ASTR 10, Vista College, Spring 2004
Instructors: Dr. Korpela
What Was Important - Material for Exam #3
The first part of the lecture discussed star formation (see Chapter 9).
The interstellar medium stuff was somewhat confusing in the book, so is
- Interstellar medium: Stuff between the stars. 75% hydrogen, 25% helium,
less than 1% other stuff (this is ~ the same as the sun)
- Evidence for ISM: dark clouds of gas/dust that block light (dark nebula)
- Evidence for gas:
- narrow absorption lines in stellar spectra
- emission at a wavelength of 21-cm from cold, neutral hydrogen
- a hot nebula that is excited or ionized can glow due to radiation
produced in emission lines (emission nebula). The color of the nebula
is dependent on the wavelength of the emission lines (pink/red)
- Evidence for dust:
- Dust radiates in infrared
- Dust can reflect light (reflection nebula, blue)
- Dust can redden (as well as dim) stars.
- Understand why reflection nebulae are blue (and the sky!).
- Understand why dust can both dim and redden starlight. Know that
the dimming effect is less strong in the infrared.
- Understand that a star forms from a giant, cold, 'dense' (by interstellar
standards, but not Earthly ones) cloud, which is big enough to form hundreds
or thousands of stars.
- Understand that it collapses to a 'protostar', and why it heats up along
the way. Gravitational energy is converted to Thermal Energy.
- Protostar is embedded in dusty cloud of gas, so hard to see, even though
it is glowing because it is warm.
- The protostar is losing energy and will keep collapsing unless there is
an internal energy source. This source is FUSION, and when it begins a
star is 'born' on the MAIN SEQUENCE!
- Stellar evolution refers to the changes in a star's structure during
its lifetime (not over several generations of stars).
- Know that LEAST massive stars live LONGEST (by a HUGE factor - have
some idea of the extremes and the value for the Sun), and why.
- Know that stars spend 90% of their lives on the main sequence, and
this is why when we plot the H-R diagram for a population of stars, we see
most stars on the main sequence. Understand why later stages of their
lives are shorter.
- Know the end products of stars of various masses! (details below)
- Sun (and stars with mass 0.2 M_sun < M < 4 or 6 M_sun): planetary
nebula and C/O white dwarf
- Cool/dim stars (M < 0.4 M_sun): haven't had time to leave the main sequence
- Massive stars (M > 8 M_sun): Supernova + neutron star or black hole
- Understand when star becomes a red giant: the core runs out
of hydrogen, so can't hold itself up against gravity, so shrinks. This
converts gravitational energy to thermal energy and so the core is now
hot enough to fuse into Helium (He). The surface layers, paradoxically,
expand and cool, so we have a BIG, RED star (you don't need to know the
details of how this happens, although the book explains it)
A "hydrogen burning shell"
generates energy which is transported to the surface layers, which therefore
expand. Expansion cools the surface, so we have a BIG, RED star.
- Understand why He requires a higher temperature to fuse, and why
the stage of helium `burning' is faster than the hydrogen fusion stage.
- Know that He fusion requires a higher temperature, and that it
is less efficient that H fusion at generating energy.
- To compare theory with observation, we look at STAR CLUSTERS.
These are groups of stars that formed all at one time (out of the same cloud of
gas), and are all at the same distance. Like taking a picture of 12-year-old
people to see what 12-year-olds are like, instead of a picture of the whole
population. Young clusters - mostly main sequence stars, lowest-mass
stars haven't yet reached the main sequence (begun to fuse H). Old clusters -
only cool/dim main sequence stars remain; have red giants and white dwarfs.
The observations match the predictions!
- For stars like the SUN:
- A "planetary nebula" forms when the outer layers of the star are
puffed off when Helium fusion ends and the surface of the star expands
(a second red giant phase). The hot, dense core is left behind and
revealed, and shrinks/cools to become a white dwarf.
- We see planetary nebulae with hot stars in the middle!
- The Pauli Exclusion Principle states that two identical electrons
can't have exactly the same energy. Since possible energy levels for
electrons are quantized, in a VERY dense gas, the electron motions
cannot be changed, since all the energy levels with lower energy are already
full. This pressure can hold up the star against gravity. For stars like
the sun, this prevents the temperature from rising high enough to
fuse Carbon. This DEGENERATE matter: resists compression; is incredibly
dense; has pressure which does NOT depend on temperature.
