I received it via an email with the following text:
This is the sunset at the North Pole with the moon at its closest point,
a scene you will probably never get to see in person.
And, you also see the sun below the moon, an amazing photo and not one easily duplicated.
You may want to pass it on to others so they can enjoy it.
The Chinese have a saying that goes something like this:
'When someone shares with you something of value,
you have an obligation to share it with others!'
I just did.. Your turn
Before reading my comments below the photograph, think about your reaction to the graphic.
When I saw it I thought that it was a beautiful image but was immediately aware that it was not a photograph.
The give away is that the crescent of the moon is very much larger than the sun. This is physically impossible as the sun and the moon appear the same size from the vantage point of the Earth. Solar eclipses show this similarity in apparent size clearly.
In reality this beautiful piece of art was produced by Inga Nielsen at the Gate to Nowhere site. (Unfortunately for mono-lingual people like me the site is in German.) The name of the work is Hideaway.
Hideaway can be found here on Neilsen's site. Note that is is found in a directory called Terragen. Terragen is software which "is a powerful solution for rendering and animating realistic natural environments". The software can be downloaded from this site.
In 1990 Voyager 1 took the original Pale Blue Dot photograph. See details at this post.
Here is Cassini's version of the Pale Blue Dot. If you look carefully the dot can be seen above the centre of the photo, just outside Saturn's main rings.
That dot is Earth.
Here is a link to a larger and clearer version of the photograph.
The explanation for Saturn's unusual colouring in the photograph is that the photo was created from 165 photos taken by Cassini when it was in the shadow of Saturn (ie Saturn was blocking out the glare of the sun).
With giant Saturn hanging in the blackness and sheltering Cassini from the sun's blinding glare, the spacecraft viewed the rings as never before, revealing previously unknown faint rings and even glimpsing its home world.
This marvelous panoramic view was created by combining a total of 165 images taken by the Cassini wide-angle camera over nearly three hours on Sept. 15, 2006. The full mosaic consists of three rows of nine wide-angle camera footprints; only a portion of the full mosaic is shown here. Color in the view was created by digitally compositing ultraviolet, infrared and clear filter images and was then adjusted to resemble natural color.
Saturn shelters the sun, creating a view that illuminates planet and its ringsThe mosaic images were acquired as the spacecraft drifted in the darkness of Saturn's shadow for about 12 hours, allowing a multitude of unique observations of the microscopic particles that compose Saturn's faint rings.
Voyager 1 was launched 33 years ago on September 5, 1977. Voyager 1 flew past Jupiter and Saturn producing many photographs and observations. Some or the photographs can be seen at this link. (Voyager 2 used the alignment of the planets to also visit Uranus and Neptune.)
Voyager 1's tasks were not complete after its groundbreaking observations at Jupiter and Saturn. When it was beyond the Saturn system, Voyager 1 was turned around and took pictures of all of the planets, including the iconic Pale Blue Dot photo of Earth - for details see this post.
Voyager 1 is still making important contributions to our understanding of the Solar System, as it maps the details of its large scale structure. The graphic below shows the major elements of the Sun's System. For details on the Helioshpere, Heliopause, Termination Shock, Heliosheath and Bow Shock see this link.
The notes below are from this source. Reference to the graphic above will assist in understanding the description.
PASADENA, Calif. – The 33-year odyssey of NASA's Voyager 1 spacecraft has reached a distant point at the edge of our solar system where there is no outward motion of solar wind.
Now hurtling toward interstellar space some 17.4 billion kilometers (10.8 billion miles) from the sun, Voyager 1 has crossed into an area where the velocity of the hot ionized gas, or plasma, emanating directly outward from the sun has slowed to zero. Scientists suspect the solar wind has been turned sideways by the pressure from the interstellar wind in the region between stars.
The event is a major milestone in Voyager 1's passage through the heliosheath, the turbulent outer shell of the sun's sphere of influence, and the spacecraft's upcoming departure from our solar system.
"The solar wind has turned the corner," said Ed Stone, Voyager project scientist based at the California Institute of Technology in Pasadena, Calif. "Voyager 1 is getting close to interstellar space."
