Daily briefing: The birth of a solar system caught 'on camera' for the first time

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,...

In the early 17th century, German astronomer and mathematician Johannes Kepler postulated three laws for the motion of planets in the solar system. His first law states that all planets orbit the Sun in an elliptical orbit, with the Sun at one of the ellipse's foci. Therefore, the distance of a planet from the Sun varies throughout its revolution around the Sun.
While in an elliptical orbit, the total energy of the planet is conserved. Therefore, the planet slows down when it is at apogee and...

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...

Speciation describes the formation of one or more new species from one or sometimes multiple original species. The resulting species are discrete from the parent species, and barriers to reproduction will typically exist. There are two primary mechanisms, speciation with and without geographic isolation—allopatric and sympatric speciation, respectively.

There is no one solvent that can dissolve every type of solute. Some substances that readily dissolve in a certain solvent might be insoluble in a different solvent. A simple way to predict which substances dissolve in which solvent is the phrase "like dissolves like". This means that polar substances, such as salt and sugar, dissolve in a polar substance like water. In contrast, non-polar substances are more soluble in non-polar solvents such as carbon tetrachloride.
This selective...

First-order systems, such as RC circuits, are foundational in understanding dynamic systems due to their straightforward input-output relationship. Analyzing their responses to different input functions under zero initial conditions reveals significant insights into system behavior.
When a first-order system is subjected to a unit-step input, its response is characterized by its transfer function. By applying the Laplace transform of the unit-step input to the transfer function, expanding the...