- If you add mass to a white dwarf (made out of degenerate matter),
the star gets squeezed tighter and gets SMALLER! This results in a
prediction of 0 radius for 1.4 solar masses, which clearly imposes a limit
on the mass of a White Dwarf (Chandrasekhar limit).
- White dwarfs are the second most common kind of star. No energy source.
The positive ions aren't degenerate, and can cool (slow down) and radiate
The energy is transported internally via CONDUCTION.
In about 10 billion years, they may become too cool/dim to see (the universe
isn't yet old enough for this to have happened).
- For lowest-mass stars (M < 0.4 M_Sun) (we'll get to this next week):
- They fuse H VERY slowly, so are long-lived, and have not
yet left the main sequence.
- They have convection throughout their interior, so new hydrogen
is always coming from the outer layers to the core => even longer-lived
- Eventually (possibly 100s of billions of years) they will
run out of energy and the He core will contract into a White Dwarf.
- For High-mass stars (M > 6 or 8 M_Sun):
- Go through initial phases much as the sun will, but faster
- Unlike the Sun, as the core contracts after it runs out of He, it
gets hot enough to fuse C and O into higher elements
- Eventually, build up a series of 'onion' layers, with shells of
various elements fusing (H-shell is outermost), and a core of Iron (Fe)
- Recall that Iron is the most tightly bound element, and TAKES energy
in either fission or fusion reactions.
- The iron core can't hold itself up, and contracts.
- Contraction causes it to heat up (gravitational energy to thermal energy)
- Various other reactions remove energy from the core (see your book)
- When the collapsing core becomes > 1.4 M_sun, electron degeneracy
can no longer support it, and it collapses VERY quickly. Protons
and electrons combine to form neutrons + neutrinos - A NEUTRON STAR is born!
- Energy from the collapse is transferred to the outer layers of
the star, which are blown up.
- Star Stuff:
- Universe began with mostly H, He. We are Carbon-based. Earth is
mostly Silicon-based. All of this was made in stars! Almost anything
heavier than H/He was made in stars. Anything heavier than Iron (Gold,
Silver, Platinum...) was made in exploding stars! We are made of Star
- Evidence for this is that (1) older stars (formed longer ago)
have fewer heavy elements and (2) elements that we believe are only
generated in supernovae (like gold) are rare (as would be expected)
- The outer layers of matter are no longer held up, and free-fall towards
the core. The core is rebounding, so some energy is transferred to the
surface layers as they bounce off.
- In addition, 99% of the energy is in neutrinos, and a little of that
energy can be transferred to the matter and further accelerate it.
- This disruption of the outer layers of the star is a SUPERNOVA, and
results in a supernova + neutron star (or black hole).
- During this violent explosion, fission and fusion occur, and elements
heavier than iron are formed.
- Observational support for Supernovae:
- Observed supernovae: previously "normal" star suddenly (few days)
becomes MUCH more luminous (10^10 L_sun). 1054 AD - Chinese and others
saw a SN - bright as full moon for several weeks. There is a nebula
where this SN occurred. Tycho Brahe saw one, as did Kepler. Expect
1-2/century in our galaxy, but many are obscured by gas/dust.
- Observe SN remnants to be expanding
- Observe Neutron stars in some SN remnants (eg Crab pulsar, see below)
- SN 1987A: detected neutrinos to confirm a 50-year-old theory of
neutron star formation during SN!
- SN 1987A: saw gamma rays with particular energies that could only have
come from short-lived radioactive Cobalt. At IR wavelengths, saw
emission lines of freshly-made cobalt, nickel. Theories of how heavy
elements are formed in SNe are supported by this.
- Over 1/2 of all stars are in multiple systems. The `Roche Lobe'
(teardrop-shaped boundary) determines whether the matter is attracted
to one star, the other, or neither. Matter within each `lobe' is
gravitationally bound to that star. The teardrop shape is determined by the
forces due to the circular orbit and the gravitational forces of the
two masses. If you have a system with a main-sequence star and a compact
object (WD, NS, BH), when the MS star becomes a red giant, it is possible
that its outer layers will no longer be bound to the giant star, but
will fall towards the compact object.
- In this mass transfer, angular momentum must be conserved. Spinning
objects need to keep spinning. If a figure skater pulls in his/her arms,
they spin faster (more times per second). This forces the infalling
material into an accretion disk.
- Accretion disk gets hot due to friction and tidal forces, and
acts as a brake, ridding the gas of angular momentum and allowing it to
fall to the white dwarf (or NS/BH). The more compact the object, the
hotter the infalling gas becomes (a marshmallow dropped from a distance
of 1 AU onto a Neutron Star releases the energy of a 3-Mton bomb!
