Category Archives: Astronomy

How do you compute the angular distance between two stars from their coordinates?


The locations of stars in the sky are given by their Equatorial coordinates, which are stated as Right Ascension and Declination and given as a pair of numbers (RA, DEC). RA is given in hours, minutes and secionds while Declination is given in degrees.

For math calculations, we want to work in degrees so we convert RA into degrees by multiplying RA x 360/24.0.

Let RA1 and DEC1 be the right ascension and declinations of Star 1 in degrees.

Let RA2 and DEC2 be the right ascension and declination of Star 2 in degrees,

The angular separation A, in degrees, between them is:

Let’s do an example.

Sirius is at RA1=6h 41m and DEC1=-16d 35′ so RA1 = 6.68h x 360/24 = 100.2 degrees and DEC1 = -16.58 degrees.

Betelgeuse is at RA2=5h 50m and DEC2=+7d 23′ so RA2 = 87.5degrees and DEC2 = 7.38 degrees. Then

cos(A) =  -0.285x0.128 + 0.958x0.9917 x cos(100.2 - 87.5)
= -0.0364 + 0.9268
= 0.890

so A = 27.1 degrees.

How do astronomers determine the size and distances of stars?


To get distances, we use a variety of techniques. The most basic one is geometric parallax. By photographing the same star 6 months apart from points 1 and 2 in earth’s orbit, the shift of the star relative to more distant background stars when R = 1 Astronomical Unit amounts to 1 second of arc at 1 parsec ( 3.26 light years), 1/2 arcsecond at 2 parsecs, 1/10 arcsecond at 10 parsecs etc. By the way, at 1 parsec, an arcsecond also subtends 206265 astronomical units.

The Hipparcos astrometric satellite has determined the distance to over 100 thousand stars in this way. Read an ESA Press Release about the mission accomplishments. For example, the distances to the Nearest 10 stars can be found in their Table of 150 closest stars which I reprint below:

Name					Parallax
Alpha Centauri C 772.33
Alpha2 Centauri C 742.12
Alpha1 Centauri C 742.12
Barnard's Star 549.01
Alpha Canis Majoris (Sirius) 379.12
Epsilon Eridani 310.75
61 Cygni A 287.13
Alpha Canis Minoris 285.93
61 Cygni B 285.42
Epsilon Indi 275.76
Tau Ceti 274.17


Note: the Parallax is measured in 1/arcseconds. To calculate the distance in parsecs you have to take 1000.0 and divide it by the parallax number in the last column above. For example, Alpha Centauri C (Proxima) is at a distance of 1000.0/772.33 = 1.295 parsecs which equals 1.295 x 3.26 = 4.22 light years. Alpha Centauri is at 1000/742 = 1.34 parsecs or 4.39 light years. I leave it as a simple calculator exercise for you to convert the parallaxes above into light years!

Stellar diameters can be measured for some nearby giant and supergiant stars by using a technique called stellar interferometry. The Navy Prototype Optical Interferometer has been operating for over a decade at Mount Wilson Observatory, and routinely measures the angular diameters of bright stars to fractions of a milli arcsecond (0.001 arcseconds) accuracy. The table below shows only a few stars that have had their diameters measured. Once their distances are accurately known…from the Hipparcos Survey…their linear diameters in millions of kilometers can easily be found.

The table below shows the sizes in multiples of the solar diameter for some typical stars that have measured angular diameters in column 5 given in arcseconds. The highest resolution of the Hubble Space Telescope is about 0.046 arcseconds. So it is just able to see Betelgeuse as a resolved ‘disk’

Name              Type      dist.    diameter     Size
Alpha Arietis     K2III    65.9 ly   0.00699      14.8
Alpha Cassiopeia  K0III    150.0     0.00569      27.4
Alpha Persei      F5Ib     592       0.00313      59.3
Alpha Leporis     F0Ib    1280       0.00177      72.5
Betelgeuse        M1Ib     425       0.054       734.4
Antares           M1Ib     520       0.041       682.2
Proxima Centauri  dM5      4.2       0.007         1.0
Polaris           F7 Ib    430       0.00328      45.1
 

The size in kilometers = 3 x 10^13 (d /3.26) (D/3600)/57.3 or 44.6 million x d x D where d = the distance in light years and D is the angular diameter in arcseconds. In terms of solar diameters (1,390,000 km) you get Size = 32 d x D solar diameters. The later formula gives you the above entries in the last column. The super giant star Betelgeuse is 734.4 times the diameter of the Sun.

What are some astronomical events that affected human history?


The kinds of things that can get humans really worked up are planetary conjunctions, solar eclipses, aurora, comets, meteor showers and meteor falls. Also, a few supernovae and novae are thrown in too since they light up the sky for days-weeks at a time. Not only have sightings of Halley’s Comet been powerful portends of gloom and doom, but certain planetary conjunctions have come at key times in human history. The table below provides a timeline of the many events that have made some historical impact since the earliest recorded sightings of solar eclipses.

Humans have been terrified by spectacular meteor showers, and in some rare instances, have been injured of killed by being hit by meteorites. There are a number of total solar eclipses that have been seen since ancient times that were mentioned in ancient texts such as the solar eclipse mentioned by Xerxes. The deaths of Herod, Augustus Caesar and Jesus Christ happened during lunar eclipses. When you tally up how many of these astronomical events have been recorded by humans and affected them in one way or another, the list is a very long one.

