1. 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/r2
so its acceleration a= GM/r2 is independent of its mass!
This prompted Einstein to formulate his gravitational theory as pure geometry.

2. Orbital Motion
A force is required to keep an object in circular motion, otherwise it would move in a straight line. Therefore the Moon does experience a force—and that force is gravity! The "falling" of the Moon is exactly balanced by the velocity of the Moon in its orbit. 2

3. Cannon “Thought Experiment”
The moon is “just falling”
The motion of the Moon is governed by the same laws as gravity at the Earth's surface. This is the first time in history that it is shown that the laws of Nature are the same on Earth as they are in the heavens. 3

4. F = ma = G Mm/r2 (m cancels out)
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/r2 (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/r2
E.g., on the Moon your weight would be 1/6 of what it is on Earth

5. Applications (cont’d)
The mass of the Sun can be deduced from the orbital velocity of the planets: MS = rOrbitvOrbit2/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)
During the course of the quarter we'll see that these two methods have been applied over and over again to determine the masses of celestial bodies.

6. The Solar System
all planets orbit in same direction (ccw as seen from above the north pole)
all orbits lie nearly in a single plane (Mercury (7deg) and Pluto (17deg) being most notable exceptions)
inner planets are small, dense, rocky (Terrestrial); outer planets are large, gaseous, low density (Jovian)
density = mass/volume
inner planets close together, outer planets further apart

7. 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
Some of this debris lands on earth as meteorites
Most of the solar system is a better vacuum than we can produce in the laboratory on earth!
Meteoroids = bodies < 100 m across

8. Size matters: radii of the Planets

9. 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
Size of solar sys ~ 1/1000 lyr; distance to nearest star ~ 4.3 lyr

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

11. The Jovian Planets Large, made out of gas, and low density Saturn
Terrestrial-type cores
Jupiter
Neptune
Uranus

12. Asteroids, Comets and Meteors
Debris in the Solar System
Some of this debris lands on earth as meteorites
Most of the solar system is a better vacuum than we can produce in the laboratory on earth!
Meteoroids = bodies < 100 m across

13. Asteroids
mostly in orbits that lie between that of Mars and Jupiter in the asteroid belt; probably just junk that never formed a planet
some have elongated orbits that cross orbits of Mars and Earth: some occasionally collide with Earth (Maybe 3 every Myrs or so)
Asteroids are also found locked into Jupiter's orbit (Trojan asteroids)
Too small and far away for surface to be visible from Earth, but close-up pictures have been returned by Galileo. Size can be estimated from brightness (assuming reflectivity is known), or from occultation of stars.
The moons of Mars, Phobos and Deimos, photographed by Viking, may have originally been asteroids.
At least one asteroid (Ida) has a moon (Dactyl)!

14. 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

15. 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)

16. Comets - Traveling Dirty Snowballs
Small icy bodies, “dirty snowballs”
Develops a “tail” as it approaches the Sun
Whipple's dirty snowball theory
Some rock, water ice, ammonia, methane, other junk
Not very dense, ~ 100 kg/m^3, masses typically about the same as smaller asteroids
Highly elliptical orbits
Halley's comet: orbit stretches from Earth's orbit to Neptune's; period 76 years, return predicted by Edmund Halley in 1705.
during 1986, Halley was photographed by spacecraft from USSR, western European consortium and Japan. Pictures show that surface of Halley is dark (covered with dirt) and that gas escapes from cracks in the surface
Tycho showed that they are celestial bodies, not weather phenomena.

17. Comet Anatomy Tail may be up to 1 A.U. long Parts of a comet:
• nucleus: icy core
• coma: sphere of gas evaporated from nucleus when it approaches the sun
• tail: ice and gas that streams away from comet.
NOTE: direction of tail is opposite to sun, not opposite to motion of comet; streaming is due to solar wind (a wind of charged particles emitted by the Sun)

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

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

20. Short- and Long-Period Comets
long period comets, mostly in orbit far from the Sun, far beyond Pluto: Oort cloud. Orbits are nearly parabolic, and not confined to plane of solar system.
A few short period comets have orbits that take them into the inner solar system. The orbits are usually close to the plane of the solar system. These are the ones more commonly seen from Earth. The source of these objects is probably a belt of comet-like bodies called the Kuiper belt beyond the orbit of Neptune. Prediction recently confirmed by HST. Pluto and Charon may indeed be the largest members of this group of bodies.
“Short” period meaning: less than 200 years

21. Halley’s Comet – a typical Comet

22. 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