Comet Halley (Edmund Halley)

The best known comet of all is Halley, which has returned with a 74-79 year period since 240 B.C. The following image shows a famous view of the full tail of Halley recorded from the Mount Wilson Observatory.

Comet Halley from Mount Wilson

Edmund Halley and His Comet

The English astronomer Edmund Halley was a good friend of Isaac Newton. In 1705 he used Newton's new theory of gravitation to determine the orbits of comets from their recorded positions in the sky as a function of time. He found that the bright comets of 1531, 1607, and 1682 had almost the same orbits, and when he accounted for the gravitational perturbation on the cometary orbits from Jupiter and Saturn, he concluded that these were different appearances of the same comet. He then used his gravitational calculations to predict the return of this comet in 1758.

A Posthumous Christmas Present Halley did not live to see his prediction tested because he died in 1742. But on Christmas night, 1758, the comet destined everafter to bear Halley's name reappeared in a spectacular vindication of his bold conjecture and of Newton's gravitational theory. Tracing back in the historical records for recordings of bright comets and their positions in the sky, it was concluded that Halley had been observed periodically as far back as 240 B.C. The most recent return was in 1986, and the predicted next appearance of Halley in the inner Solar System will be in 2061.

The Head of Halley

The Orbit of Halley's Comet

The following figure shows the orbit of Halley's Comet and its predicted location in 2024 relative to the orbits of the planets.

Halley's Comet in 2024

Blue is above the plane of the ecliptic and green is below. Almost the entire Halley orbit is below the plane of the ecliptic. Further, Halley revolves around its orbit in retrograde motion (the opposite sense from planet revolution). In the preceding view the planets revolve counter-clockwise and Halley revolves clockwise. The following image shows the same thing, but from a top view.

Halley's Comet in 2024---Top View

Notice that Halley's orbit extends essentially to the distance of Pluto, but when Halley is at its greatest distance from the Sun (aphelion) it is below the plane of the ecliptic (green color) while that portion of Pluto's orbit is above the plane of the ecliptic (blue color). The following image illustrates this more clearly. It is a view of the orbit of Halley and its 1996 position from the vantage of the ecliptic plane:

Solar System View from the Ecliptic Plane

This view illustrates clearly four important features of our Solar System:

1. How close to a plane the orbits of all planets but Pluto lie.
2. The large tilt of Pluto's orbit out of the ecliptic plane.
3. How elliptical Comet Halley's orbit is.
4. How Halley's orbit lies well below the plane of the ecliptic when it is in the outer Solar System.

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The Hot Big Bang

The big bang starts off with a state of extremely high density and pressure for the Universe. Under those conditions, the Universe is dominated by radiation. This means that the majority of the energy is in the form of photons and other massless or nearly massless particles (like neutrinos) that move at near the speed of light. As the big bang evolves in time, the temperature drops rapidly as the Universe expands and the average velocity of particles decreases.
Finally, one reaches a state where the energy of the Universe is primarily contained in non-relativistic matter (matter sufficiently massive that its average velocity is very much less than the speed of light). This is called a matter dominated universe. The early Universe was radiation dominated, but the present Universe is matter dominated. Let us now give a brief description of the most important events in the big bang.

The Cast of Characters for the Big Bang

The primary cast of characters includes:

1. Photons ("particles" of light)
2. Protons and neutrons
3. Electrons and their antiparticles the positrons
4. Neutrinos and their antiparticles the antineutrinos

Because of the equivalence of mass and energy in the Special Theory of Relativity, in a radiation dominated era the particles and their antiparticles are continuously undergoing reactions in which they annihilate each other, and photons can collide and create particle and antiparticle pairs. One says that under these conditions the radiation and the matter are in thermal equilibrium because they can freely convert back and forth. Let us now follow the approximate sequence of events that took place in the big bang in terms of the time since the expansion begins.

Time ~ 1/100 Second

At this stage the temperature is about 100 billion Kelvin and the density is more than a billion times that of water. The Universe is expanding rapidly and is very hot; it consists of an undifferentiated soup of matter and radiation in thermal equilibrium. This temperature corresponds to an average energy of the particles of about 8.6 MeV (million electron-Volts). The electrons and positrons are in equilibrium with the photons, the neutrinos and antineutrinos are in equilibrium with the photons, antineutrinos are combining with protons to form positrons and neutrons, and neutrinos are combining with neutrons to form electrons and protons. At this stage the number of protons is about equal to the number of neutrons.

