kepler’s law of orbital motion flashcards

What major 15th-century technological development in Europe enabled the rapid dissemination of scientific ideas, helping spark the Scientific Revolution?

The invention of the moveable-type printing press by Johannes Gutenberg around 1440.

In Ptolemy's geocentric astronomical model, what is the deferent?

The large circular orbit centered near the Earth along which the center of a planet's smaller epicycle moves.

In Ptolemy's geocentric model, what term describes the small circular orbit whose center moves along the deferent?

The epicycle.

What observational phenomenon was the 'Epicycle' designed to explain?

Retrograde motion (the apparent temporary backward motion of planets relative to the background stars).

What ancient artifact is believed to be the earliest known analog computer used to calculate planetary orbits?

The Antikythera mechanism.

Which ancient Greek astronomer proposed a heliocentric system roughly 18 centuries before Nicolaus Copernicus?

Aristarchus of Samos.

What fundamental geometric assumption in Copernicus's heliocentric model severely compromised its accuracy?

The assumption that planets orbit the Sun in perfect circles.

Whose meticulous 30-year naked-eye astronomical observations did Johannes Kepler use to derive his laws of planetary motion?

Tycho Brahe** (specifically his observations of Mars).

What does Kepler's First Law state regarding planetary orbits?

The orbit of each planet about the Sun is an ellipse, with the Sun located at one focus.

How is an ellipse geometrically defined in terms of its two foci (f1​ and f2​)?

It is a closed curve where the sum of the distances from any point on the curve to the two foci is constant.

Under what condition does an ellipse become a circle?

When the two foci coincide at the same central point.

What does Kepler's Second Law state about the motion of a planet around the Sun?

An imaginary line drawn from the Sun to a planet sweeps out equal areas in equal intervals of time.

According to Kepler's Second Law, where in its orbit does a planet travel at its highest velocity?

When it is closest to the Sun (at perihelion).

What proportional relationship between orbital period (T) and semi-major axis (r) is expressed by Kepler's Third Law?

The square of the orbital period is proportional to the cube of the semi-major axis: T2∝r3.

In deriving Kepler's Third Law for a circular orbit, what force provides the necessary centripetal acceleration (mrv2​)?

Newton's gravitational force between the central mass M and orbiting mass m: Fg​=r2GMm​.

What is the derived formula for the square of orbital period (T2) using Newton's Law of Gravitation?

T2=GM4π2r3​