Celestial Mechanics: Kepler’s Laws, Tides, and the Expanding Universe
Celestial Mechanics: Kepler’s Laws
Johannes Kepler, a German astronomer and mathematician, established the mathematical laws describing the motion of celestial bodies. He determined that planets move in elliptical orbits, not circular ones, around the sun. These are known as Kepler’s Laws:
- 1st Law: Planets move in elliptical orbits with the sun at one focus.
- 2nd Law: A line connecting a planet to the sun sweeps out equal areas during equal intervals of time.
- 3rd Law: The square of a planet’s orbital period is proportional to the cube of the semi-major axis of its orbit (T²/d³ = k, where k is a constant).
The sun’s gravitational force causes planets to orbit. Isaac Newton concluded that gravitational attraction is universal, governing both terrestrial and celestial motion.
Weight and Tides
Weight: The force of gravitational attraction exerted by the Earth on objects near it.
Tides: The cyclical rise and fall of sea levels, occurring roughly twice daily. The law of universal gravitation allows us to study the motion of celestial bodies and predict their speed, position, and orbital period.
Satellite Motion
The motion of satellites around the Earth follows the same principles as celestial bodies. A satellite’s speed and orbital period depend on its altitude, not its mass. Higher satellites have lower speeds and longer orbital periods.
The Universe Today
The solar system includes the sun, planets (Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune), dwarf planets (like Pluto), and other small bodies.
Edwin P. Hubble discovered galaxies beyond the Milky Way. He found that most galaxies are moving away from us, with recession velocity increasing with distance.
Hubble’s Law
Hubble’s Law: The relationship between a galaxy’s distance (d) and its recession velocity (v) is expressed as v = H * d, where H is the Hubble constant (approximately 20 (km/s) / million light-years).
The Big Bang Theory
These findings support the Big Bang theory, which suggests that the universe originated from a highly concentrated point. Following the initial explosion, the universe began to expand.