I've included the most important material in these next 2 sections in a fair
amount of detail, but tried to stick to the most important topics in this
section. Focus on 1) the characteristics of NS and WD, 2) the evidence
for various models, 3) the idea behind the lighthouse model of pulsars.
- Neutron stars: form from collapsing iron core of massive star. Must
be > 1.4 solar masses (electron degeneracy can't hold it up).
Protons and electrons are forced together into neutrons (and emit neutrinos,
which were observed for SN 1987A). Neutrons must also obey the Pauli
Exclusion Principle, and neutron degeneracy supports the neutron star.
Just like a white dwarf, there is a limit to how much mass this degeneracy
can support. For a NS, this limit is somewhere between 2 and 3 solar masses.
- So NS have between 1.4 and 2 or 3 solar masses of material, packed
into an object with radius ~ 10 km!
- What do we expect of a neutron star?
- 1.4 to 3 M_sun in 10-15 km radius
- expect faint (since very small, so blackbody radiation doesn't have
much surface area from which to emit)
- expect HOT (cool slowly since don't radiate much energy) so radiate
most in X-rays.
- expect to find some in SN remnants (since they form in SN explosions)
- spin fast (angular momentum is conserved : swirling interstellar cloud
had some spin, so stars rotate (observed), and as core collapses, it spins
- strong magnetic field (stars (like Sun) have magnetic fields - the
ionized gas drags the magnetic field with it, so as a star collapses,
the magnetic field gets squeezed tighter and so made stronger) -
about 109 to 1013 times that of the Earth's magnetic
- Compare NS to WD:
- Both form from cores of evolved stars once fusion is finished.
- Both are held up by degenerate particles
- Both are small and faint
- between 0.6 and 1.4 solar masses
- about the size of Earth
- formed from carbon/oxygen (or sometimes helium) core of low/intermediate
mass stars after outer layers become planetary nebula
- made of electrons + carbon/oxygen nuclei, held up by degenerate electrons
- cooling - no current energy source, radiating residual heat
- between 1.4 and 2 or 3 solar masses
- about 20 km across
- formed from iron core of massive stars during supernova
- made of neutrons, held up by degenerate neutrons
- cooling - no current energy source for blackbody radiation,
radiating residual heat
- BUT the rapid rotation of the strong magnetic field acts like a
generator, and drives the production of visible radiation (pulsar). Works
for neutron star because they spin faster and have bigger magnetic fields.
The energy is taken from the rotation (so they slow down). See below for
- Do we see the blackbody radiation of tiny, dim neutron stars?
- regular pulses of radio emission, with periods ranging
from a few milliseconds to 3.75 seconds (originally 33 ms was lower limit).
They slow down by a few billionths of a second per day. Pulses only last
about a millisecond.
- Why do we think they must be rotating NS? Process of elimination!
There is trouble with all other possibilities. The regular pulses could
be due to a) orbits b) vibration and c) rotation. The objects could
be i) regular stars ii) white dwarfs or iii) neutron stars. (The
key ideas here are that we used process of elimination and that the
observed slow-down of pulsars helped nail down the answer. The size
limit required by the observed short duration of each pulse is another
- Orbits won't work for periods of 33 milliseconds (too small and
fast - they'll lose energy to quickly)!
- Vibration: Smaller, stiffer objects vibrate with higher frequencies.
(think small bell, high pitch, big bell, low pitch). Hard to get the
full range of pulsar periods from one kind of object.
- Big objects that spin fast will tend to fly apart, so the short
pulsar periods indicate the objects are small. If the object is rotating,
it must be a neutron star (MS stars and WDs would fly apart)!
- Rotation can explain the full range of pulse periods.
- Clincher: Vibrating objects speed up as they lose energy (a pot lid
can convince you of this). Rotating objects slow down as they lose energy.
Pulsars slow down! So they must be rotating, and they must be neutron
stars (because bigger objects would fly apart if they rotated that fast).
- Additional Supporting Evidence:
- Some are seen associated with SN remnants (as predicted)
- We think pulsars have strong magnetic fields (because of the kind of
emission produced and the particles that are keeping the SN remnants glowing;
also because of polarization measurements of the radio beams).
- Mass estimates are consistent
- Pulsars pulse because they emit a beam that we see intermittently
(like a lighthouse). You should understand this lighthouse model -
we believe the beam is emitted from the magnetic poles of the pulsar.
