physics 362 – week 4
DESCRIPTION
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/r 2 Kepler’s laws (P 2 =k r 3 ) astronomical unit = average distance of the Earth from the Sun 1 a.u. = 149,598,073 Km. a. - PowerPoint PPT PresentationTRANSCRIPT
Physics 362 – week 4
Modern Physics Seminars
Distances in the solar systemThe 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
Trigonometric Parallax
1 a.u.
d
d = 1 a.u. / sin a.u.in radiants
Trigonometric parallax
Trigonometric parallax
Trigonometric Parallax
1 a.u.
d
d = 1 a.u. / sin a.u.
Trigonometric parallax
Parsec = distance of a star when the parallax is equal to 1”
d = 1 a.u. / sin a.u.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 galaxyv ~ 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 = Ie / r2
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
cv
cv
0obs1
1ff
cv
cv
0obs1
1
c
v1
1
1z
cv
cv
0
0obs
redshift
For approaching source
Redshift
Hubble law
v = H · r (H = Hubble constant)
Hubble lawH > 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 lawRewind 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 ) 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 has now been reintroduced to explain recent results in Cosmology