Physics of Astronomy week 2 – Thursday 15 Jan 2004 Celestial Mechanics Star Date Boas: Spherical Coordinates Gravity lecture and applicationsGravity lecture Workshop moons of JupiterWorkshop Learning plans and assignments

Boas: Spherical coordinates

Guiding Questions: Celestial Mechanics 1.How did ancient astronomers explain the motions of the planets? 2.Why did Copernicus propose that the Earth and the other planets revolved around the Sun? 3.What did Galileo see in his telescope that supported the geocentric model? 4.How did Tycho Brahe attempt to test the ideas of Copernicus? 5.What phenomenological laws did Kepler induce from Tycho’s data? 6.How do Newton’s laws explain Kepler’s conclusions? 7.Why don’t the planets fall into the Sun?

Derive Kepler’s 3d law from Newton’s second law: F=ma Gravitational forceacceleration in circular orbit F=GmM/r 2 a = v 2 /r Solve for v 2 : Speed v = distance/time = 2  r/T. Plug this into v 2 and solve for T 2 : This is Kepler’s third law: T = period and r = orbit radius.

Apply Kepler’s 3d law: For objects orbiting the Sun, a=radius in AU and p=period in years A satellite is placed in a circular orbit around the Sun, orbiting the Sun once every 10 months. How far is the satellite from the Sun? NB: This simple form of K3 only works for our solar system. Why?

A satellite is placed in a circular orbit around the Sun, orbiting the Sun once every 10 months. How often does the satellite pass between the Earth and the Sun? Sidereal and Synodic periods

We can use Newton’s gravity to approximate the size of a black hole! Not even light can escape (v=c) if it is closer than r to a black hole. This is the Schwarzschild radius: R=_____________________

4  2 r 3 = GM T 2  a 3 =p 2 for planets around the Sun Orbit radius: r(m) or a(AU); Period T(sec) or p(years) Keplerian orbits: close = faster

Solve 4  2 r 3 = GMT 2 for central mass M=_______ Earth data: period = 1 year ~ 3 x 10 7 sec orbit radius = 1 AU ~ 150 x 10 9 m M= M  = Saturn data: period ~ 30 year = __________________ sec orbit radius = 10 AU ~ ________________ m M= M  = Use Kepler’s 3d law to weigh the Sun

Use Kepler’s 3d law to weigh Jupiter.weigh Jupiter

Then, use Kepler’s 3d law to weigh galaxies and discover dark matter

Mon.19.Jan: Holiday; Tuesday Boas HW due. Tues.20.Jan: ML on Universe Ch.3: Moon & Eclipses Thus.22.Jan: ML on Universe Ch.4: Gravity & Orbits Mon.26.Jan: Workshop on Jupiter’s moons & Dark matter Tues.27.Jan: HW due on Universe 3+4; Quiz Review Physics Ch.3+4; ML Physics Ch.6 Thus. 28.Jan: Lecture and ML on Astrophysics Ch.2 Tues.3.Feb: HW due on Physics Ch.6; CO Ch.2; Quiz Learning Plan for weeks 3-4:

Tues.20.Jan: Universe Ch.3: Moon & Eclipses (Boas due) Team 1: Ch.3.1, Motion of Moon, # 23 Team 2: Ch.3.2, Motion of Moon, # 43 Team 3: Ch.3.3-4, Lunar Eclipses, # 30 Team 4: Ch.3.5, Solar Eclipses, #33 Team 5: Ch.3.5, Distances: demonstrate and diagram Eratosthenes’ calculation Thus.22.Jan: Universe Ch.4: Gravity & Orbits Team 1: Ch.4.1-2, Retrograde motion, #48 Team 2: Ch.4.3, Galileo’s observations, #50 or 52 Team 3: Ch.4.4-5, Tycho + Kepler, #35 Team 4: Ch.4.6-7, Newton + orbits, #39 Team 5: Ch.4.8, Tides #44 (or Physics Ch.6 #54) Assignments for week 3:

Mon.26.Jan: Workshop on Jupiter’s moons & Dark matter Tues.27.Jan: HW due: Physics Ch.6 # 54 Universe Ch.3 # 23, 43, 30, 43, Ch.4 # 48, 52, 35, 39, 44 Review Physics Ch.3+4; ML Physics Ch.6, Gravitation: Team 1: Ch.6.1-3, #13, 14 Team 2: Ch.6.4-5, #28 Team 3: Ch.6.6-8, #47 Thus. 28.Jan: Lecture on Astrophysics Ch.2 Team 4: Ch.2.1, #2.1 & 2.2 Team 5: Ch.2.3, #2.7 Tues.3.Feb: HW due: Physics Ch.6 # 13, 14, 28, 47, 57, 60 CO (Astrophysics) Ch.2 # 1, 2, 7, 8, 11 Assignments for week 4: