Tides are Important Roche Limit - The closer a moon is to a planet, the stronger the tidal forces it will feel (I.e. the stronger the differential gravity will be between the surface nearest the planet and that felt at the center of the moon). Within the Roche limit the differential gravity felt by the moon (or planet in the case of orbiting the Sun) will be stronger than it s self-gravity and the object will be torn apart. Examples include: Formation of rings around large planets at small radial distances Tearing apart of comets that pass close to stars/large planets** Massive gas giants orbiting close to their stars. EAS 4803/8803 - CP 7:1
Tides are Important time Comet Shoemaker-Levy 9 Impact of Jupiter Infrared Io Red Spot Courtesy HST Comet Science Team Courtesy NASA IRTF Comet Science Team EAS 4803/8803 - CP 7:2
Tides are Important Image sequence from Wikipedia EAS 4803/8803 - CP 7:3
Victims of Tidal Forces Credit NASA Hot Jupiters may be more difficult to find in more mature stellar systems due to the gravity of their nearby stars. -- ApJ 2010 EAS 4803/8803 - CP 7:4
Tidal Heating Temporal variations in tidal forces can also lead to internal heating of a planet or moon. This occurs due to the fact that planets are not perfectly rigid or perfectly fluid Thus tidal forces cause the object to change shape, but since the response is not perfect or instantaneous this leads to energy being dissipated as heat as the object changes shape. EAS 4803/8803 - CP 7:5
Torque on Oblate Planets These forces are a result of nonspherical mass distribution. Solar torque on a given planet causes precession of the rotation axis, and can lead to a different length in orbital period and varied periodicity between the seasons (called the Milankovich Cycle). Earth s obliquity is somewhat stabilized by our Moon. EAS 4803/8803 - CP 7:6
Torque on Oblate Planets Generally the strongest torques on oblate planets come from the Sun. The period of Earth s rotational axis precession is ~26,000 years. Figures modified from UOregon Migration of the North star EAS 4803/8803 - CP 7:7
Obliquity? Defined as the angle of the rotation axis. Planets like Neptune and Uranus have significant obliquity, with Mars obliquity ranging widely over solar system timescales. Without the stabilizing moon, we could potentially experience much great and unpredictable seasonal variability (Mars). Consider the rapid change in seasons Mars would experience when it undergoes a > 60º obliquity change EAS 4803/8803 - CP 7:8
Solar Heating & Energy Transport Electromagnetic Spectrum Bluer Shorter Wavelength Higher energy photons Redder Longer Wavelength Lower energy photons EAS 4803/8803 - CP 7:9
Solar Heating & Energy Transport http://xkcd.com EAS 4803/8803 - CP 7:10
Planck s s Law for Black Body Radiation ν = c / λ I ν (T) I λ (T) Figure modified from Eric W. Weisstein Specific Brightness: B ν (T) EAS 4803/8803 - CP 7:11
Limits for Planck s s Law Specific Brightness: B ν (T) 1. Rayleigh-Jeans Law: In the limit where hν << kt, most applicable for long wavelengths (such as in the radio part of the spectrum) and temperatures in the range of planetary bodies. B " ( T) # 2" 2 c kt where 2 eh" / ( kt ) $1# h" / kt 2. The Wien Law: When hν >> kt ( ) B " ( T) # 2h" 3 c 2 e $h" /( kt ) EAS 4803/8803 - CP 7:12
Wien s Displacement Law Setting the derivative of Planck s Law with respect to λ (wavelength) equal to zero, we determine the peak wavelength with respect to temperature. λν A / T, where A = 2.898 x 10 6 max = 5.88 x10 10 T, where ν max is in nm/k Hz EAS 4803/8803 - CP 7:13
Solar Spectrum, Variability, and Atmospheric Absorption EAS 4803/8803 - CP 7:14
Luminosity A useful way to describe the amount of energy emitted by an object is the luminosity (often used in astronomy to relate the energy, size and temperature of stars and intercompare their properties). Luminosity (L) = Energy flux x Area and has units J/s or W EAS 4803/8803 - CP 7:15
Hertzsprung-Russell (H-R) diagram The Sun in Perspective EAS 4803/8803 - CP 7:16
Reminder: Observatory Night Where: Roof of the Physics building What day(s): Monday Sept. 20th (Backup: Oct. 11th/13th) What time: 8:30pm Thanks to Prof. Jim Sowell! EAS 4803/8803 - CP 7:17