Our sun gives off a stream of charged particles that form a bubble known as the heliosphere around our solar system. The solar wind travels at supersonic speed until it crosses a shockwave called the termination shock. At this point, the solar wind dramatically slows down and heats up in the heliosheath.
Launched on Sept. 5, 1977, Voyager 1 crossed the termination shock in December 2004 into the heliosheath. Scientists have used data from Voyager 1's Low-Energy Charged Particle Instrument to deduce the solar wind's velocity. When the speed of the charged particles hitting the outward face of Voyager 1 matched the spacecraft's speed, researchers knew that the net outward speed of the solar wind was zero. This occurred in June, when Voyager 1 was about 17 billion kilometers (10.6 billion miles) from the sun.
Because the velocities can fluctuate, scientists watched four more monthly readings before they were convinced the solar wind's outward speed actually had slowed to zero. Analysis of the data shows the velocity of the solar wind has steadily slowed at a rate of about 20 kilometers per second each year (45,000 mph each year) since August 2007, when the solar wind was speeding outward at about 60 kilometers per second (130,000 mph). The outward speed has remained at zero since June.
The results were presented today at the American Geophysical Union meeting in San Francisco.
"When I realized that we were getting solid zeroes, I was amazed," said Rob Decker, a Voyager Low-Energy Charged Particle Instrument co-investigator and senior staff scientist at the Johns Hopkins University Applied Physics Laboratory in Laurel, Md. "Here was Voyager, a spacecraft that has been a workhorse for 33 years, showing us something completely new again."
Scientists believe Voyager 1 has not crossed the heliosheath into interstellar space. Crossing into interstellar space would mean a sudden drop in the density of hot particles and an increase in the density of cold particles. Scientists are putting the data into their models of the heliosphere's structure and should be able to better estimate when Voyager 1 will reach interstellar space. Researchers currently estimate Voyager 1 will cross that frontier in about four years.
"In science, there is nothing like a reality check to shake things up, and Voyager 1 provided that with hard facts," said Tom Krimigis, principal investigator on the Low-Energy Charged Particle Instrument, who is based at the Applied Physics Laboratory and the Academy of Athens, Greece. "Once again, we face the predicament of redoing our models."
So after travelling for 33 years at about 15 Km/second Voyager 1 is 17.4 billion kilometers from Earth, which is about 2.7 times the average distance to Pluto (from the Sun. It is the most remote human-made object. This sounds impressive but when viewed in interstella terms it has travelled only 0.0017 light-years.
The nearest star to our sun is Proxima Centauri, which is 4.2 light years away. At its current speed, Voyager 1 it would take until the year 84,000 A.D. to get to our nearest star, if it were traveling in the right direction. (It isn't.)
SETI is the Search for Extraterrestrial Intelligence. Jill Tarter is the director of the SETI institutes Centre for SETI Research. For more details follow this link.
For other perspectives on our place in the universe follow this link and this link.
This talk is by Dimitar Sasselov, and is about the Kepler mission to find exoplanets. Here is a brief bio of Sasslov from this link :
Dimitar Sasselov is an astronomer who explores the interaction between light and matter. He studies, among other things, extrasolar planets, and he's a co-investigator on NASA's Kepler mission, which is monitoring 100,000 stars in a three-year hunt for exoplanets -- including Jupiter-sized giants. Sasselov watches for exoplanets by looking for transits, the act of a planet passing across the face of its star, dimming its light and changing its chemical signature. This simple, elegant way of searching has led to a bounty of newly discovered planets.
Towards the end of the talk he mentions the Pale Blue Dot, a photograph taken of Earth from beyond Saturn's orbit. For a discussin of the Pale Blue Dot see this post.
On October 13, 1994, the famous astronomer Carl Sagan delivered a public lecture at his own university of Cornell. During that lecture, he presented this photo:
The photo above was taken by Voyager 1 in 1990 as it sailed away from Earth, more than 6 billion kilometres in the distance. Having completed its primary mission, Voyager at that time was on its way out of the Solar System. Ground Control, at Sagan's suggestion, issued commands for the distant space craft to turn around and, looking back, take photos of each of the planets it had visited. From Voyager's vast distance, the Earth was captured as a infinitesimal point of light actually smaller than a single pixel of the photo. You could easily miss the pale blue dot in the photograph if there wasn't the arrow pointing to it.