DateEventImpact
May 3,1374 BCEclipseUgarit Eclipse – oldest documented sighting
June 3,1301 BCEclipseEarly Chinese Eclipse observation
April 16,1177 BCEclipseHomer’s Odyssey
June 15762 BCEclipseAssyrian Eclipse
April 6,647 BCEclipseArchilochus Eclipse
May 28584 BCEclipseHeroditus Eclipse
October 2,479 BCEclipseXerxes Eclipse
Aug 28,412 BCEclipseSiege of Syracuse
April 15,405 BCEclipseFire in the Temple of Athena
Sept 20,330 BCEclipseArbela battle of Alexander the Great
240 BCHalleys Cometsighting by Chinese astrologers
April 17,6 BCConjunctionStar of Bethelehem in Leo/Ares
March 23,4 BCEclipseDeath of Herod
Sept 27,14 ADEclipseDeath of Augustus
33 ADEclipseCrucifixion of Jesus
37 ADAuroraCaesar sends soldiers north to put
60 ADHalleys CometNero has all possible successors executed
March 20, 71 ADEclipsePlutarch’s Eclipse
Nov 24,569 ADEclipseEclipse preceding birth of Mohammad
616 ADMeteoritemeteorite kills 10 solders in a
May 5,840 ADEclipseTreaty of Verdun
902 ADMeteor stormLeonids recorded by Arab astronomers
Dec 22,968 ADEclipseEclipse Constantinople. Leo Diaconus discovers corona.
1006 ADSupernova2 yrs. Brighter than Venus
Dec 28,1047 ADConjunctionM-J-S-Sun less than 3.4deg
1054 ADSupernova1 m= -3.5. Chinese, Japanese. Pueblo
1066 ADHalleys CometBattle of Hastings-Mass terror-Europe. Bayeux Tapestry
April 24,1146 ADConjunctionM-J-S-Sun less than 3.2 deg
1181 ADSupernova6 months. m= -1
Sep 201186 ADConjunctionM-J-S-Sun less than 7 deg
Jan 15,1192 ADAuroraSeen in Flanders
May 14,1230 ADEclipseS. Eclipse Major European eclipse
Jan 3,1285 ADConjunctionM-J-S-Sun less than 9.5 deg.
1341 ADMeteoritemeteorite shower killed people
June 21,1385 ADConjunctionM-J-S-Sun less than 3.8 deg
Nov 9,1425 ADConjunctionM-J-S-Sun less than 8.4 deg
May 22,1453 ADEclipseEclipse The fall of Constantinople
1456 ADHalleys CometBlamed for earthquakes, illness
1490 ADMeteoriteMeteorite Shower kills thousands.
March 1,1504 ADEclipseEclipse Christopher Columbus eclipse in Americas
Sept. 1511 ADMeteoriteMonk killed by meteorite fall
Feb 18,1524 ADConjunctionM-J-S-Sun less than 7 deg
1531 ADHalleys CometPisarro conquest of Incas
October 1572 ADSupernovaTycho’s SN. -4.0. Cassiopeia. lasted 483 days
1577 ADCometAristotlean crystalline spheres
October 5,1591 ADAuroraSeen in Europe
1599 ADCometsees Cortez as fulfillment of prophesy
1604 ADSupernova365 days. m= -2.6
1607 ADHalleys CometObserved by Johannes Kepler
July 9,1622 ADConjunctionM-J-S-Sun less than 7.4 deg
Aug 22,1624 ADConjunctionM-J-S-Sun less than 9 deg
Nov 171630 ADMeteor stormStorm Leonids light up sky for Keplers
1639 ADVenus transitFirst observed by human
1639 ADMeteoriteCounty meteorite kills 10s of people
ca 1650 ADMeteoriteMonk in Milano killed by meteorite. Artery
ca 1658 ADSupernovaCass-A. (3 Cass? seen by Flamsteed before
1680 ADCometGreat Comet.
Feb. 10,1681 ADAuroraSeen in Europe
1682 ADHalleys CometOrbit calculated by Edmund Halley
May 3,1715 ADEclipseEclipse Edmund Halley’s eclipse
March 17,1716 ADAuroraSeen in Europe
1729 ADCometComet of 1729
1759 ADHalleys CometFirst prediction by Edmund Halley.
1744 ADCometand famous comet de Chesaux’s Comet.
June 6,1761 ADVenus TransitT. Major international observing campaign
August 5,1766 ADEclipseEclipse Captain Cook’s eclipse
June 3,1769 ADVenus TransitT Captain Cook expeditions
1799 ADMeteor stormvon Humbolt mentions intense storm
April 26,1803 ADMeteoriteMajor fall on L’Aigle France.
Jan 15,1805 ADEclipseEclipse The Lewis and Clark Expedition eclipse
1811 ADCometComet of 1811
Nov 12,1833 ADMeteor stormStorm Major Leonid shower terrified millions.
1835 ADHalleys CometBlamed for Alamo massacre and NY
Sept 15,1839 ADAuroraGreat Aurora seen in England
1843 ADCometComet of 1843
Nov. 17,1848 ADAuroraGreat Aurora. California Cuba, Europe. Telegraphs.
Aug. 28,1859 ADAuroraGreat Aurora. Cuba, Rome, Europe.
1858 ADCometComet
Sept. 2,1859 ADAuroraAthens. San Salvador. Major white light flare.
Sep 2,1861 ADConjunctionM-J-S-Sun less than 3.6 deg.
1861 ADCometComet of 1861
Feb 4,1872 ADAuroraGreat Aurora Mexico, Athens, India
Dec. 91874 ADVenus TransitT Venus Transit. Major international expeditions
Jan 22,1879 ADEclipseEclipse Zulu War Eclipse
