MadSci Network: Astronomy

Re: Can precession occur in the opposite direction?

Date: Fri Sep 21 14:30:39 2001
Posted By: Randall Scalise, Faculty, Physics, Southern Methodist University
Area of science: Astronomy
ID: 999537413.As

Dear Arthur,
I will first describe the precession of the equinoxes, then I will explain why it occurs in the direction that we observe.

Imagine that you are in space far above the North Pole of the Earth. You will see our planet rotating anti-clockwise (or counter-clockwise) once per day about an axis that runs through the North and South Poles. You will also see the Earth revolving anti-clockwise around the Sun once per year.

The mathematical plane containing the Earth's equator is not the same as the plane containing the Earth's orbit around the Sun (the plane of the ecliptic). These two planes intersect at an angle of approximately 23.445778 degrees. The Earth's rotational axis precesses clockwise (opposite to its sense of rotation) with a period of about 25,730 years. This means that, in different epochs, different stars become the "pole star." [The current pole star is Polaris, but, in a mere 13,000 years, Vega will become the pole star.]

The equinoxes (vernal and autumnal) are the directions along which the Earth's equatorial plane and the plane of the ecliptic intersect. The equinoxes also precess clockwise along the celestial equator, which is just the projection of Earth's equator on the celestial sphere.

Now, why does the Earth's rotational axis precess clockwise? The Earth is not spherical; it bulges at the equator due to its rotation. If the Earth were completely spherical, none of the other members of the solar system could exert a gravitational torque on it. As it is, the Moon exerts the largest gravitational torque on the Earth; and the Sun exerts a torque on the Earth about half as large as the Moon's torque. The torques due to other bodies are small enough to be neglected. The combined gravitational torque of the Moon and the Sun tries to align the Earth's rotational axis perpendicular to the plane of the ecliptic. This torque causes the Earth's rotational axis to precess clockwise.

You said:

Spin a gyroscope. Apply a torque by pushing the tip of the axis. The gyroscope wobbles. The wobble is in the direction of spin.

For a gyroscope, the precession is only in the direction of the rotation if you push down on the tip, that is, if you try to make the axis of rotation horizontal. If you were instead to push up on the axis (to make the axis vertical) then the precession would be in the direction opposite to the rotation. The latter case applies to the spinning Earth because the Moon and Sun try to make the Earth's axis of rotation perpendicular to the plane of the ecliptic. You could achieve this effect, called "retrograde precession," by tying a helium balloon to the tip of the gyroscope that does not touch the ground.

You also can experience this phenomenon yourself. Obtain a bicycle wheel mounted on an axle, and a low-friction swiveling stool. Many interactive science museums have this apparatus. Spin the bicycle wheel rapidly anti-clockwise as seen from above and tilt the axle roughly 23 degrees from the vertical. This wheel represents the Earth. Sit on the stool and ensure that the stool is not rotating. Now try to make the wheel axle vertical. You and the stool will begin to precess clockwise as seen from above.

--Randall J. Scalise

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