great articles
Which foundational concept did Hipparchus discover by comparing his star positions to those recorded a century earlier?
What mathematical tool, essential for quantitative modeling, did Hipparchus develop and create the first known tables for?
What complex geometric feature did Claudius Ptolemy use in his geocentric model to account for the retrograde motion of planets?
What was the key assumption Nicolaus Copernicus retained in his heliocentric model that Johannes Kepler later proved incorrect?
What crucial pre-telescopic observation did Tycho Brahe make that demonstrated the heavens were not unchangeable?
What groundbreaking calculation did Johannes Kepler derive from Tycho Brahe's precise positional data?
What key set of telescopic discoveries made by Galileo Galilei provided overwhelming observational evidence for the heliocentric view?
Isaac Newton's theory of universal gravitation provided the underlying physics that explained the mechanics of which prior astronomical finding?
What essential cosmological tool did Henrietta Swan Leavitt develop by discovering the period-luminosity relationship for Cepheid variable stars?
What critical confirmation did Edwin Hubble provide regarding the 'spiral nebulae'?
What specific observational data provided Vera Rubin with hard evidence confirming the existence of invisible matter in the universe?
What condition must a plane satisfy to create a great circle when intersecting a sphere?
How does the radius of a great circle compare to the radius of the sphere it lies upon?
What do lines of longitude, such as meridians on Earth, represent geometrically?
If two points chosen on a sphere are antipodal, how many great circles can pass through both?
Which terrestrial example is cited as the most famous great circle on Earth?
What geometric feature distinguishes a great circle from any other circle drawn on a sphere?
What is the term for the shortest path between two points along the surface of a sphere?
How many unique great circles are defined by two distinct, non-antipodal points on a sphere?
What are most lines of latitude, such as the Tropic of Cancer, classified as geometrically on Earth?
In the mathematical definition of a great circle plane ($ax + by + cz = 0$), what does the vector $(a, b, c)$ represent?