Time ~ 1/10 Second

Now the temperature has dropped to several times 10 billion Kelvin and the density is a little over 10 million times that of water as the Universe continues to expand. Because a free neutron is slightly less stable than a free proton, neutrons beta decay to protons plus electrons plus neutrinos with a half-life of approximately 17 minutes. Thus, the initial approximately equal balance between neutrons and protons begins to be tipped in favor of protons. By this time about 62% of the nucleons are protons and 38% are neutrons. The free neutron is unstable, but neutrons in composite nuclei can be stable, so the decay of neutrons will continue until the simplest nucleus (deuterium, the mass-2 isotope of hydrogen) can form. But no composite nuclei can form yet because the temperature implies an average energy for particles in the gas of about 2.6 MeV, and deuterium has a binding energy of only 2.2 MeV and so cannot hold together at these temperatures. This barrier to production of composite nuclei, which allows the free neutrons to be steadily converted to protons, is called the deuterium bottleneck.

Time ~ 1 Second

The temperature has dropped to about 10 billion K as the Universe continues to expand, and the density is now down to about 400,000 times that of water. At this temperature the neutrinos cease to play a role in the continuing evolution, but the deuterium bottleneck still exists so there are no composite nuclei and the neutrons continue to beta decay to protons. At this stage the protons abundance is up to 76% and the neutron abundance has fallen to 24%.

Time ~ 13.8 Seconds

The temperature has now fallen to about 3 billion K. The average energy of the particles in the gas has fallen to about 0.25 MeV. This is too low for photons to produce electron-positron pairs so they fall out of thermal equilibrium and the free electrons begin to annihilate all the positrons to form photons. The deuterium bottleneck still keeps appreciable deuterium from forming and the neutrons continue to decay to protons. At this stage the abundance of neutrons has fallen to about 13% and the abundance of protons has risen to about 87%.

Time ~ 3 Min 45 Sec

Finally the temperature drops sufficiently low (about 1 billion K) that deuterium nuclei can hold together. The deuterium bottleneck is thus broken and a rapid sequence of nuclear reactions combines neutrons and protons to form deuterium, and the resulting deuterium with neutrons and protons to form the mass-4 isotope of helium (alpha particles). Thus, all remaining free neutrons are rapidly "cooked" into helium. Elements beyond helium-4 cannot be formed because of the peculiarity that there are no stable mass-5 or mass-8 isotopes in our Universe and the next steps in the most likely reactions to form heavier elements would form mass-5 or mass-8 isotopes.

Time ~ 35 Minutes

The temperature is now about 300 million K and the Universe consists of protons, the excess electrons that did not annihilate with the positrons, helium-4 (26% abundance by mass), photons, neutrinos, and antineutrinos. There are no atoms yet because the temperature is still too high for the protons and electrons to bind together.

Time ~ 700,000 years

The temperature has fallen to several thousand K, which is sufficiently low that electrons and protons can hold together to begin forming hydrogen atoms. Until this point, matter and radiation have been in thermal equilibrium, but now they decouple. As the free electrons are bound up in atoms the primary cross section leading to the scattering of photons (interaction with the free electrons) is removed and the Universe (which has been very opaque until this point) becomes transparent: light can now travel large distances before being absorbed.

Production of the Light Elements in the Big Bang

One important success of the big bang model has been in describing the abundance of light elements such as hydrogen, helium, and lithium in the Universe. These elements are produced in the big bang, and to some degree in stars. Analysis of the oldest stars, which contain material that is the least altered from that produced originally in the big bang, indicate abundances that are in very good agreement with the predictions of the hot big bang. One particularly sensitive test involves the abundance of deuterium. Because deuterium has a nucleus that is very weakly bound compared with most nuclei, it is very sensitive to the conditions in which it is formed (as we have just seen): if the temperatures are too high, deuterium breaks apart, and it can only be formed when there are free neutrons to combine with protons. Detailed analysis of the deuterium abundance gives very strong support to the hot big bang picture.