1881 ADCometComet of 1881
Nov 18,1882 ADAuroraGreat Aurora, Cuba, Mexico, US. Telegraph outages..
1882 ADCometComet. Photographed for first time.
Dec 6,1882 ADVenus TransitT Photos and major public interest.
March 30,1886 ADAuroraGreat Aurora. England, China, Japan, India
Feb. 13,1892 ADAuroraGreat Aurora. Iowa, New York
Mar. 30,1894 ADAuroraEngland
1897 ADMeteoritekills horse. New Martinsville WV.
Sept. 9,1898 ADAuroraGreat Aurora. Omaha, Tenn. New York
1899 ADMeteor stormNo Leonids. Public disappointed in astronomers
Nov. 11903 ADAuroraGreat Aurora.Europe,N. America. France telegraphs
1907 ADMeteoriteMeteorite kills Wan family
June 30,1908 ADMeteoriteTunguska Explosion
Sept. 25,1909 ADAuroraGreat Aurora. Singapore.
1910 ADHalleys CometComet Hysteria. Suicides. Mayhem. Deadly gas.
January 1910 ADCometGreat Daylight Comet of 1910
April 17,1912 ADEclipseEclipse The ‘Titanic’ eclipse
April 25,1915 ADMeteoriteChina. Meteorite rips womans arm off.
July 4,1917 ADEclipseEclipse Lawrence of Arabia’s eclipse
August 7,1917 ADAuroraGreat Aurora. New York. Illinois
May 29,1919 ADEclipseEclipse Einstein’s Eclipse
March 22,1920 ADAuroraGreat Aurora Boston, Washington, Norway
May 14,1921 ADAuroraGreat Aurora. England. Samoa, Jamaica.
Jan 24,1925 ADEclipseEclipse NY City’s Winter Morning eclipse
Jan. 26,1926 ADAuroraGreat Aurora. US, Scandinavia. London blackout
Dec 8,1929 ADMeteoriteMeteorite kills a person in Yugoslavia
August 31,1932 ADEclipseEclipse Great Maine eclipse
Jan 25,1938 ADAuroraGreat Aurora. US. North Africa. Fatima Aurora
March 24,1940 ADAuroraGreat Aurora. N. Dakota. Blackout in N.East
Sept. 18,1941 ADAuroraGreat Aurora. TV/Radio disruption in N. America
July 26,1946 ADAuroraGreat Aurora. Boston, Tenn.
1948 ADMeteorFireball. 2300 pound meteor recovered
Nov. 6,1951 ADMeteoriteBremerton, Wash. Man injured by meteorite
1954 ADMeteoriteinjures woman. Sylacauga, Alabama.
Feb. 24,1956 ADAuroraIceland, Alaska. Intense cosmic ray blast.
Sept 13,1957 ADAuroraGreat Aurora. Mexico
Feb 10,1958 ADAuroraGreat Aurora. N. America, USSR. SW Blackout
October 1965 ADCometIkeya-Seki
Nov 17,1966 ADMeteor stormStorm Major Leonid shower over Central U,S.
Feb 8,1969 ADMeteoriteAllende fall. Famous and spectacular
March 23,1969 ADAuroraNorth America
Sept 28,1969 ADMeteoriteMurchison fall. Spectacular and famous.
March 1970 ADCometComet Bennett – very bright
August 4,1972 ADAuroraGreat Aurora. N.America, Canada, Scandinavia.
August 10,1972 ADFireballDaytime over Grand Tetons – 1000 tons.
January, 1974 ADCometKohoutek – a big but famous fizzle
March, 1976 ADCometComet West
March 5,1981 ADAuroraGreat Aurora. Colorado.
February 1987 ADSupernovaLarge Magellanic Clouds. Optically discovered.
March 13,1989 ADAuroraGreat Aurora. Canada, US. Quebec Power Blackout
October 9,1992 ADMeteoritePeekskill meteorite hits car.
July 16,1994 ADCometShoemaker-Levy collides with Jupiter
March 26,1996 ADCometHyakutake – Very bright
Jan 11,1997 ADSolar stormStorm Telstar 401 satellite damaged
April, 1997 ADCometHale-Bopp. Much celebrated
May 5,2000 ADConjunctionM-J-S-Sun less than 18 degrees
Oct 14,2001 ADMeteoriteCanadian Fireball.
July 15,2000 ADSolar stormStorm Bastille Day Storm
April 2,2001 ADSolar stormStorm Major X20 Solar Flare
March, 2003 ADMeteoriteSeveral Illinois towns hit by debris. Damage
June 8,2004 ADVenus transitFirst observation in 122 years.
June 6,2012 ADVenus transitSecond observation in 122 years.
February 15,2013 ADMeteoriteExplodes over Chelyabinsk and injurs 1,500 people
June 13, 2014 ADMoonFull moon on Friday ther 13th
August 21, 2017 ADEclipseFirst total solar eclipse over Continental USA in over 30 years
March 31, 2018 ADMoonTwo Blue Moons in same year January 31 and March 31
December 21, 2020 ADConjunctionSaturn and Jupiter 7 arcminues apart
April 13, 2029 ADAsteroidApophis comes within 19,000 miles of Earth
__________________________________________________________________________________________________
Note: Abbreviations - Venus T. (Venus Transit of Sun). S. Exlipse (Total Solar Eclipse),
S. Storm (Solar Storm), Halley's C. (Halley's Comet), L. Eclipse (Lunar Eclipse), 
M. Storm (Intense meteor shower -  Meteor Storm)