Not all observers will see a given pulsar, because the beam has to be
pointed towards you. In addition, if the magnetic pole is on the spin
axis, the pulsar won't pulse because the beam doesn't swing around (if
a lighthouse beam pointed up, but the lighthouse still rotated the same
way, the beam would ALWAYS point up).
- What makes a pulsar shine? This is harder. A NS
spins so fast and has high enough B field that it acts like a
generator and creates an electric field around itself (changing magnetic
fields generate electric fields and vice versa - this is why we
have electromagnetic waves). The field
is so intense that it rips charged particles (mostly e-) out of the
surface near the poles and accelerates them to high velocity. These
accelerated electrons emit photons travelling in the same direction
as the electrons. Thus, the photons leave the neutron star in
narrow beams emanating from the magnetic poles. If the magnetic axis
is tilted with respect to the axis of rotation, then the neutron star will
sweep the beams around the sky.
- Notice that our model of pulsars matches the expectations of a neutron
star (small, dense, rapidly rotating, strong magnetic field, sometimes
found in supernova remnants, mass between 1.4 and 3 solar masses)
- Support for the lighthouse model:
- the energy the Crab pulsar has lost equals the energy the
Crab nebula (SN remnant) needs to keep shining!
- polarization measurements indicate that the radio emission is
coming from a region with a magnetic field like that expected for a spinning
- Some pulsars are extremely fast! Shortest period is about 1.5 milliseconds
(spins 640 times/second) (discovered 1982).
- The escape velocity of an object (speed you need to escape from
its gravity) is sqrt(2 G M / R) because as you squeeze the mass into
a smaller size (R decreases), its surface gravity
(G M m / R2) goes up.
- You can imagine squeezing any object into a small enough volume
that the escape velocity is bigger than THE SPEED OF LIGHT! So nothing,
not even light, can escape! The radius at which this occurs is called
the Schwarzschild radius . Any object smaller than its
Schwarzschild radius is a black hole. (Rs = 2 G M / c2)
- In the context of GR, light, when trying to move in a straight line,
ends up going in a circle around the black hole because of the curvature of
- event horizon is the boundary of the region within which
we can know nothing about the object because not even light can escape
- A BH is not voracious. As long as you stay outside the
event horizon, you can escape (assuming you can go fast enough - there might
be technical difficulties). If the Sun were replaced with a BH of the
same mass (ie shrink the matter in the Sun to a size smaller than 3km
(the Schwarzschild radius of the Sun)), the planets would not waver in
their orbits! It would get cold and dark, but the orbits would not change,
because orbits depend only on gravity, which depends only on the mass of
the object and your distance from it!
- A BH forms when the iron core of a massive star collapses but is
too massive to be held up by neutron degeneracy. The way to distinguish
between a NS and a BH is by measuring its mass, (which is difficult).
- A BH in a binary star system can acquire mass from a companion star
(see above). This material forms an accretion disk, and gets hot, so it
emits X-rays. To find a black hole, look for an object bigger than several
(say, 5) solar masses that is emitting X-rays! You won't be seeing the
BH, but the matter falling into the BH.
- Know that a compact object surrounded by an accretion disk
might send out a jet (and in which direction)
- Know that we see objects that (based on these criteria) we believe
to be black holes. Know also that this isn't absolute proof of their
existence! Perhaps some (as yet undiscovered) form of pressure halts
the collapse of these objects?
Milky Way Galaxy:
- Know the basic components of the Galaxy: Disk, bulge, halo,
spiral arms, dark matter corona,
- Know what each component is made of, and their properties
- Understand how we know that we're in the disk of a spiral galaxy
(both from visible light observations alone, and then (more easily)
from infrared/radio observations).
- Understand how we know we're not in the center
(both from visible light observations alone, and then (more easily)
from infrared/radio observations).
- Understand how we figure out how far from the center we are:
Understand how we find the distances to globular clusters
from variable stars (CALIBRATION!)
- Know what we can see by using infrared light instead of visible
light. This is because DUST blocks visible light!
- Know that cold hydrogen emits light at a particular radio
wavelength - 21cm! This is also not obscured by dust.
- Know that we use infrared or radio observations to help us map
the spiral arms in our own galaxy. We DID NOT focus on the spiral
structure of our galaxy.
- Know how we measure the mass of a Galaxy! We need to
know the orbit of an object around the galactic center. For
example, we need to know the Sun's speed around the center, and
its distance from the center. Understand how this relates to
measuring the mass of Stars, and how it differs.