The Steady State Model

The big bang model had an early challenger that was called the steady state model. The steady state model did the cosmological principle one better by invoking what has been termed the perfect cosmological principle: Not only is the Universe the same at all places and in all directions when averaged over a large enough volume; it is the same for all time too. Since the Universe was known to be expanding, the steady state model had to postulate continuous creation of matter in the space between the stars and galaxies to maintain the same density over time and thus satisfy the perfect cosmological principle of a universe unchanging in time on large scales. This violates the law of mass-energy conservation, but the rate of mass creation that is required is far too small to be detectable by any conceivable experiment, so it cannot be ruled out experimentally (the rate that is required is to create approximately 1 hydrogen atom per cubic centimeter every 10¹⁵ years).

The Triumph of the Big Bang

For a time, the steady state theory and the big bang theory competed with each other, but eventually observations all but ruled out the steady state theory while providing strong support for the big bang. Probably the two most important observations were

1. Deep space radio telescope observations (which therefore peered far back in time because of the finite speed of light) indicating that the early Universe looked very different from the present Universe. For example, there appear to be more quasars at great distances, implying that there were more quasars in the early Universe than the present one. This contradicted the steady state hypothesis that the Universe was unchanging over time on large scales.
2. The discovery of the cosmic microwave background to be discussed shortly, that appeared to permeate all of space. This was an expected consquence of the big bang model, but was very difficult to explain in any simple way in the steady state theory.

As a consequence of these and other findings, the steady state theory is no longer considered viable by most astronomers.

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Dark Matter

There are many reasons to believe that the universe is full of "dark matter", matter that influences the evolution of the universe gravitationally, but is not seen directly in our present observations.

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FIGURE: Superposed on an optical picture of a group of galaxies is an X-ray image taken by ROSAT. The image shows hot gas (which produces X-rays) highlighted in false red color . The presence of this confined gas indicates that the gravity in groups and clusters of galaxies is larger than that expected from the matter that we can observe in those galaxies.

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The adjacent image exhibits one recent piece of evidence for undetected matter: the hot gas seen in the X-ray spectrum would have dispersed if it were held in place only the by gravity of the mass that is producing light in this image (the so-called "luminous mass"). The nature of this dark matter, and the associated "missing mass problem", is one of the fundamental cosmological issues of modern astrophysics.

Hot Dark Matter and Cold Dark Matter

Discussions of dark matter typically consider two extremes

• Hot Dark Matter
• Cold Dark Matter

Hot dark matter is composed of particles that have zero or near-zero mass (the neutrinos are a prime example). The Special Theory of Relativity requires that massless particles move at the speed of light and that nearly massless particles move at nearly the speed of light. Thus, such very low mass particles must move at very high velocities and thus form (by the kinetic theory of gases) very hot gases. On the other hand, cold dark matter is composed of objects sufficiently massive that they move at sub-relativistic velocities. They thus form much colder gases. The difference between cold dark matter and hot dark matter is significant in the formation of structure, because the high velocities of hot dark matter cause it to wipe out structure on small scales.

Tutorial on Current Status of Dark Matter

The following is a brief tutorial on this issue (Source):