Can gravity affect the speed of light?


Gravity can certainly warp and distort the ‘straight-line’ path of a light ray. This Hubble image is of the Einstein Ring LRG 3-757 in which the central massive galaxy has warped the image of a background galaxy into a ring of light. (Credit: ESA/Hubble & NASA)

The speed of light is something measured with a local apparatus in an inertial reference frame, using the same meter stick and clock. A gravitational field has zillions of such ‘locally inertial reference frames’ which are described by freely-falling observers for short intervals of time and small regions of space. In all of these tiny domains, an observer would measure the same velocity for light as guaranteed by special relativity. To ask what the speed of light is over a domain where gravitational forces make a reference frame ‘non-inertial’ and not moving at a constant speed, is an ill-defined question in special relativity. As soon as you try to measure the speed of such an impulse, you would be using a clock and a meter stick which would not be the ‘proper time and space’ intervals for the entire region where the gravitational field exists.

Gravity can affect the speed of light. If you measure the speed over a large enough region that special relativity and its requirement of a flat spacetime is not satisfied. In the presence of curved spacetime, conventional local measurement techniques do not work and so you cannot define the speed of light in exactly the same way that you do under laboratory conditions in ‘flat’ spacetime. In fact, in curved spacetime even the concept of conservation of energy is not easily defined because the curvature of space itself changes the definition. Conservation of energy only works in flat spacetime.

What are the ’10 dimensions’ that physicists are always talking about?


This stunning simulation of Calabi-Yau spaces at each point in 3-d space was created by  Jeff Bryant and based on concepts from A.J. Hanson, “A Construction for Computer Visualization of Certain Complex Curves,” in “Computers and Mathematics” column, ed. Keith Devlin, of Notices of the American Mathematical Society, 41, No. 9, pp. 1156–1163 (American Math. Soc., Providence, November/December, 1994). See his website for details.

We know that we need at least 4 to keep track of things: The three dimensions of space that give us freedom to move Up-Down, Left-right, and forward-backward, plus the dimension of time. These dimensions of spacetime form the yellow gridwork in the image above. At each intersections you have a new location in space and time, and mathematically there are a infinite number of these coordinate points. But the real world may be different then the mathematical ideal. There may not be an infinite number of points between 0 and 1, but only a finite number.

We know that you can sub-divide space all the way down to the quantum realm and to distances and times of 10^-20 cm and 10^-30 seconds and spacetime still looks perfectly smooth to the physics we observe there, but what if we go down even further? Since the 1940s, a simple calculation using the three fundamental constants h, c and G has turned up a smallest quantum distance of 10^-33 cm and 10^-43 seconds called the Planck Scale. In our figure above, the spacings in the yellow grid are at this scale of intervals, and that is the smallest possible separation for physical processes in space and time..it is believed.

Since the 1970s, work on the unification of forces has uncovered a number of ideas that could work, but nearly all require that we add some additional dimensions to the four we know. All of these extra dimensions are believed to appear at the Planck scale, so they are accessible to elementary particles but not to humans.In string theory, these added dimensions are rolled up into identical but complex mini-geometries like the ones shown above.

No one has the faintest idea how to go about proving that other dimensions really exist in the microcosm. The energies are so big that we cannot figure out how to build the necessary accelerators and instruments. We know that Mother Nature is rather frugal, so I would be very surprised if more than 4 dimensions existed.There have been many proposals since the 1920s to increase the number of dimensions to spacetime beyond the standard four that relativity uses. In all cases, these extra dimensions are vastly smaller than an atom and are not accessable to humans…fortunately!

Current string theory proposes 6 additional dimensions while M-theory allows for a seventh. These additional dimensions are sometimes called ‘internal degrees of freedom’ and are related to the number of fundamental symmetries present in the physical world at the quantum scale. The equations that physicists work with require these additional dimensions so that new symmetries can be defined that allow physicists to understand physical relationships between the various particle families.

They think these are actual, real dimensions to the physical world, only that they are now ‘compact’ and have finite sizes unlike our 4 dimensions of space and time which seem almost to be infinite in size. The figure above shows what these compact additional dimensions look like, mathematically. Each point in 4 dimensional space-time has another 6 dimensions attached to it which ‘particles and forces’ can use as extra degrees of freedom to define themselves and how they will interact with each other. These spaces are called Calabi-Yau manifolds and it is their 6-dimensional geometry that determines the exact properties of fundamental particles.

Do not confuse them with ‘hyperspace’ because the particles do not actually ‘move’ along these other dimensions. They are not ‘spatial’ dimensions, but are as unlike space and time as time is unlike space!

What facts disprove the Big Bang theory?

The current, seemingly comprehensive theory of the origin and evolution of our universe is called inflationary, big bang cosmology. This theory explains how our universe emerged from a singularity of high temperature and density and expanded and cooled. As it did so, space dilated at a faster-than-light pace and cooled so that the familiar elementary particles and forces could produce the cosmic background radiation and a variety of complex particles as the universe expanded. By about three minutes after the Big Bang, the ratio of hydrogen to helium had been cosmologically established, and so had the amount of cosmic background photons and neutrinos. In addition, during the rapid ‘inflation’ period, irregularities in the cosmic density of matter were established as well as a background of gravitational radiation.

