How can I calculate the tilt of the Earth using trigonometry?

In summary, the Earth has a tilt of about 23.439281° to -23.439281°, which causes the changing of seasons as it faces the sun at different points along the Tropic of Cancer and Tropic of Capricorn. The conversation discusses a MatLab program that shows a 3D Earth equatorial model with rings at the equator and at the maximum and minimum tilt points. The person is seeking help with the trigonometric equation for the loop ring that connects the tilt points through the origin. They provide an example of the equations they have used, but are having trouble finding a set of equations to calculate the Earth's tilt for a given obliquity of 23.439281°. They
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Earth has a tilt to it about 23.439281° to -23.439281° from the Tropic of Cancer to the Tropic of Capricorn. The tilt faces the sun at differrent points from 23.439281° to -23.439281° creating the seasons etc. I have written a preliminary MatLab program showing the 3D Earth Equitorial Model plus some rings at the equator and at the tilt maxima and minima. What I need is some help with the trigonomic equation of the 3D loop ring that connects the two tilt maxima and minima thru the origin. Here is an example of what I have. Center loop:

x = r * cos(theta) * sin(phi)
y = r * sin(theta) * sin(phi)
z = r * cos(phi)

where r = 6378100, phi = 90 and theta = 0 - 360
 

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I have had nothing but trouble finding a set of equations to calculate the Tilt of the Earth trigonometrically for a theta (0 to 2pi) and a given Obliquity = 23.439281° (for Earth). Please disregard the MatLab program above. Any suggestions would be much appreciated.
 
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Related to How can I calculate the tilt of the Earth using trigonometry?

What is the Tilt Model of the Earth?

The Tilt Model of the Earth, also known as the Axial Tilt Model, is a scientific theory that explains the tilt of the Earth's axis. It proposes that the Earth's axis is tilted at an angle of approximately 23.5 degrees from its orbital plane around the sun.

What causes the tilt of the Earth's axis?

The tilt of the Earth's axis is primarily caused by the gravitational pull of the sun and other planets in our solar system. This gravitational force causes the Earth's axis to wobble and tilt as it rotates around the sun.

What are the effects of the Earth's tilt?

The Earth's tilt has several effects on our planet. One of the most significant effects is the change of seasons. As the Earth orbits the sun, the tilt of its axis causes different parts of the Earth to receive varying amounts of sunlight, resulting in the four seasons we experience. The tilt also affects the length of daylight hours and the intensity of sunlight in different regions.

Is the tilt of the Earth constant?

No, the tilt of the Earth's axis is not constant. It has undergone changes over millions of years due to various factors such as gravitational forces, geological events, and the redistribution of mass on Earth's surface. However, these changes are relatively small and occur over long periods.

How is the tilt of the Earth measured and monitored?

The tilt of the Earth's axis is measured using specialized instruments such as inclinometers and tiltmeters. These instruments can detect even small changes in the Earth's tilt. The tilt of the Earth is also continuously monitored by satellites and ground-based observatories to track any significant changes that may occur.

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