From Newton to Einstein If we use Newton

From Newton to Einstein • If we use Newton II and the law of universal gravity, we can calculate how a celestial object moves, i. e. figure out its acceleration, which leads to its velocity, which leads to its position as a function of time: ma= F = GMm/r 2 so its acceleration a= GM/r 2 is independent of its mass! • This prompted Einstein to formulate his gravitational theory as pure geometry.

Orbital Motion

Cannon “Thought Experiment” • http: //www. phys. virginia. edu/classes/109 N/more_stuff/App lets/newtmtn. html

Applications • From the distance r between two bodies and the gravitational acceleration a of one of the bodies, we can compute the mass M of the other F = ma = G Mm/r 2 (m cancels out) – From the weight of objects (i. e. , the force of gravity) near the surface of the Earth, and known radius of Earth RE = 6. 4 103 km, we find ME = 6 1024 kg – Your weight on another planet is F = m GM/r 2 • E. g. , on the Moon your weight would be 1/6 of what it is on Earth

Applications (cont’d) • The mass of the Sun can be deduced from the orbital velocity of the planets: MS = r. Orbitv. Orbit 2/G = 2 1030 kg – actually, Sun and planets orbit their common center of mass • Orbital mechanics. A body in an elliptical orbit cannot escape the mass it's orbiting unless something increases its velocity to a certain value called the escape velocity – Escape velocity from Earth's surface is about 25, 000 mph (7 mi/sec)

The Solar System

Contents of the Solar System • Sun • Planets – 9 known (now: 8) – Mercury, Venus, Earth, Mars (“Terrestrials”) – Jupiter, Saturn, Uranus, Neptune (“Jovians”) – Pluto (a Kuiper Belt object? ) • Natural satellites (moons) – over a hundred • Asteroids and Meteoroids – 6 known that are larger than 300 km across – Largest, Ceres, is about 940 km in diameter • Comets • Rings • Dust

Size matters: radii of the Planets

The Astronomical Unit • A convenient unit of length for discussing the solar system is the Astronomical Unit (A. U. ) • One A. U. is the average distance between the Earth and Sun – About 1. 5 108 km or 8 light-minutes • Entire solar system is about 80 A. U. across

The Terrestrial Planets • Small, dense and rocky Mercury Mars Venus Earth

The Jovian Planets • Large, made out of gas, and low density Saturn Jupiter Uranus Neptune

Asteroids, Comets and Meteors Debris in the Solar System

Asteroids

Asteroid Discovery • First (and largest) Asteroid Ceres discovered New Year’s 1801 by G. Piazzi, fitting exactly into Bode’s law: a=2. 8 A. U. • Today more than 100, 000 asteroids known • Largest diameter 960 km, smallest: few km • Most of them are named • about 20 of them are visible with binoculars

How bright does a planet, moon, asteroid or comet appear? • Apparent brightness of objects that reflect sunlight do depends on three things: – Size of the object (the bigger the brighter) – Distance to the object (the closer the brighter) – “Surface” properties of the object (the whiter the brighter, the darker the dimmer) • Technical term: Albedo (Albedo =1. 00 means 100% of incoming radiation is reflected)

Comets - Traveling Dirty Snowballs • Small icy bodies, “dirty snowballs” • Develops a “tail” as it approaches the Sun

Comet Anatomy • Tail may be up to 1 A. U. long

Comet Tail • Two kinds of tails: • Dust • Ion (charged particles)

Shapes Comet Giacobini. Zinner (1959) • Ion tail 500, 000 km long • Coma: 70, 000 km across Comet Hale-Bopp (1997) • Tail 40° long as seen from earth

Short- and Long-Period Comets • “Short” period meaning: less than 200 years

Halley’s Comet – a typical Comet

Halley’s Comet – Now and then • Halley’s Comet in 1910 • Top: May 10, 30° tail • Bottom May 12, 40° tail • Halley’s Comet in 1986 • March 14, 1986