This is a profound and moving photograph, to which my pedestrian prose cannot do justice, instead I will quote Sagan's beautiful descrtiption:
We succeeded in taking that picture [from deep space], and, if you look at it, you see a dot. That's here. That's home. That's us. On it, everyone you ever heard of, every human being who ever lived, lived out their lives. The aggregate of all our joys and sufferings, thousands of confident religions, ideologies and economic doctrines, every hunter and forager, every hero and coward, every creator and destroyer of civilizations, every king and peasant, every young couple in love, every hopeful child, every mother and father, every inventor and explorer, every teacher of morals, every corrupt politician, every superstar, every supreme leader, every saint and sinner in the history of our species, lived there on a mote of dust, suspended in a sunbeam.
To my mind, there is perhaps no better demonstration of the folly of human conceits than this distant image of our tiny world. To me, it underscores our responsibility to deal more kindly and compassionately with one another and to preserve and cherish that pale blue dot, the only home we've ever known.
The soundtrack of the video below is Sagan's extended description from which the paragraphs above were taken:
Towards the end of the video you may have noticed another famous space photograph - Earthrise:
The photograph was taken during the Apollo 8 mission to the moon.
Apollo 8 was the first human spaceflight mission to leave Earth orbit; the first to be captured by and escape from the gravitational field of another celestial body; and the first crewed voyage to return to planet Earth from another celestial body – Earth's Moon.
Here is a video that starts with the Earthrise photo and includes an Earthrise video and an Earthset video:
Awareness of the fragility of our Pale Blue Dot and the damage that we are doing to it has increased dramatically since the two photographs were taken.
Twenty years after the Pale Blue Dot photo was taken, Voyager 1 is nearing the edge of the Solar System, as this link demonstrates.
For an even more humbling view of our place in the Universe go to this post on the Hubble Ultra Deep Field.
For a post on the search for extrasolar planets try this post.
For a post on the Search for Extraterrestrial Intelligence see this post.
Recently the Cassini probe has taken its own version of the Pale Blue Dot, illustrated below. The dot, which is the Earth, can be seen above the centre of the photograph, just outside the bright ring of Saturn.
I will finish this post with the first five minutes of Carl Sagen's classic series Cosmos which is now thirty years old. Although the series was first aired on television 14 years before the Pale Blue Dotphoto, there is a prophetic image 46 seconds into the film.
Here is a description of the photo taken from this web page.
This is an image of Earth and the Moon, acquired at 5:20 a.m. MST on 3 October 2007, at a range of 142 million kilometers, which gives the HiRISE image a scale of 142 km/pixel and an Earth diameter of about 90 pixels and a Moon diameter of 24 pixels. The phase angle is 98 degrees, which means that less than half of the disks of the Earth and Moon have direct illumination. We could image Earth/Moon at full disk illumination only when they are on the opposite side of the sun from Mars, but then the range would be much greater and the image would show less detail.
On the day this image was taken, the Japanese Kayuga (Selene) spacecraft was en route from the Earth to the Moon, and has since returned spectacular images and movies.
On the Earth image we can make out the west coast outline of South America at lower right, although the clouds are the dominant features. These clouds are so bright, compared with the Moon, that they are saturated in the HiRISE images. In fact, the RED-filter image was almost completely saturated, the blue-green image had significant saturation, and the brightest clouds were saturated in the IR image. This color image required a fair amount of processing to make a nice-looking release.
The Moon image is unsaturated but brightened relative to Earth for this composite. The lunar images are useful for calibration of the camera.
We can feel awe in many different contexts including: religion, art, genius, science ...
Watching the video I felt wonder and amazement at the talents of the people who produced this science and the beauty (art) of the images. Contemplating the enormity of the universe is the closest that I can get to religious wonder.
Luckily the sky was clear tonight, as looking into the western sky there appeared a beautiful and rare sight - a conjuction of the three brightest objects in the night sky: the Moon, Venus and Jupiter.
