Astronomy 1 - Lecture Notes Wednesday
for September 23, 1998



LECTURE :

Finish Solar and Lunar Eclipses (see Sept 21 Lecture)	
Some Planetary Nomenclature:
	Conjunction (Inferior and Superior)
	Opposition
	Elongation
	DIAGRAM

History of Astronomy

Time Map of 1500-1700
The Heliocentric Model of the Solar System and Evidence
	- Venus and Phases (see text diagrams) 
	- Mars and Retrograde Motion


Laws of Planetary Motion - Kepler

------------------------------------------
1st Law:  Eliptical Orbits
		- focus, eccentricity, semi-major axis
		- perihelion, aphelion
			DIAGRAM of Ellipse Points

Construction of an ellipse (pin and string)
	1. Length of string between pins at focus = L = 2a
	2. Distance between pins = 2c
	3. Eccentricity = Distance between focii/ Length of String = c/a

Aphelion-Perihelion
DIAGRAM of Ellipse Sizes and Parameters
aphelion distance = ra = (1 + e)a
perihelion distance = rp = (1 - e)a

	Example: Mars Eccentricity e = 0.093
		a = 1.524
		perihelion = 1.39 AU	aphelion = 1.67 AU
	distance range at opposition
		Closest 0.39 AU 	Farthest 0.67 AU
	Example: Planet Size  (diameter = 6800 km)
		perihelion  angular size = 6800km/0.39/1.5x108km * (206,000)
				= 24"arc
		aphelion angular size = 0.39/0.67* 24" = 14" arc
	   on other side of solar system distance = 2.524 AU
		angular size = 0.39/2.524 * 24" = 4" arc

Kepler's 2nd Law.
	Areal Velocity = area swept out by radius vector per time = constant
		= area of ellipse/ period of orbit = (pi)ab/P
		[pi = 3.1416]
Example at perihelion and aphelion
DIAGRAM of Second Law Mathematics at Perihelion/Aphelion
	Area = Areal velocity x time
	Area of triangle at aphelion or perihelion = ravat/2 = rpvp t/2
so  va = rpvp/ra
Mercury e = 0.206	a = 0.39 AU
ra = a (1+e) = 0.47AU
rp = a (1-e) = 0.31AU		ra/rp = 1.52
So   vp/va = 1.52  Mercury travels 52% faster at perihelion than aphelion

Synodic Versus Siderial Period (see "More Precisely 9-1" p210)
	DIAGRAM on the Synodic Period of Planets
	-Synodic period = opposition to opposition 
			or conjunction to conjunction

Rate relative to Earth = Rate of Earth - Rate of Planet
	(These are orbital periods)
360/ Psynodic = 360/PEarth - 360/Psiderial
1/Psynodic = 1/PEarth - 1/Psiderial

Example:  Mars Period (opposition to opposition)
Earth siderial period = 1.00 year
Mars siderial period = 1.88 years
1/Psyn = 1/1 - 1/1.88 = 0.468
Psyn = 2.14 years = 781 days
So Mars is at opposition every 2 years and 51 days whereas it is back at the 
same point in its orbit every 1.88 years.

Last Oppositon = 17 March 1997  (Julian Day 2540524.5)
Approximate Next Oppostion =2540524.5 + 782 
		= Julian Day 1541306.5 =  7 May 1999 
(NOTE: This is approximate because Mars' orbit is eccentric 
and does not move uniformily in all parts. If you use ECU 
it will give you the correct date: How would you use ECU?)
METHOD:
	1. Set ECU for approximate date of opposition
	2. Center and Lock on Mars (located in center of screen)
	3. Set time steps to 1 day
	4. Step through days until azimuth = 180o at midnight AST.
(At opposition Mars will be on your local celestial meridian at midnight.)
Result = April 27, 1999

Retrograde Motion
Differential Speed of the Planets in their orbits
ECU (marsopp.cfg)
Dates Mars is Stationary 	March 16, 1999
				June 5, 1999
	Approximately 80 days of East to West Motion

Kepler's 3rd Law
	P2 = a3		or     P = a3/2
P = period in earth years
a = semi-major axis in AU
(does not work with other units in this form!!)
Trivial for Earth  12 = 13

example: Mercury a = 0.387 AU
	then P = 0.3871.5 = 0.241 years = 88.0 days
Synodic Period:
1/Psyn = 1 - 1/0.241 = -3.15
Psynodic = 0.318 years = 116 days from conjunction to conjunction
L.Bogan - Sept 23, 1998