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Lecture 19: The &

The Moon & Mercury

•The Moon and Mercury are similar in some ways •They both have: –Heavily cratered –Dark colored surfaces –No atmosphere –No water •They also have some interesting differences: –The Moon is much smaller than Mercury –Mercury has a much larger core –They have different formation histories

The Moon & Mercury

1 The Moon •The Moon is the only of the •It has no atmosphere, no water, and no sound. The Moon is completely desolate •With no atmosphere to moderate the surface temperature, the daily variation is extreme:

™Tnoon = 400 K (above boiling point of water)

™Tnight = 100 K (below freezing point of water) •The surface of the Moon has been altered by thousands of meteorite and asteroid impacts •The crater evidence has been preserved, since there is no wind or water erosion

Motion of the Moon •The Moon revolves around the Earth with a period of approximately one •It keeps the same face pointed towards Earth at all times •The Moon’s is not in the same plane as Earth’s orbit around the (it is tilted by 5.2o) •Therefore, are infrequent

Earth

Sun

Orbit of Moon

Moon

The Moon •The lunar orbit is not perfectly circular – the eccentricity is e = 0.055 •The average Earth-Moon distance is 384,000 km (237,000 miles) •The perigee distance is 363,000 km (closest to Earth) •The apogee distance is 405,000 km (farthest from Earth)

2 The Moon •The sidereal period of the lunar orbit is 27.3 Earth days •This is one “sidereal month,” measured relative to the stars •The synodic period of the Moon’s orbit is 29.5 Earth days

1 synodic month later

1 sidereal month later Distant Star Sun Orbit of Moon

starting point Moon Earth

The Moon •Hence 29.5 Earth days is one “synodic month,” measured relative to the Sun •The synodic period is the time between full , or new moons, etc.

1 synodic month later

1 sidereal month later Distant Star Sun Orbit of Moon

starting point Moon Earth

3 Phases of the Moon

Eclipses •Can occur only if the alignment is precise (Earth, Moon, and Sun line up exactly) •The Moon’s orbit is tilted by 5.2o relative to the ecliptic •Therefore, the Moon, Earth, and Sun must lie along the “Line of Nodes”, which is the intersection of the two orbital planes •Eclipses can be Lunar (Moon becomes darker) or Solar (Sun becomes darker)

Line of Nodes

Solar Sun

4 Eclipses

Eclipses

5 Tidal Locking

•The Moon always keeps the same face pointed towards the Earth •The spin period relative to the stars is exactly equal to the orbital period, 27.3 Earth days •Since these periods are equal, we say that the Moon is tidally locked, in a around the Earth

Tidal Force

Tidal Force

•The Moon is in a synchronous orbit, but the Earth is not. Why is this? Because: ™The tidal force of the Moon on the Earth is 2GM M R F = earth moon earth earth D3 ™The tidal force of the Earth on the Moon is 2GM M R F = earth moon moon moon D3

™The tidal force exerted on the Moon by the Earth is therefore 20 times larger than that exerted on the Earth by the Moon

6 Tidal Locking

•The tidal force exerted on the Moon by the Earth is 20 times larger than that exerted on the Earth by the Moon •The Moon is 80 times less massive than the Earth and therefore the effect of the tidal force is much stronger •The tidal force of the Earth causes a tidal bulge in the crust of the Moon

Tidal Heating

•In the distant past, the Moon did spin relative to the Earth, and that caused the tidal bulge to ripple around the Moon, like the on Earth •The motion of the tidal bulge on the Moon caused distortion of the rocks, leading to frictional heating of the lunar crust

Tidal Heating

•The heating caused the gradual dissipation of the lunar spin. •The kinetic energy of the Moon’s spin has been used to heat the lunar crust •The same effect is gradually slowing down Earth’s spin •Conservation of is causing the Moon to move away from the Earth 1-2 cm per year

7 Tidal Locking

•Eventually, the Moon with have an average orbital distance of about 550,000 km (compared with the current average distance of 384,000 km) •When this happens, the Earth will be tidally locked to the Moon, and then the Earth will therefore always show the same face towards the Moon •This will take about 1012 years to happen

The Moon

•The includes heavily cratered highlands and less cratered lowlands, or “maria”

•The maria (seas) are dark colored, flat regions created by ancient lava flows highlands •The highlands (terrae) are bright areas elevated several maria kilometers above the maria

The Moon

•Since the Moon is in synchronous orbit around the Earth, the was completely unknown until it was first explored by spacecraft in the 1960’s

8 The Moon

•The far side of the Moon is more heavily cratered, and contains a smaller amount of dark maria

•This suggests that the crust is thicker on the far side, and the molten material forming the maria was pulled towards the Earth •The tidal force of the Earth may have caused this while the Moon was much more molten than it is now

The Moon

•Geologically and biologically, the Moon is dead: ™No ™No volcanoes ™No internal geological activity •However, there are moonquakes that occur when meteorites impact on the surface •Moonquakes have been detected by seismometers left on the Moon by the Apollo astronauts •These seismometers sent back radio signals to Earth until 1977 •They helped us study the Moon’s interior structure

Mercury

•Mercury’s orbit is elliptical, with eccentricity e = 0.2056 •The average Sun-Mercury distance is 0.39 AU (58,766,000 km) •The perihelion distance is 0.31 AU (closest to Sun) •The aphelion distance is 0.47 AU (farthest from Sun) •Mercury always appears close to the Sun in the sky

