Transcript Gravitational mass

Chapter 33
Astrophysics and Cosmology
© 2006, B.J. Lieb
Some figures electronically reproduced by permission of Pearson Education, Inc.,
Upper Saddle River, New Jersey Giancoli, PHYSICS,6/E © 2004.
Ch 33
1
Stars and Galaxies
•Our sun is a very average star
•Energy of sun is from fusion in center
•Sun is located in Milky Way Galaxy
•Milky Way has about 100 billion stars
•About 100 billion galaxies in universe
Ch 33
2
Stars and Galaxies
Ch 33
3
General Theory of Relativity
•concerned with accelerated reference frames
•Principle of Equivalence: No observer can determine whether
he or she is accelerating or is in a gravitational field.
Ch 33
4
Inertial and Gravitational Mass
Inertial Mass: resistance to force
F  ma
Gravitational mass: gravitational force of attraction
depends on the products of the two masses
FG  G
m1 m2
r2
Throughout this course we have assumed that these two
“masses” are equal, but are they?
•Experiments with an accuracy of a few parts in 1012
show no difference between inertial and gravitational
mass.
•Principle of Equivalence says they are equal.
Ch 33
5
•Light beam in constantly moving elevator moves directly
across because of special nature of light
•In accelerated elevator, light beam is bent because of
increasing velocity of elevator
•Principle of Equivalence says that there is no difference
between accelerated frame and frame in gravitational field
Ch 33
6
Bending Light Rays passing near the Sun
•
Consider three stars in the sky.
•
If the light from one of these stars passes very near the Sun,
whose gravity bends the rays, the star will appear higher than it
actually is.
Ch 33
7
Curved Space
•Light beam must travel by the shortest, most direct path
•Can explain bending of light ray by assuming space is
curved.
•In Euclidian geometry, the sum
of the angles in a triangle must
be 1800
• if sum >180 0 space is
positively curved
•If sum < 1800 space is
negatively curved
Ch 33
8
Black Hole
Black Hole is a massive collapsed star.
• Gravity is so strong that photons can’t escape from its
surface.
•Can see X-Rays from matter being pulled into it.
Ch 33
9
Expanding Universe
•Hubble measured the distance to galaxies by measuring
the brightness of certain stars whose intrinsic brightness
was known
•the velocity of galaxies was determined by the Doppler
effect
•all galaxies showed a redshift (spectral lines were shifted
toward lower frequency indicating they moved away from
the earth.)
•doesn’t mean we are at center of universe
Ch 33
10
Hubble’s Law
•Hubble found a linear relationship between the velocity ( v ) of galaxies
away from us and the distance to the galaxy ( d ).
•The slope of the line is H, called the Hubble Constant.
v  Hd
H
Ch 33
22 km
7 km
s
s

106 light  years 106 light  years
11
Example 33-1 If a galaxy is traveling away from us at 10.0% of
the speed of light, roughly how far away is it?
v  Hd
v
d
H
(0.10)(3.00108 m / s)

2.2 104 m / s / Mly
d  1.4 10 ly
9
So the light left the galaxy 1.4 billion years ago.
Ch 33
12
Hubble’s Law
We can use this to estimate the age of the universe:
Assume that the universe a galaxy at distance d from has been
moving away from us since the start of the universe and
calculate how long that has been.
Ch 33
d
d
1 (106 light  years)(1013 km / light  year)
t 


 15 billion years
s
v Hd H
(22 km )(3  107
)
s
light  year
13
Big Bang
0→10-43seconds
•four forces unified, theory ≈ ???
10-43→10-35sec.
Grand Unified Theory Era
•gravity was a separate force
•no distinction between quarks and leptons
Ch 33
14
10-35 →10-4 seconds Hadron Era
•strong force is separate force
slight excess of quarks over anti-quarks results in excess of
nucleons over anti-nucleons
10-4→ 10 seconds Lepton Era
slight excess of electrons over positrons results in only electrons
after annihilation
Ch 33
15
10-4→ 300,000 year Radiation Era
•radiation dominates (photons and neutrinos)
300,000 year → now
Matter Dominated Era
•atoms formed
•stars and galaxies formed
•Universe is matter dominated
Ch 33
16
Future of Universe
Can the gravitational force reverse expansion of the
universe? Answer depends on average density
critical density c = 10-26 kg / m3
3)
(
a
few
nucleons
per
m
.
 < c curvature is negatively curved and universe
expands forever
 > c curvature is positive and universe expansion is
reversed
Ch 33
17
Big Surprise!!
Recent evidence suggests that the universe is expanding at
an accelerating rate.
.
Ch 33
18
Dark Energy
•There is now evidence that the expansion of the universe is
accelerating
•This would imply the existence of an unknown force which
has been given the name “Dark Energy”. Dark implies that
astronomers can’t see it.
.
•It is interesting that Einstein had included a fudge factor in the
General Theory of Relativity called the “Cosmological
Constant” that explained the stability of the universe.
•When it was discovered that the universe is expanding then
the Cosmological Constant was not necessary so Einstein
considered it his biggest mistake.
•Now we find that the Cosmological Constant may explain the
acceleration that has been recently observed.
Ch 33
19
Best Estimate of Mass-Energy in the Universe
73 % dark energy
27% subject to the known gravitational force
23% is dark matter (matter that astronomers
can’t detect)
4% is baryons and leptons
Ch 33
20