The spectacular results of the WMAP satellite , along with the results from COBE and a number of other high-precision studies of the cosmic background radiation have now established that the universe is 13.7 billion years old, and that its space geometry is exactly ‘flat’. Also, according to the most recent WMAP ‘pie graph’ above, the amount of the gravitating matter in ordinary stars and gas is only 4.6%. The rest of the gravitating ‘mass’ of the observable universe is in the form of Dark Matter (24%), with an additional contribution of Dark Energy (71.4%). It is this Dark Energy that is causing our universe to expand at an accelerated pace, which has been observationally detected using distant supernovae.

There have been over the years several potential rivals to Big Bang cosmology, but with the exception of Steady State theory, none have attracted more than a handful of interested supporters. The reason is that they failed to predict, or offer explanations for, some basic observations that are widely agreed upon to be key tests of any cosmological theory, even by the rivals to Big Bang theory!

DeSitter Cosmology ca 1917 – The universe is presumed to be entirely empty of matter, but expands exponentially in time because of the presence of a non-zero cosmological constant. This refutes nearly every observational fact now available, including the actual rate of expansion which follows a linear, Hubble law, not an exponential expansion law with time. Also, the density of matter in the universe is not zero because we are here, and so are a lot of other stars and galaxies!

Einstein Static Cosmology ca 1917-The universe does not expand, and is static in time. The cosmological constant is precisely tuned to balance the attractive tendency of matter. Like DeSitter cosmology, it also fails to agree with modern observations, because the universe is expanding linearly with time. It is also unstable to the slightest perturbation in the value of this constant.

Lemaitre Cosmology ca 1924 – The universe started with a ‘big bang’ with no cosmological constant. The initial state was a giant radioactive atom containing all the matter in the universe near absolute zero. This theory agrees with the observed expansion, but fails to explain the existence of the cosmic background radiation and the universal abundances of hydrogen, helium and deuterium because it requires the decay of a single massive ‘super atom’ at the instant of the Big Bang.

Steady State Cosmology ca 1950 – Developed by Fred Hoyle and Thomas Gold, it proposes that the universe has been expanding for eternity and that new galaxies are created, atom by atom, in intergalactic space ‘out of empty space’. This theory had its heyday in the 1950’s and 1960’s, but was never able to explain convincingly where the cosmic background radiation came from, why it is so isotropic, and why its temperature is fixed at 2.7 K. It also provided no clues as to why there ought to be a universal abundance ratio for hydrogen, helium and deuterium.

Cold Big Bang Cosmology ca 1965 – Developed by David Layzer at Harvard, it proposes that the Big Bang occurred, but that the initial state was at absolute zero and consisted of a pure solid of hydrogen. This fragmented into galaxy-sized clouds as the universe expanded. It provided no explanation for where the cosmic background field came from and why it is isotropic and at a temperature of 2.7 K.

Hagedorn Cosmology ca 1968 – Physicist Robert Hagedorn proposed that all of the details of big bang theory are probably true, except that the early history of the universe had a limiting temperature of about 1 trillion degrees because the structure of matter has an infinite ladder of ‘fundamental particles’ out of which electrons, protons and neutrons are constructed. This has been refuted with the discovery that quarks exist which place any limiting temperature for the early history of the universe at temperatures well above 1000 trillion degrees.

Brans-Dicke Cosmology ca 1955 – Einstein’s equation for gravity in general relativity is modified to include a ‘scalar’ field. This field causes the value of the constant of gravity to change slowly over billions of years. This also leads to a modification of the early history of the universe. Experimental searches for a change in the constant of gravity show that it has not changed to within experimental error during the last 2 – 3 billion years. It would cause the evolution of the Earth-Moon system to be significantly altered, and the evolution of the Sun to be severly modified. Neither of these effects have been observed.

Old Inflationary, Big Bang Cosmology ca 1980 – Developed as a ‘toy’ model by Alan Guth in 1980. The Inflationary era which ended 10^-34 seconds after the Big Bang caused the nucleation of innumerable ‘bubbles’ of true vacuum which merged together to form a patina of matter and radiation in a very lumpy configuration. The cosmic background radiation, however, shows that the universe is very smooth to 1 part in at least 10,000 since about 300,000 years after the Big Bang. There is no evidence for such a turbulent and lumpy transition era.

Oscillatory Big Bang Cosmology ca 1930 – This a a possible modification to Big Bang cosmology that differs only in that the current expansion will be replaced by a collapse phase and then an expansion phase etc etc. There is no evidence that there was ever a prior expansion-collapse phase. The universe also does not seem to have enough matter to make it a ‘closed’ universe destined to recollapse in the future; an important requirement for any future oscillation cycle.

Big Bang Cosmology with added Neutrino Families ca 1970 – Big Bang cosmology is largely correct, except that to solve the ‘missing’ or ‘dark’ matter problem, new families of neutrinos have to be added to the universe. This would change the cosmological abundance ratios of helium and deuterium relative to hydrogen so that the current observed values no longer are possible. There is also no experimental evidence that more than 3 types of neutrinos exist; and these are already consistent with the measured cosmological abundances.

Chronometric Cosmology ca 1970 – Developed by I. Segal at MIT, it proposes that space-time has a different mathematical structure than the one that forms the basis for Big Bang cosmology. So far as we can tell, the major disagreement is in the rate of the expansion of the universe which comes out as a quadratic law between distance and expansion speed, rather than the linear Hubble Law. This proposal seems to be inconsistent with what has been observed for distant galaxies during the last 3-4 decades. There may be other disagreements with Big Bang cosmology, but Chronometric cosmology has not been explored deep enough to make testable predictions in these other areas.