1. If inflation is correct the density of the Universe should be exactly the closure density. Luminous stars and galaxies contribute only about 0.5% of the closure density, so 99% of the Universe is in the form of dark matter. We may speculate on what particles could make up this dark matter.
2. The known neutrinoes have problems as candidates for dark matter because they are relativistic (hot dark matter) and therefore they erase fluctuations on small scales. Thus, relativistic neutrinos could form large structures like superclusters, but would have trouble forming smaller structures like galaxies. These arguments might be at least partially invalidated if one of the types of neutrinos (the tau neutrino is the obvious candidate) is considerably more massive than the electron or muon neutrino.
3. On smaller scales such as galaxies and clusters of galaxies, dynamical estimates of the mass based on rotation curves or velocity dispersions of galaxies indicate that 90% (not 99%) of the total mass is not seen ("sub-luminous"). This implies that the mass density of the Universe is 10% of the closure density. In this case, the sub-luminous mass could be normal (baryonic) and be locked up in stellar remnants (white dwarfs, neutron stars, black holes) or just in very dim stars called "Brown Dwarfs". There is recent evidence for possible observation of one of these very dim Brown Dwarfs.
4. Although inflation demands that the Universe have a density equal to its critical density (and inflation is necessary to solve certain problems of the standard big bang model like the horizon problem) there has never been any observational evidence to support this high of mass density. Most dynamical studies suggest values of 10-20% of closure density. These studies are based on large scale deviations from Hubble expansion velocities (peculiar velocities).
5. Large scale structure (e.g. the distribution of galaxies) is very hard to understand, particularly in light of the relatively smooth microwave background as measured by the COBE satellite. One way to accomodate this is to go to a mixed dark matter model in which you have some hot dark matter (for the large scale) and some cold dark matter to act as a seed for galaxy formation. None of those models, however, fit the data using the critical density. The best models to date suggest mixed dark matter and an overall cosmological mass density of 20-30% of closure. Hence, to retain inflation, with its inescapable prediction that the Universe must be flat, requires re-invoking Einstein's cosmological constant - meaning the universe has vacuum energy (negative pressure) and is currently accelerating. This makes our cosmology complicated but much data is pointing this way.
6. Supernova 1987a neutrino time of flight studies as well as the Solar Neutrino experiment are consistent with the neutrino having a mass, but a very small mass, not one that can cosmologically dominate. We cannot currently test for various supersymmetric particles which would only be created at very high energy (e.g. the early universe) - so there remain many viable potential particles that are consistent with the Standard Model of particle physics, that would remain unnoticed in any accelerator experiments.

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Matter in the Universe

Matter is generally considered to be anything that has mass and volume. The volume is determined by the space in three dimensions that it occupies. The mass is determined by its rest mass (or invariant mass), which is measured by the acceleration a body has when a force is applied. The greater the mass, the slower the acceleration for the same force. Matter is thus a general term for the substance of which all observable physical objects consist

The matter in the universe is created by the big bang, but not in the form that we see today. First, there is very strong evidence that most of the matter in the Universe is in the form of unseen or dark matter - matter that (at least so far) cannot be seen by standard astronomical methods, but whose presence can be inferred because it influences the Universe gravitationally. The nature of this dark matter is one of the most important unsolved problems in science.
Second, the big bang produces mostly the light elements hydrogen and helium (Here is a java applet illustrating big bang synthesis of the elements). The heavier elements must be produced later, by stars. Furthermore,

1. Many of the heavier elements cannot be produced by stars in the stable periods of their lives - they must be produced in violent explosions associated with the death of stars.
2. The heavier elements produced either in the stable portion of stellar evolution, or in violent explosions, can only be distributed through the universe by such explosions.

Thus, the existence of the heavy elements, and the biology built on them, depends crucially on violent processes taking place in stars and galaxies.

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Cosmology

Cosmology is the study of the larger issues: how "big" is the Universe, does it have an "end", what is its large-scale structure, how old is the Universe, how long will it live?

Cosmology is the study of the origin and the development of the Universe. As such, it is concerned with the large scale, both with respect to distance, and with respect to the past and future for the Universe.

The Central Themes of Modern Cosmology

The central tenet of modern cosmology is the idea that the Universe is expanding, and that this implies that at some time in the distant past it was incredibly dense and hot. This "explosion" from a hot, dense initial state is called the big bang (or sometimes the hot big bang, to emphasize the high temperature during its occurrence). Some of the most important problems in cosmology are associated with understanding how galaxies and clusters of galaxies formed, and determining the nature of the mass of the Universe (we can only identify 10 percent of what we know from its gravitational influence must be there!).

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Motion of the Sun

The Sun is in motion, just like any other star.

Motion of the Sun Relative to Local Stars

First, the Sun and the other stars in its vicinity partake of the general rotation of the galaxy (the Milky Way Galaxy rotates once about every 225 million years). This corresponds to an average velocity of about 220 km/s. The space velocities that we measure for other stars then correspond to deviations from this average motion for the stars around the Sun. This happens because the Sun and the stars near it are on somewhat different orbits around the center of the galaxy, so at any one time the Sun is overtaking some stars and being passed by others.

The Solar Apex and Antapex

This motion of the Sun with respect to the local field of stars is in the direction of an imaginary point in the constellation Hercules, near the bright star Vega. This point is called the solar apex, and the Sun is moving toward it (relative to the nearby stars) at a net speed of about 19.7 km/s. The point on the opposite side of the sky from which the Sun appears to be moving away is called the {\em solar antapex}.
Thus, every second we move about 20 km closer to the star Vega. However, there is plenty of time before we get there: Vega is 26.5 light years away! As an exercise, calculate how long it will take the Sun (and therefore the Earth) to travel 26.5 LY at a speed of 20 km/s.

