The picture above of a spining top is a model for the Earth. Precession is causing it's axial tilt to rotate in a circle.
So that when there is no tilt there can't be any precession?
Yes, without an axial tilt, no precession would occur, and the Earth would revolve in a fixed position, relative to the faraway stars. We would always have the same star pattern above our heads, with the same Northern and Southern pole stars (if there was a star lined up just right on each hemisphere.).
And are the inclination degrees of the precession and the tilt related or the same.
The tilt is relatively constant, 23.5 degrees, but the precession, which in the case of Earth takes 26,000 years, means that the axial tit will point, in relation to farway stars, in different directions.
However, Nutation creates a small but significant in the angle of tilt of the Earth towards the Sun. This has the effect of altering the position of both the polar circles and the tropical circles.
The moon is also involved in this process, the greatest component of the nutation of Earth is similiar to that of the precession of the orbital nodes of the Moon, with a period of 18.6 years.
My thanks to Jim for pointing this out.
Our pole star is now Polaris, in the Ursa Major constellation, but in 3000 BCE, the faint star Thuban in the constellation Draco was the North Star.
Tilt And Precession
The phenomenon we call "precession" was discovered by Greek astronomer Hipparchus when he compared his own circa 200 BC records with older charts. What he saw was that the equinoxes in his day (where the sun's path crosses the celestial equator) were in a different position among the stars than the 150-year-old comparison charts showed. This is due to a gyroscopic wobble of earth's spin axis that takes 26000 years to complete.
In this wobble motion, the tilt of the earth stays roughly constant at 23.4 degrees but the orientation is always changing.
Changes in Precession Rate
When, in about 1,500 million years, the distance of the Moon, which is continuously increasing from tidal effects, has increased from the current 60.3 to approximately 66.5 Earth radii, resonances from planetary effects will push precession to 49,000 years at first, and then, when the Moon reaches 68 Earth radii in about 2,000 million years, to 69,000 years. This will be associated with wild swings in the obliquity of the ecliptic as well. Ward, however, used the abnormally large modern value for tidal dissipation. Using the 620-million year average provided by tidal rhythmites of about half the modern value, these resonances will not be reached until about 3,000 and 4,000 million years, respectively. However, due to the gradually increasing luminosity of the Sun, the oceans of the Earth will have vaporized long before that time (about 2,100 million years from now).