2.1: THREE WAYS WHICH THE MOON AFFECTS THE MOTION AND                 ORIENTATION OF THE EARTH.

 

1)      ANGLE OF TILT OF THE EARTH’S AXIS

2)      SPEED OF AXIAL ROTATION

3)   PRECESSION

 

2.1.1: TILT OF THE EARTH’S AXIS:

The Giant Impact is credited with giving the Earth its tilt of 23.5 degrees in relation to the perpendicular (straight up). The resultant Moon is credited with keeping it relatively stable, between 21.5 and 24.5 degrees, in a cycle of 41,000 years.

 

Fig 7: Tilt of Earth

Our Moon can do this only because it is large enough (one-sixth of Earth’s mass). Only Pluto has a satellite that is just as large in comparison to its planet. By contrast, Mars, with only two tiny moons, has an axial tilt varying between 15 and 35 degrees over a 50,000-year cycle.

 

 

2.1.2: SPEED OF AXIAL ROTATION:

When the Moon first formed after the Giant Impact, it was much nearer to the Earth (20,000km or 20 times nearer than present.) Both bodies exerted a pull on each other causing huge tidal forces. The tides produced frictional force, which resulted in the slowing on both the Earth’s and the Moon’s speed of rotation. The resultant imparting of angular momentum then caused the Moon to move further away.

Tides slow Earth's rotation and enlarge Moon's orbit

Fig 8: Spin of Earth

This process is still ongoing, with the Earth’s days shortening by 0.0015 milliseconds per year and the Moon moving away at about 3.8cm a year. The Moon is no longer slowing its rotation as it is in orbital synchronicity with the Earth. That means that it takes just as long for it to rotate a full 360 degrees on its axis as it does to orbit once round the Earth. Will the Moon move so far out that it may actually leave its orbit altogether? No worries; The Sun is set to explode long before that!

           

2.1.3: EFFECT OF MOON ON PRECESSION:

“Precession of the equinoxes”, is the effect whereby the Earth’s rotation axis sweeps out a cone centred on the ecliptic pole, completing one revolution in about 26,000 years. Cause of motion is the force exerted on the spinning Earth by the Sun and the Moon.

 

Figure 9: The Earth's precession

                                                                                                                                     

I)         a) Consider the Sun alone, at or near the June solstice.

b) Sun ‘sees’ the top part (North Pole) of the Earth tilted towards it (by about 23.5 degrees, the angle of the ecliptic) and sees the nearer part of the Earth’s equatorial bulge below centre and further part above centre. (See fig.1)

c) Although the Earth is in a free fall, the gravitational force on the nearer part of the equatorial bulge is greater than that on the further part, so there is a net force x acting as if to eliminate the tilt.

d) Six months later, at the December solstice, the same thing is happening in reverse except that force x is still trying to eliminate the tilt.

e) In between, that is at the equinoxes, the force shrinks to zero.

f) Force acting on a spinning body causes a precessional motion of the spin axis at right angles to the force, and this is what happens to the Earth.

g) The motion varies through the year, going through two maxima, but always acting in the same direction.

     

II)        a) The Moon produces the same effect, adding a contribution to the precession, which peaks twice per month.

b) The Moon’s proximity to the Earth compensates for it’s smaller mass and weaker gravitational attraction, and it in fact contributes to most of the precession effect.

 

                                                                  

                                                           SUN                         EARTH                 MOON

Fig 10:  “Straightening” of Earth’s axis of rotation by Sun and Moon.

 

The complex interactions between the three bodies produce a precession motion that is wobbly rather than completely smooth. However the main 26,000-year component is on such a grand scale that it dwarfs the remaining terms, the biggest of which has an amplitude of 17’ and a period of 18.6 years. The difference of scale makes it easier to treat these two components of the motion separately. The main 26,000-year effect is called luni-solar precession and the smaller, faster periodic terms nutation.

However, note that it is a misconception that precession is caused by the Sun and nutation caused by the Moon. Precession and nutation are simply two different frequency components of the same physical effect. In fact, the Moon is responsible for two-thirds of the Earth’s precession.

 

Fig 11: Earth’s precession as seen by standing at the North Pole,

where the north celestial pole is at zenith and observing how that point changes with time.

 

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