Secular changes in the lunar elements

While simple harmonic motion and uniform circular motion may be two separate concepts, they correlate and interlink with each other. Simple harmonic motion is an oscillatory motion in a system where the net force can be described by Hooke's law, while uniform circular motion is the motion of an object in a circular path at constant speed.
There is an easy way to produce simple harmonic motion by using uniform circular motion. For instance, consider a ball attached to a uniformly rotating...

In the years before Newton, a general belief prevailed that different laws governed objects in the sky than objects on Earth. When Kepler wrote down the three laws of planetary motion, explaining in detail the geometrical properties of the planetary orbits around the Sun, there was no immediate idea to discern their connection with more fundamental laws. It was Isaac Newton who, in 1665–66, figured out the connection between planetary motion, the motion of the moon around the Earth, and the...

Throughout its ~4.5 billion year history, the Earth has experienced periods of warming and cooling. However, the current drastic increase in global temperatures is well outside of the Earth’s cyclic norms, and evidence for human-caused global climate change is compelling. Paleoclimatology, the study of ancient climate conditions, provides ample evidence for human-caused global climate change by comparing recent conditions with those in the past.

The earth's gravitational field produces a 'twisting force' perpendicular to the angular momentum of a spinning mass (such as a spinning top) that causes the mass to 'wobble' around the gravitational field axis in a phenomenon called precession. Similarly, the magnetic moment (μ) of a spinning nucleus precesses due to an external magnetic field directed along the z-axis. The precession of the magnetic moment vector about the magnetic field is called Larmor precession, and the angular frequency...

Newton's law of gravitation describes the gravitational force between any two point masses. However, for extended spherical objects like the Earth, the Moon, and other planets, the law holds with an assumption that masses of spherical objects are concentrated at their respective centers.
This assumption can be proved easily by showing that the expression for gravitational potential energy between a hollow sphere of mass (M) and a point mass (m) is the same as it would be for a pair of extended...