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Physics 362 – week 4
Modern Physics Seminars
Distances in the solar system
The movement of the planets is described using celestial
mechanics
 F = G mM/r2
 Kepler’s laws (P2=k r3)
 astronomical unit = average distance of the Earth
from the Sun
 1 a.u. = 149,598,073 Km
Distances beyond the solar system
Trigonometric parallax
a
Trigonometric Parallax
d
1 a.u.
p
 d = 1 a.u. / sin p ~ 1 a.u. / p
(p in radiants)
Trigonometric parallax
Trigonometric parallax
a
Trigonometric Parallax
d
1 a.u.
p
 d = 1 a.u. / sin p ~ 1 a.u. / p
Trigonometric parallax
Parsec = distance of a star when the parallax is equal to 1”
d = 1 a.u. / sin p ~ 1 a.u. / p
(p in radiants)
1 pc = 1 a.u. / (1”  1 rad) = 206,265 a.u.
1 pc = 3.1 1013 Km = 3.26 light-years
Trigonometric parallax
Closest star: Alpha Centauri is 1.3 pc away
Parallax = 0”.76
Only a small number of stars can be measured!!!
Current accuracy: ~0”.005  dmax~200 pc
Distance scales
Distances beyond 200 pc
Motion of the sun in the galaxy
v ~ 30 Km/s ~ 4.1 a.u. / year
In 10 years 41 a.u.
 Can be used to measure up to ~ 2000 pc
Distances beyond 200 pc
Calibrated candles!!!
Light intensity:
Id = I e / r 2
we can measure Id, and if we know Ie
 we can evaluate r
Calibrated candles
•Stars from the H-R diagram
•Variable stars
•Type II supernovae
•Galaxies
Spectroscopy
f obs  f0
1 vc
For approaching source
1 vc
  obs   0
1 vc
1 vc
1 vc
 obs   0 
v
z


1 
0

c
1 vc
redshift
Redshift
Hubble law
 v = H · r (H = Hubble constant)
Hubble law
H>0
 The universe is expanding
Earth at the center of the Universe?
NO!
H = v / r ~ 70 km / s / Mpc
 H = time-1
vmax = c
 Rmax = vmax / H = 6000 Mpc
~ 2 1023 Km = 2 1010 light/years
Hubble law
Rewind the film
 BIG BANG!!!
Age of the universe:
Objects at distance = R = v / H
 Time to get this far:
T = R / v = 1 / H ~ 6.2 1017 s ~ 1.5 1010 years
(15 Billion years)
Einstein and Hubble
• The theory of general relativity predicts a dynamic
universe (either expanding or contracting)
• Einstein didn’t believe in a dynamic universe and
modified his theory, introducing an extra term (the
vacuum energy density L) in his equations, to have a
static universe
• When Hubble published his results Einstein defined
his modified theory “the biggest blunder of my life”
• A term similar to L has now been reintroduced to
explain recent results in Cosmology