The Earth, Moon and Mercury Comparison

Astronomy 1
Lecture Notes
Monday, November 2, 1998

READ: Text Chapter (Chaisson and McMillan) # 8 The Moon and Mercury

Astronomical Events
Wednesday, Nov 4, 1998
Last Lecture: (subjects yet to be covered) 
Physical Properties of the Earth, Moon and Mercury
	Cratering - Process, Timing, Age Judgement
		Process:
			v ~ 30 km/s
			   20 m diameter object
			m ~ 107 kg	Energy ~ 1017 Joules
				vaporization of object + shock wave
				compression and decompression of surface
		Crater diameter ~ 10 x diameter of object
		Crater depth ~ 1/5 crater diameter
	eg. 20m object --> ~200 m diameter crater, ~40 m deep
		much larger fracture zone beneath 
	History of the Moon:
		Molten and differentiation --> highlands
		Cratering decreasing with time
		Late, Heavy cratering at 700 million years
		Lava Flow to form Maria of dark basaltic rock
		Later cratering
	Origin of Moon
		1. Small Iron (core)
		2. Rocks show few volatiles
		3. Different from Earth

		Earth		Moon		Mercury
Radius		6378		1738		2440	km
		1		0.27		0.38	R(Earth)
Mass		6x1024		7.4x1022	3.3x1023	kg
		1		1/81		1/18
density		5500		3300		5400
R(core)		3500		200		1800
V(core)		0.16		0.0015		0.4	fraction of planet volume
Mass(core)	0.32		0.04		0.6	fraction of planet mass
Magnetic Field	1		0		0.01	fraction of Earth
Escape Velocity	11.2		2.4		4.3	km/s
g		9.8		1.6		3.7	m/s2
Atmosphere	1		none		1x10-12
		N, O				Na, K
Rot. Period	1 day		27.3 day	58.65 days
Surface T	 ~ 283 K	103-383 k	88-700 K
Axial Tilt	23.5		1.5		0
Surface	Eroded			Cratered	Cratered	

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Viewing the Moon - its Orbit and Rotation:
	Rotation = Revolution (Same Face to the Earth all the time) = 27.3 days
	Libration allows us to see 59% of surface
		1. North and South +/- 6.5 degrees due to axial tilt of 1.5 degrees 
			and 5 degree tilt of its orbit
		2. East West +/- 7 degrees because of eccentricity of Orbit (e = 0.055)
			(constant rotation but no constant velocity in orbit)
		3. Parallax from Earth (small effect)
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Radar Ranging for the rotation rate of Mercury
Surface features can not be seen from Earth visually, 
and not rotation can be seen that way.

Note: There are a range of delays of the return of the radar.
	Time of travel to Mercury and Back 2x(0.61 AU) = 2x305 s = 610 s = 10 minutes
Shortest delay - Spot in the center of Mercury's disk
Longest delay - Ring at the edge of Mercury's disk
Range of delay = time of travel of Mercury's diameter (4880 km)
		= 16 milliseconds
Doppler Shift at each delay gives rotation rate as shown in figure above
	Maximum Surface Speed = 0.003 km/s
	Maximum Doppler Shift = v/c = 0.003/300,000 = 10-8
		for f = 3 GHz = 3x109 
		shift = 30 Hz

The diagram above shows the frequency distribution of three radar pulses
reflected from Mercury with three different delay times. The longest 
delayed pulse is from the edge of the disk and has the most Doppler
shift in it and reveals the rotation speed of Mercury.
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Rotation of Mercury 58.65 versus revolution of 88.0 days 
       = exactly 2/3 of a Mercury year.
In 2 revolutions, Mercury rotates exactly 3 times. So it shows the same
face to the Sun at every perihelion --> Hot spots on the equator on 
opposites sides of Mercury - at the equator



Cause of 'locking' of rotation with revolution:
1. Orbit of Mercury is very eccentric (e = 0.206) 
	It is 50% farther away at aphelion than perihelion
2. Tides vary as the inverse cube of the distance
	Tides are 3.5 times stronger from the Sun at
	perihelion than aphelion. (1.52)3 = 3.5
3. Mercury density is not exactly isotropic
	ie. it is not uniform in all directions
4. Result: Angular movement in orbit at perihelion = 
	Rotation Rate = 6.1o/day
	Revolution around the Sun at Perihelion = 6.3o/day
	Revolution around the Sun at Aphelion = 2.8o/day
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Relative Size and Intensity of the Sun at Mercury

Poles of Mercury are cold (no tilt of the rotation axis)