9 Mercury

•The angle between Mercury and the Sun (as viewed from Earth) is called the elongation •Based on the size and shape of Mercury’s orbit, we find that ™Elongation = 18o (perihelion) ™Elongation = 28o (aphelion) •Hence Mercury never appears very far from the Sun as viewed from Earth

Mercury & the Sun

Mercury

•Mercury can be viewed with the naked eye only when the Sun’s light is blocked ™Just before dawn ™Just after sunset ™During total

•Sunrise:

10 Mercury

•Why is Mercury visible for no more than two hours? •The Earth rotates 360o in 24 hours, or

o o 360 = 15 24 hr hr •Since the maximum elongation of Mercury is 28o, the maximum time for the Sun to rise after Mercury is 28o ∆ t = = 2 hours 15o / hr

Mercury

•Mercury shines by reflected sunlight, just like the Moon •With the naked eye, only the first or third quarter phases are visible

•Using large telescopes, Mercury can be viewed even during the daytime by filtering out the sunlight •Mercury Messenger website

Phases of Mercury

11 Moon

Mercury

•The albedo of an object is the fraction of the incident light that is reflected ™Albedo = 0.1 for Mercury ™Albedo = 0.1 for Moon ™Albedo = 0.4 for Earth ™Albedo = 0.7 for •Even though Mercury’s albedo is so low, it appears very bright because it is so close to the Sun

Mercury’s Orbit

•The semi-major axis of Mercury’s orbit is a = 0.39 AU

Mercury

Sun

a

•Kepler’s third law relates the semi-major axis to the orbital period

12 Mercury’s Orbit

•Kepler’s third law relates the semi-major axis a to the orbital period P

2 3 ⎛ P ⎞ = ⎛ a ⎞ ⎜ ⎟ ⎜ ⎟ ⎝ years⎠ ⎝ AU ⎠

•Solving for the period P yields

3/ 2 ⎛ P ⎞ = ⎛ a ⎞ ⎜ ⎟ ⎜ ⎟ ⎝ years ⎠ ⎝ AU ⎠ •Since a = 0.39 AU for Mercury, we obtain P = 0.244 Earth years or P = 88 Earth days

Mercury’s Orbit

•Since Mercury is closer to the Sun than the Earth is, it’s apparent motion can be retrograde •Transits occur when Mercury passes in front of the solar disk as viewed from Earth •This happens about once every 10 years

Mercury (1 hour increments)

Bulk Properties of the Moon

•It is interesting to compare the bulk properties of the Moon and Mercury •We have for the radius and mass of the Moon

™Rmoon = 1,700 km = 0.25 Rearth 25 ™Mmoon = 7.4 x 10 g = 0.0125 Mearth •The volume is therefore given by

4 V = π R 3 moon 3 moon

25 3 •Hence Vmoon = 2 x 10 cm

13 Bulk Properties of the Moon

•The average density of the Moon is therefore × 25 ρ = Mmoon = 7.4 10 g moon × 25 3 Vmoon 2 10 cm

•We obtain ρ = −3 moon 3.5 g cm

•This is similar to the density of the surface rocks in the Earth’s crust •The Moon does not contain much iron, or a large, dense core

Gravity on the Moon

•We can compute the surface acceleration for the Moon using Newton’s laws: - GMm F = mA = R 2

•Solving for the surface acceleration A yields - GM A = R 2

Gravity on the Moon

•Using the lunar values for the mass and radius, we obtain for the surface acceleration

= - GMmoon = −2 Amoon 2 1.7 ms R moon

•For the Earth we the surface acceleration obtained is

= - GMearth = −2 Aearth 2 9.8ms R earth

14 Gravity on the Moon

•The ratio of the lunar and Earth accelerations is

Amoon = 1 Aearth 6

•Hence objects on the Moon weigh about 1/6 of their weight on Earth

•Example: moon jump by 180 lb astronaut, who weighs 30 lbs on the Moon

15 Bulk Properties of Mercury

•We have for the radius and mass of Mercury

™Rmercury = 2,439 km = 0.38 Rearth 26 ™Mmercury = 3.3 x 10 g = 0.05 Mearth •The volume is therefore given by

4 V = π R 3 mercury 3 mercury

25 3 •Hence Vmercury = 6.1 x 10 cm

Bulk Properties of Mercury

•The average density of Mercury is therefore M × 26 ρ = mercury = 3.3 10 g mercury × 25 3 Vmercury 6.1 10 cm

•We obtain ρ = −3 mercury 5.4 g cm

•This is similar to the average density of the Earth •Hence Mercury probably contains a large, dense core

Comparison with the Earth

•The average density of the Earth is equal to

−3 ρΘ = 6 g cm

•The density of water is ρ = −3 water 1 g cm

•The density of rock is ρ = − −3 rock 2 4 g cm

16 Gravity on Mercury

•Using Mercury’s values for the mass and radius, we obtain for the surface acceleration

= - GMmerc = −2 Amerc 2 3.7 ms R merc

= −2 •For the Earth we have found that Aearth 9.8ms •The ratio of the Mercury A and Earth surface merc = 0.38 accelerations is therefore Aearth

•Hence objects on Mercury weigh about 1/3 of their weight on Earth

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