Newton's Theorem of Revolving Orbits - Orbital Precession

Orbital Precession

If k is close, but not equal, to one, the second orbit resembles the first, but revolves gradually about the center of force; this is known as orbital precession (Figure 3). If k is greater than one, the orbit precesses in the same direction as the orbit (Figure 3); if k is less than one, the orbit precesses in the opposite direction.

Although the orbit in Figure 3 may seem to rotate uniformly, i.e., at a constant angular speed, this is true only for circular orbits. If the orbit rotates at an angular speed Ω, the angular speed of the second particle is faster or slower than that of the first particle by Ω; in other words, the angular speeds would satisfy the equation ω2 = ω1 + Ω. However, Newton's theorem of revolving orbits states that the angular speeds are related by multiplication: ω2 = kω1, where k is a constant. Combining these two equations shows that the angular speed of the precession equals Ω = (k − 1)ω1. Hence, Ω is constant only if ω1 is constant. According to the conservation of angular momentum, ω1 changes with the radius r

\omega_{1} = \frac{L_{1}}{m r^{2}};

where m and L1 are the first particle's mass and angular momentum, respectively, both of which are constant. Hence, ω1 is constant only if the radius r is constant, i.e., when the orbit is a circle. However, in that case, the orbit does not change as it precesses.

Read more about this topic:  Newton's Theorem Of Revolving Orbits

Famous quotes containing the word precession:

    “But how is one to make a scientist understand that there is something unalterably deranged about differential calculus, quantum theory, or the obscene and so inanely liturgical ordeals of the precession of the equinoxes.”
    —Antonin Artaud (1896–1948)