- Notice that by looking at the Doppler shift of the 21-cm line of hydrogen,
we can measure how much mass is inside different radii. Know that
the mass keeps increases even as the luminous matter drops off.
90% of the Galaxy's mass is stuff we CANNOT see! We don't
even know what much of it is.
- The Halo is full of old stars low in heavy elements. The globular
clusters are 13 to 17 billion years old. Orbits of halo stars and clusters
are random (like a swarm of bees).
- The disk is full of younger stars with more heavy elements. Open
clusters no more than 7 million years old. Orbits
of objects in the disk are circular.
- There are two populations of stars: disk, halo (but really it is
a gradation from one to the other, not completely distinct populations)
- Heavy elements (heavier than H, He) are produced only in Stars!
So it makes sense that the earliest stars formed from material lacking in
heavy elements. As their material is mixed back into the interstellar
medium (supernovae, planetary nebulae), younger stars will have more
- Galaxy formed from GIANT swirling cloud, which collapsed. As collapse
began, clumps formed the globular clusters and halo stars (which
explains their random orbits, old age, and low heavy-element abundance).
Collapse continued, and conservation of angular momentum forced gas/dust
into a disk. Halo objects continued in original orbits. The disk
undergoes a continuing process of star formation. (This explains circular
orbits, younger age, and increased heavy elements of disk stars).
- A few problems with the above scenario: For example: the youngest globular
clusters are at the outer edge of the halo, the bulge contains some of
the oldest stars (and in this model, you'd expect bulge to form last),
where are the first stars with NO heavy elements? etc.
- Part of the answer may be that our galaxy has cannibalized other,
smaller ones. There is possible evidence for this happening right now!
- Know and understand the main evidence for a supermassive black hole
at the center of our galaxy (and exactly how such a black hole explains
- Understand how we can tell there are spiral arms in our own galaxy
(use distances to hot, young, blue stars; open clusters; clouds of
- Understand why spiral arms are related to star formation, and why
only young objects (things associated with star formation) are found there.
Why are old stars not good tracers of spiral arms?
- For each theory, imagine I'm in court trying to convince you of my
theory - I need to back it up with evidence! Notice that sometimes
not all of the evidence quite fits the theory! This might mean the whole
theory is wrong, or it might mean the observations are in error, or it
might mean that we need to modify or add something to the existing theory.
You should be able to apply this to the theory of galaxy formation.
- We talked about the difference between a theory being adequate
to explain the observations, and necessary. In the former case,
the theory can explain all of the observations (and perhaps better/more simply
than another theory), but it isn't the ONLY possibility. The theory is
necessary if we have no other theory that can come close to
explaining the observations.
- We discussed using the process of elimination to choose between theories.
If we have eliminated all but one
of our theories because only one fits the observations, then we still need
to look further. We may not have thought of all of the possibilities!
Has the theory made predictions which have been confirmed by further
observations? In this context, think about the theory of pulsars as
being associated with rotating neutron stars. In this case, further
observations have supported (but never proven!) the theory. On the other
hand, in the case of black holes (about 5 solar masses, not the supermassive
ones) in binary star systems, we have no additional evidence beyond "it's the
only thing we can think of with these properties". It is always possible that
some unkown physics halts the collapse, and the object isn't truly a
"black hole" as we have defined them.
- Know the general characteristics of the 3 kinds of galaxies, and that
they cover a wide range of sizes, masses, luminosities.
- We know galaxies are far beyond our own galaxy because we can measure
- Understand why we need to know the distances to galaxies to measure
their sizes, luminosities, and masses.
- Masses: understand how we use gravity to measure galaxy masses, and
how this leads to the conclusion that we can't see 90% of the mass!
- Understand the idea behind using "standard candles" and "standard rulers"
to get distances to galaxies. Understand the idea behind the "distance
ladder": we need to calibrate each method using the methods that came
before it. Common standard candles include Cepheid variable stars and
White-dwarf (Type Ia) supernovae.
- Know what we mean by Hubble's Law. More distant galaxies are moving
away from us faster. Understand that we need to
measure distances (see above) and recessional velocities (via doppler
shifts) for many galaxies to determine the Hubble constant.
- Once we know the Hubble constant, a measurement of the redshift
of a distant galaxy is sufficient to give an estimate of its distance.
- Understand that we think Hubble's Law is a result of the expansion
of space-time. This expansion carries the galaxies with it! This
explanation implies the universe has no center. It does NOT imply
that the galaxies themselves are expanding (they are held together
by gravity) or that the universe's expansion explains all the
relative motions of galaxies. Galaxies also move relative to one
another due to their gravitational interactions.
