1. Read BEFORE coming to class:
Lecture 6 Phys 1810
Read BEFORE coming to class:
Electromagnetic Radiation 3.1 to 3.4
Energy
Thermal Radiation Box 3-2
Flux and Luminosity
(L equation in Box 17-2)
Spectra 4.1, 4.2
Kirkhhoff’s Laws
Radio Emission 18.4
Doppler shift: 3.5, Box 3-3, 4.5
TODAY: LAST DAY TO REVISE CLASSES
Password change on Friday!
Given out in Class, not .
New folk please see Mr. Cameron
about labs.

2. Let’s weigh the sun! Re-arrange the velocity equation and substitute.
Exercise – weigh the Earth using the moon.(Look relevant values in textbook.)

3. Weighing the sun

4. Weighing the sun How does this compare with the Earth’s mass?
Many ways to calculate co-efficients.
Can get the mass of black holes and galaxies  Dark Matter.
Mass of Earth ~ 6* 10^24 kg. Do exercise to measure it using the moon.
How does this compare with the Earth’s mass?
What else can we “weigh” with this equation?

5. General Relativity: Gravitational Lensing

6. A single galaxy lensing a background galaxy.
Seeing Gravity
A single galaxy lensing a background galaxy.
(hubblesite.org “gravitational lens”)

7. General Relativity (GR):
Motivation:
The speed of light is measured to remain constant regardless of speed of observer.
Newton’s laws are inaccurate for extraordinarily concentrated masses & large accelerations.
GR is geometrical view  concept of gravitational field.
GR has 4 dimensions: 3 spatial dimensions & 1 time dimension  spacetime.
Playing ball hockey on a flat bed truck, an observer on the road side measures the speed of the ball + the truck’s speed. However a light beam from the Starship Enterprise would be measured by someone in a shuttle outside the ship as c.
GR is a geometrical view -- not the force between objects (Newton)
 concept of a gravitational field – not the “string” of force between 2 objects (Newton)
GR has spacetime rather than a separate constant time (Newton) which we are used to.

8. General Relativity (GR):
Uses Einstein’s Field Equations.
Definition: The presence of mass curves spacetime and we interpret the curved motion (i.e. orbits) of particles in curved spacetime as acceleration due to a force, i.e. gravity.
In the case of small mass or small acceleration, Einstein’s Field Equations reduce to Newton’s laws of gravity & F = ma
Really is a “law” rather than a theory.
Reduce 4 dimensions to 2D so I don’t have to use the field equations. You can only consider what is happening on the surface of the 2Ds.
curve not just happen around the object’s equator but in all directions… However can’t go off surface – i.e. like painting
… can’t ask what is on the back… so nothing wonky can go on off the surface.
4D object
An example is a scarf. Put a large ball on it and it bends the scarf. Any other ball on the surface will then feel the curvature and move accordingly.
Applicable to everything from the precession of the planet Mercury to your cell phone.
On the shuttle (in orbit therefore accelerating) the astronauts measure time, using atomic clocks, to be moving slower than the folk in mission control  spacetime!
Not an overthrow of Newton’s Laws – not a revolution – but an evolution.

9. Newtonian Gravity – instantaneous. GR - S. Krasnikov 2014
Speed of Gravity:
Newtonian Gravity – instantaneous.
GR - S. Krasnikov 2014
“General Relativity lacks the notion of the speed of gravity. This is inconvenient and the present paper is aimed at filling this gap up.”
This is at the Theory and Prediction stage paper by Fomalont and Kopeikin paper -- they interpret a constant in their equations as the speed of propagation of gravity and hence claim it provides an indirect measurement of this quantity. However they also write that there are other interpretations of their equations, and indeed some of the alternatives are by Kopeikin.   Their interpretation in this paper was quite contentious according to the prestigious journal Nature.

10. occur in strong gravitational events such as neutron star mergers
Speed of Gravity:
GR - what is actually predicted by Einstein is the propagation speed of gravitational WAVES, not gravity.
occur in strong gravitational events such as neutron star mergers
not measured yet (see LIGO and LISA projects.
theorists want propagation speed of GR waves = c.
You have probably read about gravitational waves rather than the speed of gravity. Imagine an isolated star -- there could be no gravitational waves, just the curvature of spacetime.
Evidence that there are grav. waves – Nobel prize to Hulse and Taylor: 2 pulsars in orbit… decay of orbit provides another proof of GR but did not measure the waves.

11. Please write out your own notes and thoughts about GR, speed of gravity, gravity waves, fields, and black holes. Feel free to ask me to review concepts during my office hour on Mondays at 3pm.

12. Radiation
Cygnus region of the Milky Way Galaxy. Supernova Remnants, star forming clouds, gas and dust. None of the data used to create this image are seen with the human eye (i.e. invisible!)
Jayanne English and A. Russ Taylor for CGPS

13. Demo

14. Created by vibrating charges.
Waves in what?
Electrical Force: attractive or repulsive.
Every charged particle has electic field.
EM waves need no medium.
Created by vibrating charges.
Radiation travels through a vacuum – no medium - so waves in what?
[Efld == electric field; F == force; ptl == particle]
Electrical force: e.g. static cling, sparks off cats. If another charged ptl in fld, then it will be attracted or repulsed.
Efld Force inversely proportional to distance^2, like gravity.
Cause a charge to vibrate (move up & down) , say due to heat or collisions,  wave travels through the Efld. i.e. Efld changes due to a disturbance which travels through space as a wave. F of Efld on distant ptl changes.

15.  a B field accompanies a changing E field.
Magnetic Field (B field) analogous to E field.
for magnetized objects
B fields exert a force on moving charged particles.
moving charged particles create B fields.
 a B field accompanies a changing E field.
Demos to show link between E & B fields.
Objects like magnetized needle in compass, Earth’s magnetic poles.
B is conventionally written with an arrow on top.

16. 3 demos were shown. Can you recall them and what concepts they illustrated? Feel free to drop by Allen 514 Mondays at 3pm to discuss these.