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...

No object with a finite mass can travel faster than the speed of light in a vacuum. This fact has an interesting consequence in the domain of extremely high gravitational fields.
The minimum speed required to launch a projectile from the surface of an object to which it is gravitationally bound so that it eventually escapes the object’s gravitational field is called the escape velocity. The escape velocity is independent of the mass of the object. Merging the idea of escape velocity with the...

Although black holes were theoretically postulated in the 1920s, they remained outside the domain of observational astronomy until the 1970s.
Their closest cousins are neutron stars, which are composed almost entirely of neutrons packed against each other, making them extremely dense. A neutron star has the same mass as the Sun but its diameter is only a few kilometers. Therefore, the escape velocity from their surface is close to the speed of light.
Not until the 1960s, when the first neutron...

Flame photometry, also known as flame emission spectrometry, is a technique used for the qualitative and quantitative analysis of elements present in a sample using a flame as the source of excitation energy. The concept of flame photometry was realized in the early 1860s by Kirchhoff and Bunsen, who discovered that specific elements emit characteristic radiation when excited in flames. The first instrument developed for this purpose was used to measure sodium (Na) in plant ash using a Bunsen...

In a flame photometer, when a solution like potassium chloride is aspirated into the flame, the solvent evaporates, leaving behind dehydrated salt. This salt dissociates into free gaseous atoms in their ground state. Some of these atoms absorb energy from the flame, leading to their excitation. The excited atoms return to the ground state, emitting photons at characteristic wavelengths. Because only electronic transitions are involved, the resulting emission lines are very narrow. The intensity...

An ellipse is a fundamental conic section defined by the constant sum of distances from any point on its curve to two fixed points, known as the foci. This geometric property can be physically demonstrated using a pencil, string, and two pins. By anchoring the string at both ends and maintaining it taut with a pencil, one can trace the outline of an ellipse.The shape and extent of the ellipse are determined by its eccentricity, e, defined as the ratio of the distance between the center and a...