- Know the evidence for galaxy interactions, and why we expect them
more often than collisions between stars.
- Understand the role of galaxy interactions/collisions/mergers
in the history of galaxy evolution. What is the support for this
idea? This is probably not the whole story, however.
- Know the general phenomena observed for "active" galaxies
(giant radio lobes, jets, extremely luminous galaxy centers...)
- Know why we believe quasars are the extremely luminous
cores of distant galaxies.
- Understand how they both can be explained by the "unified theory":
A supermassive black hole surrounded by a rotating accretion disk,
- Know and understand how galaxy mergers/collisions trigger
the unusual "activity" in the galaxy cores, and evidence for
Cosmology can be confusing! Don't despair. Try to understand the
key concepts, and don't fret over the details of each step in the Big
- Understand infinity
- Don't fret over Olbers' Paradox, but notice that Assumptions are important!
- Understand the difference between the universe as a whole (may
be infinite in size) and the observable universe (finite in size)
- Understand the basic assumptions of homogeneity, isotropy
- The Geometry of space-time: understand the 2-d analogies for
the closed, flat, and open universes.
How can the universe be finite but unbounded?
- Expansion of the universe:
- Hubble's Law
- how the redshift of light is explained by the expansion
- everything expands away from us, but we are NOT at the center
of the universe - the universe has neither a center nor an edge
(we are at the center of the observable universe)
- Standard model of the Big Bang:
Focus on the evidence supporting this model:
- Hubble's law implies the universe is expanding:
- How is the Hubble constant related to the age of the universe?
- Understand how gravity should be slowing the expansion, and
how this affects the above.
- observed hydrogen/helium abundances explained:
- Understand why nucleosynthesis during the Big Bang produced only
- cosmic background radiation (CBR) observed;
- Understand the source of the cosmic background radiation (CBR): When was
it emitted? What event caused its emission? How hot was the gas? What
temperature is observed (and why)?
- Know that the expansion of the universe, the observed light element
abundance, and the observation of the CBR are the key pieces of evidence
supporting the Big Bang.
- Understand that the CBR is very uniform, and that it is difficult
to explain the observed structure of the universe (quasars already exist
at 7% of current age) from such a uniform beginning. Know that
'seeds' (irregularities) grew by gravitational attraction to form the
structure we see today. We can only get such early structure if these
seeds are dark matter (specifically Cold Dark matter, made up of massive,
and slowly moving particles - which means massive neutrinos can't
be the only kind of dark matter, or even the most prevalent).
- Is the universe open or closed? Why is this
related to the mass and energy density of the universe? What is the fate of
the universe in each case?
- Currently, by observing the tiny irregularities in the CBR, we
conclude that the universe must be nearly flat. The predictions
of Big Bang nucleosynthesis, combined with our measurements of light-element
abundances, indicates that "normal" matter can only be 4% of the density
required to "close" the universe, or make it flat. Our measurements
(by gravity) of dark matter account for another 21% of the required density
(notice that this stuff has to be mostly WIMPs or something even
more exotic - but not "normal" matter). Where's the other 70%? In 1998,
measurements of White-dwarf supernovae hinted that the universe might be
accelerating (speeding up its rate of expansion), instead of slowing
its rate of expansion due to the mutual gravitational attraction of
its matter. The "cosmological constant" describing this "dark energy"
of empty space has a mass-equivalent of about 74% of the density required
to make the universe flat. Of course, this neat picture might well have
some flaws on closer examination!
To confuse you even more we're talking about relativity this week.
- Relativity is an attempt to account for the fact that all observers,
regardless of their motion, measure the same value for the speed of light.
- The only way this is possible is if time is not a constant for all
observers. The rate at which time passes depends upon how you are moving.
- A clock moving at high rate relative to you runs slower than one not moving
with respect to you.
- Length is also dependent on velocity. An object moving with respect to you
is contracted along the direction of its motion.
- Things can only be said to be truly simultaneous if they happen at the same
time and in the same place.
- One event can cause another only if the time between the events is more than
the time it takes light to travel between the two events. All observers
regardless of velocity would see these events occur in the same order.
- If two events are separated by less time than the time it would take light
to travel between their locations, then one could not have caused the other.
The order in which these events occur can be different for different observers.
- Time can be treated like a dimension perpendicular to the spacial
dimensions. Velocity rotates the local time axis relative to an observer.
- Twin paradox. Each sees the other's clock running slower, but the moving
twin sees the distance traveled as being shorter.