back

1
Welcome back to 8.033!
2
Astrophysical evidence for black holes 1)
Supermassive BHs in centers of most (all?)
galaxies - existence of quasars, huge jets -
stellar motions gt 106 - 109 solar masses -
orbiting gas disks gt size less than 0.4
lightyears (cant be stars) - devoured star
incident gt size less than 0.4 A.U. - X-ray
spectra reveal disk extending in to 6-20M!
3
Astrophysical evidence for black holes 2)
Stellar mass BHs - Stars orbiting massive
invisible companion - Maximum neutron star mass
is 3 solar masses - Best example V404 Cygni
partner mass 122 solar
masses. - Older example Cygnus X1 - X-ray
variability puts upper limit on size - Appears
that no surface
4
(No Transcript)
5
MIT Course 8.033, Fall 2004, Lecture 23 Max
Tegmark

• PRACTICAL STUFF
• PS9 extension until Monday 6PM
• Review session when?

• TODAYS TOPICS
• Applications of the orbital equations
• Radial orbits
• Circular orbits
• Near-circular orbits Mercury perihelion
  precession
• Gravitational lensing
• What really happens near the event horizon

6
Java orbit simulator
7
CIRCULAR ORBITS
8
(No Transcript)
9
(No Transcript)
10
Interesting circular orbits
Photon orbit
Tourist orbit
Last stable orbit
Classical limit
11
GENERAL ORBITS
12
Perihelion advance 43 arcseconds/century
13
GPS
14
GPS uses a constellation of 24 NAVSTAR
satellites that are 11,000 miles above the
earth's surface. 
15
(No Transcript)
16
(No Transcript)
17
(No Transcript)
18
(No Transcript)
19
(No Transcript)
20
(No Transcript)
21
(No Transcript)
22
(No Transcript)
23
(No Transcript)
24
(No Transcript)
25
(No Transcript)
26
(No Transcript)