1. Physics of Astronomy Winter Week 6 - Thus.16.Feb.2006 Astro-A: Universe 4 – Gravity and Orbits Pre-lab – brief discussion Astro-B: Finish C&O Ch.2 2:30 Seminar 4:00 Lab in CAL 1234 Let’s look at the sky together after lab! Looking ahead (remember to take Universe Ch.4 online quiz)

2. Astro-A: Universe 4 – Gravity & Orbits Ptolemy: Circular orbits about Earth Copernicus: Circular orbits about Sun Kepler: Elliptical orbits about Sun

3. We derived Kepler’s 3d law from Newton’s 2d 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.

4. For objects orbiting the Sun, Kepler’s law simplifies to a 3 = p 2, where 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?

5. Sidereal (real: P) and Synodic (apparent: S) periods: 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?

6. We can use Newton’s gravity to approximate the size of a black hole! Knowing the gravitational force between two bodies m and M, we can find their gravitational energy: In order for an object (say, m) to escape M’s gravity, It needs sufficient kinetic energy K=1/2 mv 2 …

7. Use energy conservation to find the size of R 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 (for v=c) =_____________________

8. Lab Hand in before lab: Excel practice results Pre-lab Lab this afternoon Read lab guidelines Take notes in a bound notebook Write up report this weekend

9. Astro-B: C&O Ch.2: Gravity & orbits Kepler’s laws (for M>>m) Generalization (for M~m) K1: orbits are elliptical- about center of mass K2: equal areas in equal times- conservation of L K3: Center of mass Virial Theorem

10. Center of Mass reference frame Total mass = M = m 1 + m 2 Reduced mass =  Total angular momentum L=  r v =  r p v p (Pick any point, e.g. perihelion: r p and v p ) p.50

11. Virial Theorem = /2 where = average value of f over one period For gravitationally bound systems in equilibrium, the total energy is always one-half of the potential energy. Ex: Use K3 in E orbit = T + U for circular orbit: New HW: 2.8, 2.9

12. Looking ahead Monday TuesdayWedThusFri