a relatively slower rate. This is qualitatively what Venus has. The scenario establishes retrograde rotation as a consequence of the merger of nearby planets. This makes plausible the origin of Venus as the merger of two smaller planetoids in nearby orbits.