PHY134 Introductory Astronomy Tides and Matter 1
Leftovers Earth is in free fall under gravity of Sun, so Sun’s gravity has no effect on Earth! Almost none. There are remnants of gravity even in freefall: tidal forces These 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-fall Difference in free-fall acceleration (from center of Earth) acts as a tidal “force” 2
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How Strong is this Force? 4
What about the Moon? 5
The Tides Moon deforms water so bulge faces Moon. As Earth rotates, bulge moves around Earth so tides repeat every 24h 48m Earth’s rotation drags bulge East so lags Moon by about 12m Sun exerts tidal force towards Sun about ½ as strong. At full/new Moon act together creating intense spring tides. At quarter Moon counteract to create weak neap tides 6
Even More Tides When Moon formed – molten and closer - Earth’s 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 Moon Since tidal bulge on Earth is dragged East of Moon, tidal force of Moon tries to align it. This in fact slows Earth’s rotation, transferring angular momentum to the Moon which thus recedes into higher orbit (G. Darwin, 1898) 7
What 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 8
Matter By early 1900s: a unified understanding through atomic theory All matter made of a hundred or so elements – types of atoms labeled by These bind to form molecular compounds Three states: solid, liquid, gas Bulk properties determined by microscopic dynamics Temperature is a measure of average random motion of atoms and molecules In ideal gas measured in pressure in 9
States At low temperature and sufficient pressure form (almost) incompressible liquid. Density decreases with temperature: hot fluid rises In equilibrium with gravity pressure increase with depth proportional to density In solid state positions of atoms fixed – maintain shape under external force Perturbations travel through matter as sound waves with a speed characteristic of the material We hear sound in air. 10
Waves Periodic disturbances characterized by frequency in Traveling at speed produce periodic wave with wavelength Amplitude is value of the perturbation at maximum Energy flux in carried by wave is When two waves meet disturbances add If opposite sign - subtract! 11
Doppler Effect Sound from a moving source heard at higher/lower when source approaching/receding Doppler (1842) source receding 12
Heat Transfer An object hotter than environment will lose energy until temperatures equilibrate Conduction: Heat can be transferred through continuous contact. Rare in astronomy Convection: Physical motion of fluid carries energy. Works well when heating from below - Heated fluid less dense so rises Radiation: Hot objects glow losing energy to light 13
Luminosity and Brightness Sun is hot so radiates energy at a rate Luminosity in Brightness is flux in At a distance radiation distributed uniformly on surface of sphere 14