Alfven Cosmology ca 1960 – Developed by physicist Hans Alfven, it proposes that the universe contains equal parts of matter and anti-matter. No explanation is made for many of the other observational facts in cosmology. If there were equal parts of matter and anti-matter, there ought to be regions in the universe where these were in contact to produce X-rays or gamma rays due to the annihilation process. No such large-scale background has ever been detected that can be attributed to proton or electron annihilation.

Plasma Cosmology ca 1970 – The matter in the universe, on the largest scales, is not neutral, but has a very weak net charge which is virtually undetectable. This causes electromagnetic forces to dominate over gravitational forces in the universe so that all of the phenomena we observe are not the products of gravitation alone. This is an intriguing theory, but other then denying their importance, it cannot easily explain the origin of the cosmic background radiation, its isotropy and temperature, and the abundances of helium and deuterium.

The basic observations that are agreed to me cosmological tests for any theory are:

1…. The universe is expanding. – This is a large-scale observation which spans the entire observable universe so it must be ‘cosmological’

2…. There exists a cosmic background radiation field detectable at microwave frequencies. – Why doesn’t it occur at other frequencies and only seen in the microwave region, covering every direction of the sky?

3…. The cosmic microwave background field is measurably isotropic to better than a few parts in 100,000 after compensation is made for the relativistic Doppler effect caused by Earth/Sun/Milky Way motion. – This is a large-scale property of this phenomenon that has nothning to do with the Milky Way or other galaxies so it must be a cosmological feature.

4…. The cosmic microwave background radiation field is precisely that of a black body. – Many other kinds of radiation are known, but NONE have exactly a black body spectrum. Only the cosmic background radiation is a perfect black body to the limits of our ability to measure its spectrum.

5…. The cosmic microwave background radiation field has a temperature of 2.7 K. – Why 2.7 K? Why not 5.019723 K. Only Big Bang cosmology predicts a relic radiation at a temperature near 3 degrees and not some other value.

6…. There does exist a universal abundance ratio of helium to hydrogen consistent with the current expansion rate and cosmic background temperature. – Whether we look at the compsition of stars, planets or even gas clouds in distant galaxies, we always seem to come upon a ‘universal’ constant ratio of helium to hydrogen and deuterium to hydrogen. There must be an explanation for this that has nothing to do with just our solar system or Milky Way.

7…. The cosmological abundance of deuterium relative to hydrogen and helium is consistent with the levels expected given the current expansion rate and density. – If the universe expanded faster, then there would be less time for heavier elements such as helium and deuterium to form.

8…. There are only three families of neutrinos. – Although we have not confirmed this to be true in the vicinity of distant galaxies, we do see the same kinds of elements and physics occurring out there, especially supernovae whose physics depend very sensitively upon the numbers of distinct types of neutrinos, and the constancy of the underlying ‘weak interaction’ physics.

9…. The night sky is not as bright as the surface of the Sun. – A simple but profound observation which can only be resolved by the correct distribution of stars in the universe, their ages, and the expansion of the universe.

10… The cosmic background radiation field is slightly lumpy at a level of one part in 100,000 to 1,000,000. – Why is this? And why by this amount?

11… There are no objects that have ages indisputably greater than the expansion age of the universe. – Our universe nearby does not seem to have very old stars older than 20 billion years even though their properties should be easily recognizable and a simple extension of the physics and evolution of the oldest stars we do see.

12… There are about 10,000,000,000 photons in the cosmic background radiation field for every proton and neutron of matter. – This is an important ‘thermodynamic’ number which tells us how the universe has evolved up to the present time. Why is its entropy so huge?

13… The degree of galaxy clustering observed is consistent with an expanding universe with a finite age less than 20 billion years. – A direct observation which again tells us that gravity has not had a long time to act to build up large complex structures in today’s universe.

14… There are no elements heavier than lithium which have a universal abundance ratio. – What process created these heavier elements?

15… The universe was once opaque to its own radiation. – This must follow from the black body shape of the cosmic background radiation.

16… The universe is now dominated exclusively by matter and not a mixture of matter and anti-matter. – Only a few contenders to Big Bang cosmology make any attempt at explaining this direct observation.

So there you have it. This is not a game of billiards where the cue ball (data) is carefully lined up so that Big Bang theory comes out looking inevitable. Any of these other theories have been repeatedly invited to take their best shot too, and the results are always the same. The proponents have to intervene to even get their theories to pony up a simple prediction for any of these cosmological data.

The biggest prediction of Big Bang cosmology lies in its very foundations. It is based on the inerrancy of general relativity and how this theory accounts for gravity under extreme conditions. Its basic predictions have been tested many times, and new exotic phenomena such as the Lenze-Thirring effect and gravity waves have also been predicted and confirmed by the theory. It seems to be a flawless explanation for how grfavity workd, but if it is accurate, then we need lots of Dark Matter and Dark Energy in the universe in addition to the 5% of stars and gas that we can see. That is the big problem.

Dark matter is found not only on the cosmic scale but in regions as small as galaxies. In fact it was discovered in galaxies long before WMAP made its first studies. Our own Milky Way seems to have six times more gravitating stuff orbiting its center than in all the luminous matter and gas clouds we can detect. In fact, any large systems of matter we have studied have this Dark MAtter problem. Some physicists have interpreted this as an actual breakdown in General Relativity itself, but their proponents cannot find an extension or replacement for general relativity that makes Dark Matter go away. Meanwhile, physicists have not detected any of the particle candidates for Dark matter at the Large Hadron Collider or other labs around the world.

