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PHY134Introductory AstronomyTides and Matter1LeftoversEarth is in free fall under gravity of Sun, soSuns gravity has no effect on Earth!Almost none. There are remnants of gravity even in freefall: tidal forcesThese are due to the fact that gravitational acceleration is different at different points. So not all points of an extended object can possibly be simultaneously in free-fallDifference in free-fall acceleration (from center of Earth) acts as a tidal force

23How Strong is this Force?4What about the Moon?5Tidal Bulge Simulation5The TidesMoon deforms water so bulge faces Moon. As Earth rotates, bulge moves around Earth so tides repeat every 24h 48mEarths rotation drags bulge East so lags Moon by about 12mSun exerts tidal force towards Sun about as strong. At full/new Moon act together creating intense spring tides. At quarter Moon counteract to create weak neap tides66Even More TidesWhen Moon formed molten and closer - Earths tidal forces deformed it so it froze with permanent bulge. Tidal forces keep this bulge aligned with direction to Earth: tidal locking is why we always see same side of the MoonSince tidal bulge on Earth is dragged East of Moon, tidal force of Moon tries to align it. This in fact slows Earths rotation, transferring angular momentum to the Moon which thus recedes into higher orbit (G. Darwin, 1898)7George Darwin (son of Charles) 38mm/yr7What Now, Aristotle?Applying universal laws leads to unified understanding of many phenomena!In space, everything is in free-fall. Trajectories are Keplerian orbits. Internal structure controlled by tidal forces is powerful. Learn more about matter and forces

8MatterBy early 1900s: a unified understanding through atomic theoryAll matter made of a hundred or so elements types of atoms labeled by These bind to form molecular compoundsThree states: solid, liquid, gasBulk properties determined by microscopic dynamics

Temperature is a measure of average random motion of atoms and moleculesIn ideal gas

measured in

pressure in 9StatesAt low temperature and sufficient pressure form (almost) incompressible liquid.Density decreases with temperature: hot fluid risesIn equilibrium with gravity pressure increase with depth proportional to density

In solid state positions of atoms fixed maintain shape under external forcePerturbations travel through matter as sound waves with a speed characteristic of the materialWe hear sound in air.

10SlinkyFree-falling cup10WavesPeriodic disturbances characterized by frequency inTraveling at speed produce periodic wave with wavelength Amplitude is value of the perturbation at maximumEnergy flux in carried by wave isWhen two waves meet disturbances addIf opposite sign - subtract!11Waves PhETInterference PhET11Doppler EffectSound from a moving source heard at higher/lower when source approaching/recedingDoppler (1842)

source receding

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L = l0 vT = l0 vl/c12Heat TransferAn object hotter than environment will lose energy until temperatures equilibrateConduction: Heat can be transferred through continuous contact. Rare in astronomyConvection: Physical motion of fluid carries energy. Works well when heating from below - Heated fluid less dense so risesRadiation: Hot objects glow losing energy to light13Luminosity and BrightnessSun is hot so radiates energy at a rateLuminosity inBrightness is flux inAt a distance radiation distributed uniformly on surface of sphere

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aT

FT = maT

a a1 2R

D

a =GMD2

a+ a1 + 2

RD

a =GM

(D +R)2

a+ =GM

(D R)2

aT =2GMR

D3

= 2GMR2

MM

RD

3= 2g

1.989 10305.972 1024

6371

1.496 1083

= 5.14 108g

aMoonT = aT

MMoonM

DMoonD

3= aT

7.348 10221.989 1030

3.844 1051.496 108

3= 2.2aT

~F = m~a

P

N/m2

Z

hmv2

2i = 3

2kBT

PV = NkBT

T

K

kB = 1.381 1023 JK

f = c

A

/ A2

J/sm2

=Wm2

f

Hz = s1

c

= 0(1 + v/c)

v > 0

b

b =L

4R2

L

J/s = W

W/m2

R