Kepler’s first law(or law of elliptic orbits)—Each planet moves about the Sun in
an orbit that is an ellipse, with the Sun at one of the two foci of the ellipse.
Kepler’s second law(or the law of areas)—An imaginary straight line joining a
planet to the Sun will sweep out equal areas of the ellipse in equal periods of time.
Kepler’s third law(or the harmonic law)—The square of the period of a planet’s
revolution is directly proportionate to the cube of the semi-major axis of its orbit.
How did Pierre-Simon de Laplaceapply mathematics to astronomy?
French mathematician, astronomer, and physicist Marquis Pierre-Simon de Laplace
(1749–1827) was one of the first to work out the gravitational mechanics of the solar
system using mathematics. In his Mécanique Céleste(Celestial Mechanics), Laplace
translated the geometrical study of mechanics used by Isaac Newton to one based on
calculus (or physical mechanics). He also proved the stability of the solar system, but
only on a short time scale. Laplace is also known for his theory about the formation of
the planets. He believed they originated from the same primitive mass of material, a
theory now known as Laplace’s nebular hypothesis. His other studies included major
contributions to differential equations and to the theory of probability.
What are astronomical unitsand light years?
An astronomical unit is one of the more common measurements used in astronomy.
It is a distance equal to the average distance from the Earth to the Sun, or 92,960,116 289
MATH IN THE PHYSICAL SCIENCES
What astronomical event with mathematical significance
occurred on December 25, 1758?O
n December 25, 1758, the appearance of a comet we now call “Halley’s Comet”
(or Comet Halley) proved a famous astronomer’s predictions (unfortunately, it
was 16 years after his death). From around 1695, Edmond Halley (1656–1742; also
seen as Edmund Halley) carefully studied comets, especially those with parabolic
orbits. But he also believed that some comets had elliptical orbits, and he thus the-
orized that the comet of 1682 (now Comet Halley) was the same comet that
appeared in 1305, 1380, 1456, 1531, and 1607. In 1705 he predicted that the comet
would appear again 76 years later—in 1758—a prediction that came true.
Such a calculation was a great feat in those days, with Halley even taking
into account the comet’s orbital perturbations produced by the planet Jupiter.
Even today, the comet maintains its 76-year cycle. Its last appearance was in
1986; it will again appear in the year 2062.