So Dark Matter can be added to Big Bang cosmology, but we don’t yet know what kind of physical material it is, or whether there might be something subtly wrong with General Relativity itself.

Where in the universe did the Big Bang happen?

The Big Bang did not happen inside the 3-d space of our universe, at least that’s what our best understanding of physics seems to be telling us during the last 100 years! That means it did not happen ‘over there’ a billion light years beyond Antares.

The only guide we have for answering this question is Big Bang cosmology and Einstein’s general theory of relativity. These make very specific predictions for what happened to space and time during the Big Bang.

The figure above (Credit: Martin Kornmesser, Luis Calcada, NASA, ESA/Hubble) shows the expansion of the universe predicted by general relativity. Note that the latitude and longitude positions of the ‘star’ galaxies remains the same but the distance between them is dilating as the radius of the sphere increases. This is a representation of how our universe is expanding. From this geometric analogy, if the surface of the sphere represented the 3-d volume of our universe at a specific time since the big bang, you see that the volume of space is increasing but space isnt being added in from some where else! This is a sphere in 4-dimensions with a 3-d surface, in geometric analog to a 3-d basket ball with a 2-d surface. Also, as you shrink the sphere’s radius, the volume of 3-d space decreases steadily until it approaches the condition where the radius is zero. You can do this with a mathematical ‘balloon’ but not a real one. At zero radius we also have the condition where the 3-d volume of space also vanishes.

Now suppose that this spherical surface was filled with atoms. As you shrink the volume of space, the density of this matter increases steadily. When you get close to the time where the radius is zero, the average density of matter in the 3-d space of this sphere has grown enormously. When the radius becomes zero, the density becomes infinite and we have what physicists call a singularity.

So, the best, non-mathematical description that any cosmologist can create for describing the Big Bang is that it occurred in every cubic centimeter of space in the universe with no unique starting point. In fact, it was an event which our mathematics indicate, actually brought space and time into existence. It did not occur IN space at a particular location, because it created space ( and time itself) as it went along. There may have existed some state ‘prior’ to the Big Bang, but it is a state not described by its location in time or space. This state preceded the existence of our time and space.

A Gallery of Geomagnetic Storms with DIY Equipment

It has been over a year since I published my book on how to build DIY magnetometers that can detect geomagnetic storms. The $8.00 B/W book ‘Exploring Space Weather with DIY Magnetometers‘, is available at Amazon by clicking [HERE]. It contains 146 pages with 116 illustrations and figures that describe six different magnetometers that you can build step-by-step for under $50.00.

Over the last year I have posted at my Astronomy Cafe blog, and at various LinkedIn groups, the magnetograms from my most sensitive magnetometers to show how well they capture the rapid changes of Earth’s magnetic field during a geomagnetic storm. Since I started posting these DIY magnetograms on Linkedin, they have received over 13,500 views so there seem to be a lot of teachers, amateur astronomers and space weather enthusiasts interested in my DIY technology.

On the NOAA Scale, these storms are stronger than G2 and are currently happening every month or so during the sunspot-maximum period. This blog is my Gallery of the storms I have detected so far. I also show the data for each storm event observed from the Fredericksburg Magnetic Observatory (FRD) located about 200 miles south of my suburban Maryland location. This will give you a sense of just how accurate my designs are compared to the far more expensive, professional-grade systems.

By the way, the July 14, 2023 magnetogram ‘spots’ shows what can be accomplished by a simple $5.00 soda bottle magnetometer if you follow a design with a laser pointer and a 7-meter projection distance as described in my book.

Ok…so here are the magnetograms in reverse chronological order starting from the most recent storms and working down the list to the earlier ones towards the end of 2023. I am only presenting the magnetograms and not a lot of supporting information about the circumstances of the storms themselves. For this information, visit the Spaceweather.com website and in the upper right corner of the webpage in the Archive area enter the date of the storm and you will be able to see a lot of info and even amateur photos of the resulting aurora themselves.

Blog 1: DIY Magnetometers for Studying Space Weather

Blog 2: The Great Storm of May 10, 2024.

Blog 3: The Minor Storm of May 13, 2024.

October 10-12, 2024, Major Kp=8-9, Great Aurora. FRD magnetic observatory plot (red) versus the RM3100 (black). Single-digit Kp index numbers on top row (from 2 to 9). The features that look like sudden ‘glitches’ at Kp=9, 8 and 7 seem to be very real and rapid changes in the D-component (angular displacement). 1000 units on the vertical axis corresponds to 200 arcseconds or 3.3-arcminutes variation.

August 12, 2024. Major Kp=8 storm. Green arrows are the Sq current variations. FRD (red) and RM3100 (black).

August 2, 2024 Kp=7 storm event. FRD(black) and RM3100 (blue).

June 23, 2024, Kp=8. Sq minima (arrows). Storm event (blue bar).

May 12, 2024, Kp=6 storm. FRD(red), RM3100 (black), Photo (blue), Hall (green).

May 10, 2024 Kp=8-9 major geomagnetic storm.

May 5, 2024 storm Kp=4-5. FRD(red), RM3100 (black)

March 23, 2024. Diurnal Sq dips (arrows) and a strong geomagnetic storm (hour 40). FRD data (red) and RM3100 data (black).

November 27, 2023. Minor Kp=6 storm at running UT of 83-86 . FRD data (yellow), RM3100 (grey), photoelectric magnetometer (orange), Hall sensor (blue)

November 5, 2023. A significant Kp=7 geomagnetic storm superposed on a few wobbles due to Sq current effects.