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Limitations of the Human Eye

The human eye is a remarkable biological invention, a shining triumph of the process of evolution. Although the human eye was the detector that started us on mankind's exploration of the Cosmos, it has some shortcomings that ultimately limit that exploration:

1. The eye has limited size and therefore limited light-gathering power.
2. The eye has limited frequency response, since it can only see electromagnetic radiation in the visible wavelengths.
3. The eye distinguishes a new image multiple times a second, so it cannot be used to accumulate light over a long period in order to intensify a faint image.
4. The eye cannot store an image for future reference like a photographic plate can.

Astronomers have developed a variety of instruments and techniques to supplement the human eye and to alleviate these shortcomings. As a result, in modern research astronomy, very few observations are made any more by an astronomer looking directly through an optical telescope.

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Planet found in nearest star system to Earth

This artist’s impression shows the planet orbiting the star Alpha Centauri B, a member of the triple star system that is the closest to Earth. Alpha Centauri B is the most brilliant object in the sky, and the other dazzling object is Alpha Centauri A. Our own Sun is visible to the upper right. The tiny signal of the planet was found with the HARPS spectrograph on the 3.6-meter telescope at ESO’s La Silla Observatory in Chile. // Credit: ESO/L. Calçada/N. Risinger

The observations extended over more than four years using the HARPS instrument and have revealed a tiny signal from a planet orbiting Alpha Centauri B every 3.2 days.

 European astronomers have discovered a planet with about the mass of the Earth orbiting a star in the Alpha Centauri system — the nearest to Earth. It is also the lightest exoplanet ever discovered around a star like the Sun. The planet was detected using the HARPS instrument on the 3.6-meter telescope at the European Southern Observatory’s (ESO) La Silla Observatory in Chile.

Alpha Centauri is one of the brightest stars in the southern sky and is the nearest stellar system to our solar system, only 4.3 light-years away. It is actually a triple star — a system consisting of two stars similar to the Sun orbiting close to each other, designated Alpha Centauri A and B, and a more distant and faint red component known as Proxima Centauri. Since the 19th century, astronomers have speculated about planets orbiting these bodies, the closest possible abodes for life beyond the solar system, but searches of increasing precision had revealed nothing. Until now.

"Our observations extended over more than four years using the HARPS instrument and have revealed a tiny, but real, signal from a planet orbiting Alpha Centauri B every 3.2 days," said Xavier Dumusque from the Geneva Observatory in Switzerland and the University of Porto in Portugal. "It's an extraordinary discovery, and it has pushed our technique to the limit!"

The European team detected the planet by picking up the tiny wobbles in the motion of the star Alpha Centauri B created by the gravitational pull of the orbiting planet. The effect is minute. It causes the star to move back and forth by no more than 20 inches (51 centimeters) per second, about the speed of a baby crawling. This is the highest precision ever achieved using this method.

Alpha Centauri B is very similar to the Sun but slightly smaller and less bright. The newly discovered planet, with a mass of a little more than that of Earth, is orbiting about 3.7 million miles (6 million kilometers) away from the star, much closer than Mercury is to the Sun in the solar system. The orbit of the other bright component of the double star, Alpha Centauri A, keeps it hundreds of times farther away, but it would still be a brilliant object in the planet's skies.

This same team found the first exoplanet around a Sun-like star in 1995, and since then there have been more than 800 confirmed discoveries, but most are much bigger than Earth, and many are as big as Jupiter. The challenge astronomers now face is to detect and characterize a planet of mass comparable to Earth that is orbiting in the habitable zone around another star. The first step has now been taken.

"This is the first planet with a mass similar to Earth ever found around a star like the Sun. Its orbit is very close to its star, and it must be much too hot for life as we know it," said Stephane Udry from the Geneva Observatory, "but it may well be just one planet in a system of several. Our other HARPS results and new findings from Kepler both show clearly that the majority of low-mass planets are found in such systems."

"This result represents a major step towards the detection of a twin Earth in the immediate vicinity of the Sun. We live in exciting times!" said Dumusque.

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