1. Homework #4
An asteroids closest approach to the Sun (perihelion) is 2 AU, and farthest distance from the Sun (aphelion) is 4 AU.
1) What is the semi major axis of its orbit?
2) What is the period of its orbit?
3) What is it’s eccentricity?

2. Homework #4 continued
4) A set of keys is dropped from the top of the Empire State building in New York. How fast will they be going when they hit a poor tourist on the ground 9 seconds later?
5) How tall is the Empire State Building?
6) An astronaut drops his set of keys from the same height as the Empire State Building on the Moon (1/6th the gravity of Earth), how fast is it going when it hits the Lunar surface?

3. Homework #4 last page
7) What is the maximum resolution of your eyes (assume the wavelength range that your eyes are sensitive to is 300 – 700 nm and that your iris is ½ cm in diameter.
8) What size eye would be required to see in the radio with the same maximum resolution of your eyes? (use 21 cm for the wavelength of typical radio waves)
9) What is the maximum resolution of the VLBA (longest baseline = 5000 km) at a wavelength of 21 cm?

4. Gravitational Potential Energy for the surface of the Earth is:
mgr (where r is the radius of the Earth)
F = ma = mg
= GmME/r2 = m (GME /r2)
so: g = GME /r2
and: mgr = m(GME /r2) r
So, Gravitational Potential Energy = m(GME /r)

5. Escape Velocity set: ½ m v2 = GmME /r ½ v2 = GME /r vesc = 2GME /r
for a mass m to escape from the Earth (of mass ME)
½ v2 = GME /r
vesc = GME /r

6. Orbital Paths
Extending Kepler’s Law #1, Newton found that ellipses were not the only orbital paths.
possible orbital paths
ellipse (bound)
parabola (unbound)
hyperbola (unbound)

7. Changing Orbits
orbital energy = kinetic energy + gravitational potential energy
conservation of energy implies:
orbits can’t change spontaneously
An object can’t crash into a planet unless its orbit takes it there.
An orbit can only change if it gains/loses energy from another object, such as a gravitational encounter:
If an object gains enough energy so that its new orbit is unbound, it has reached it’s escape velocity.

8. How do we do astronomy? We look at stuff
We collect stuff that travels to us from far away – matter and radiation – this is what we mean by “look”

9. What is light?
Newton showed that white light is composed of all the colors of the rainbow.

10. Four Ways in Which Light can Interact with Matter
emission
absorption
transmission
reflection

12. But, what is light?
In the 17th Century, Isaac Newton argued that light was composed of little particles while Christian Huygens suggested that light travels in the form of waves.
In the 19th Century, Thomas Young demonstrated that light bends slightly around corners and acts like interfering waves.

13. Light f  = c E = hf E a f Light as a wave Light as a particle
A vibration in an electromagnetic field
through which energy is transported.
Dual Nature
Light as a wave
f  = c
Light as a particle
E a f
E = hf
photon
Planck’s constant h = 6.6 x J s

14. Scottish physicist James Clerk Maxwell showed mathematically in the 1860s that light must be a combination of electric and magnetic fields.

15. Our first key idea is that visible light is only a small part of the complete spectrum of light. You may wish to spend some time explaining the various things shown in this figure… You may also want to repeat this slide at various points to summarize other ideas.