ASTA01H3 Lecture Notes - Lecture 2: Axial Tilt, Libration, Angular Diameter
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ASTA01- Chapter 2 User’s Guide to the Sky: Patterns and Cycles
• More than 2100 years ago, astronomer Hipparchus compared a few of his star
positions with those made by other astronomers nearly two centuries before him.
§ He realized that the celestial poles and equator were slowly moving relative
to the stars.
§ Later astronomers understood that this apparent motion is caused by a
special of Earth called precession.
• If you have ever played with a toy top or gyroscope, you may recall that the axis
of such a rapidly spinning object sweeps around relatively slowly in a circle.
§ The weight of the top tends to make it tip.
§ This combines with its rapid rotation to make its axis sweep around slowly in
• Earth spins like a giant top, but it doesn’t spin upright relative to its orbit around
§ You can say either that Earth’s axis is tipped 23.5°from vertical or that Earth’s
equator is tipped 23.5° relative to its orbit.
§ “obliquity” 23.5°
• Earth’s large mass and rapid rotation keep its axis of rotation pointed toward a
spot near Polaris (alpha Ursa Minoris).
§ Its axis direction would not move if Earth were a perfect sphere.
§ However, Earth has a slight bulge around its equator.
§ The gravity of the Sun and Moon pull on this bulge, tending to twist Earth’s
axis upright relative to its orbit.
• The combination of these forces and Earth’s rotation causes Earth’s axis to
precess in a slow circular sweep – taking about 26 000 years for one cycle.
• As the celestial poles and equator are defined by Earth’s rotational axis,
precession moves these reference marks.
• You would notice no change at all from night to night or year to year.
• Precise measurements, though, reveal their slow apparent motion.
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• Over centuries, precession has dramatic effects.
§ Egyptian records show that 4800 years ago the north
celestial pole was near Thuban (alpha Draconis).
§ Now, the pole is approaching Polaris and will be
closest to it in about 2100.
• In about 12,000 years, the celestial pole will have moved
to the apparent vicinity of the very bright star Vega (alpha
• The figure shows the apparent path followed by the north celestial pole over
thousands of years.
The Cycle of the Sun
• Rotation is the turning of a body on its axis.
§ Revolution is the motion of a body around a point outside the body.
§ Earth rotates on its axis – and that produces day and night.
§ Earth also revolves around the Sun – and that produces the yearly cycle.
The Annual Motion of the Sun
• Why don’t we see stars during the day?
• Even in the daytime, the sky is actually filled with stars.
§ However, the glare of sunlight fills Earth’s atmosphere with scattered light,
and you can only see the brilliant blue sky.
• If the Sun were fainter and you could see the stars in the daytime, you would
notice that the Sun appears to be moving slowly eastward relative to the
background of the distant stars.
• This apparent motion is caused by the real orbital motion of Earth around the
Ø Note that your viewing angle in the figure makes the Earth’s orbit seem very
elliptical when it is really almost a perfect circle.
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