October 30, 2023. Three days of Sq variations and no geomagnetic storms. FRD data (red), RM3100 magnetometer (black), photoelectric magnetometer (blue), Hall effect magnetometer (orange).

July 14, 2023. Kp=4 geomagnetic storm (blue bar) with three cycles (yellow) of the diurnal Sq current. Red line = FRD data. Spots = soda bottle magnetometer.

The Minor Storm of May 13, 2024

We had a minor geomagnetic storm on Monday just after the major storm on Saturday that everyone saw. This minor storm launched a CME caused by an X-5.8 solar flare on Friday, but despite early estimates it might rival the major storm, it was a glancing blow to Earth’s magnetic field and caused no aurora over much of the Lower-48 States. Many had hoped they would get to see an aurora in Maryland and other mid-latitude locations but the storm was too week to be seen in most states that had enjoyed the Great Storm of May 10-11.

Nevertheless, my DIY magnetometers did show some life for this Kp=6 event as shown below. This time I had three different magnetometers operating. The top numbers are the 3-hour Kp indices. The red trace is from the Fredricksberg Magnetic Observatory. The black trace is from the RM3100-Arduino system. The blue trace is from the Differential Hall Sensoe system. The green trace os from the Differential Photocell Magnetometer. The two dips marked with ‘Sq’ are the diurnal Sq variations, which were recorded by all magnetometers.

All three designs are described in detail in my book Exploring Space Weather with DIY Magnetometers,

The Great Storm of May 10, 2024

We just passed through the biggest ‘solar storm’ in the last 20 years caused by the massive naked-eye sunspot group called AR-3664. Its size was 15 times the diameter of Earth and rivaled the size of the famous Carrington sunspot of September, 1859. Since it first appeared on May 2, it remained inactive until May 9 when it released an X2.2-class solar flare at 10:10 UT.

This enormous and violent release of energy stimulated the launch of six coronal mass ejections of which three merged to become an intense ‘cannibal CME’ that arrived near Earth on May 10 at 16:45 UT. Its south-directed magnetic field was perfect for imparting the maximum amount of energy to our planet’s magnetosphere. For a transit time of about 24-hours, it was traveling at a speed of about 1,700 km/s when it arrived. It sparked a G5-level extreme geomagnetic disturbance with a Kp index of 9 between May 10, 21:00 UT and May 11, 03:00 UT.

On May 9th at 06:54 UT AR-3664 produced an X-3.9 flare. This was followed on May 11 with a fourth major X-5.8 flare at 1:39 UT, which caused an immediate shortwave radio blackout across the entire Pacific Ocean that lasted for several hours. It is expected that the May 11 flare sparked anoher CME that may arrive near Earth on Monday evening May 13.

The last G5 geomagnetic storm that we experienced was way back in October 28 to November 5, 2003. These Halloween Storms caused power outages in Sweden and damaged transformers in South Africa. Despite many recent cautionary comments in the news media about cellphone and satellite outages and power grid problems, as yet none of these have been identified but perhaps in the next few weeks these technological impacts may start to be mentioned as anecdotes begin to surface.  

Unfortunately, many areas on the East Coast were covered by clouds during this three-day period and missed the opportunity to see these major aurorae. However, my DIY magnetometer (see my earlier blog on how to build your own $50 magnetometer (located in Kensington, Maryland (latitude 39o N) was able to keep up with the invisible changes going on, and produced a very respectable record of this entire storm period. As a scientist, I am often working with things I cannot directly see with my eyes, so the fact that I had my trusty magnetometer to reveal these invisible changes around me was pretty cool!

This graph shows a side-by-side comparison of the data recorded by my RM3100 magnetometer (black) and the magnetometer at the Fredericksberg Magnetic Observatory (red). I have shifted and rescaled the plots so you can more easily see how similar they are. This is very satisfying because it shows that even a simple home-made magnetometer can perform very well in keeping up with the minute changes in the geomagnetic field. This plot shows the variation in the so-called D component, which is the local magnetic declination angle. Mathematically is is defined by D = arctan(Bx/By). It’s the angle relative to geographic North that your local compass points.

Below is a slightly different graph of the RM3100 data. As you can see in the first part of the above plot between 36 and 63 UT hours, the smooth change is caused by the diurnal Sq current effect that is correlated with the solar elevation angle. During this storm period, it is assumed to have behaved smoothly during the actual storm, so in the graph below I have subtracted it from the magnetometer data. The result is that I have now isolated the changes due to the storm itself. The top row of numbers are the 3-hour Kp index averages from NOAA. The marked times are for EDT in Maryland. Universal Time is 4 hours ahead of EDT.

This was, indeed, a very powerful storm that lasted about 42 hours. This places it among a handful of exceptional geomagnetic storms that includes the great Carrington Storm of August 28 to Septemer 5, 1859.

Why is this important? Well, in the grand scheme of things it may not matter much, but as an astronomer it is still a lot of fun to have access to the invisible universe from the comfort of my suburban home. I will let geophysicists have all the fun deciphering all the bumps and wiggles and what they tell us about our magnetic field and solar storms!

Meanwhile, my gear is primed and ready to go to detect this Monday’s next storm. Some predict that it may be even bigger then the one we just experienced. It’s interesting how the Carrington Storm was actually two major storms separated by a few days, with the CME from the first storm also canibalizing several other CMEs that were also enroute.