Planetary science: The Moon's tilt for gold

The origin of Earth's ocean tides has been a subject of continuous investigation for over 2000 years. However, the work of Newton is considered to be the beginning of the proper understanding of the phenomenon. Ocean tides are the result of gravitational tidal forces. These same tidal forces are present in any astronomical body; they are responsible for the internal heat that creates the volcanic activity on Io, one of Jupiter's moons, and the breakup of stars that get too close to...

In the early 17th century, German astronomer and mathematician Johannes Kepler postulated three laws for the motion of planets in the solar system. He formulated his first two laws based on the observations of his forebears, Nikolaus Copernicus and Tycho Brahe.
Polish astronomer Nikolaus Copernicus put forth a theory that stated a heliocentric model for the solar system. According to this heliocentric theory, all the planets, including Earth, orbit the Sun in circular orbits.
On the other hand,...

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...

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...

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 early 17th century, German astronomer and mathematician Johannes Kepler postulated three laws for the motion of planets in the solar system. In 1909, he formulated his first two laws based on the observations of his forebears, Nikolaus Copernicus and Tycho Brahe. However, in 1918, he published his third law of planetary motion, which gives a precise mathematical relationship between a planet's average distance from the Sun and the amount of time it takes to revolve around the Sun. It...