After Margaret and I had watched it for a few minutes we had a phone call from Michelle to tell us about it. I took a photograph of it but the result did not do the original justice.
Luckily there are people who are better photographers than me who published there efforts on the Web.
Here are three of them.
This was taken in Melbourne, by Gary Ayton, published at this site.
Gary describes the photo as follows:
I took the opportunity to play with my Canon 1DMIII with EF 24-105mm L lens from my letterbox.
For the tech heads, I removed the UV filter to minimise lens flare from the street light and the settings used were 24mm focal length, f/4, 3200ISO, 0.5sec exposure.
No post-processing, just resizing and compression for the web. Click on the image for a 1000 pixel wide view.
I also tried with an Olympus OM 21mm and 24mm lens but whilst both gave excellent results, they did have a more pronounced lens flare.
Of course, I could have moved over to the park and avoided the street light but I felt this added interest and lit up the foreground nicely.
Gary's site has some wonderful photographs, take a look!
This picture was displayed at the National Geographic site .
This photo was published at the Astronomy Picture of the Day site .
The following is a quote from the site:
Pictured above is the scene as it appeared from Mt. Wilson Observatory overlooking Los Angeles, California, USA after sunset on 2008 November 30
The crescent moon is obvious. The brighter planet to the left is Venus. It is relatively close to us. The last of the three, Jupiter, is on the other side of the sun, so although it is intrinsically the brightest of the three it is the least bright because of its greater distance.
In September 1941 Isaac Asimov published his short story Nightfall. (In 1990, two years before Asimov's death, he collaborated with author Robert Silverberg on a novel-length revision of the original story.)
The story was inspired by a quotation by Ralph Waldo Emerson:
If the stars should appear one night in a thousand years, how would men believe and adore and preserve for many generations the remembrance of the city of God!
The fictional planet Lagash (Kalgash in the novel adaptation) is located in a stellar system containing six stars (Onos, Dovim, Trey, Patru, Tano, and Sitha), which keep the whole planet continuously illuminated; total darkness is unknown, as are more distant stars. A number of observations came together from academics in different departments of Soro University which lead to a startling conclusion:
A psychologist is studying the effects of prolonged exposure to darkness
An archaelogist discovers evidence that civilisation has suffered multiple cyclical collapses about every 200 years
A journalist has learned some of the ideas of the group known as the Apostles of Flame, who believe the world would be destroyed in a darkness with the appearance of Stars that unleash a torrent of fire
An astronomer calculates that once every 2049 years when there is only one star in the sky an eclipse (by a dark moon circling the planet) will plunge Kalgash into darkness
If you haven't read the novel and you have a penchant for Science Fiction get it out of your library and have a read. The book is a psychological thriller, but the reason for my posting on it is astronomical.
The six stars in Kalgash's system are obviously very close together. The primary sun of Kalgash is about the same difference from its star as the Earth is from the Sun. The other distance mentioned is a binary system (two stars revolving around each other) that is just further away than Saturn in the Solar System. A multiple star system this compact seemed something of a stretch.
Recently a real system that is even more compact has been discovered. This is called by the exciting name, BC 22 5866, and consists of four stars.
Universe Today describes the system as follows:
The stars are paired up together into binary groupings, and then these two pairs orbit a common centre of gravity. One pair orbits each other in less than 5 days - at a distance of a mere 0.06 astronomical units (1 AU is the distance from the Earth to the Sun). The second pair takes 55 days to complete an orbit, at a distance of 0.26 AU.
And finally, the two pairs take about 9 years to orbit one another at a distance of 5.8 AU - within the orbit of Jupiter in our own Solar System.
One AU is almost 150,000,000 kilometres, so 0.06 AU is 9,000,000 Km. Given that our sun is 1.4 million kilometres in diametre, a separation of two stars by 9 million Kms is very close. The second pair are closer than As Mercury's distance from to the Sun is 0.36 AU, the second pair of stars in BC 225866 are closer than our sun to its nearest planet.
The stars in the system are too close to be resolved in the largest telescopes available. The configuration of the BC 225866 was determined by spectroscopic methods. It will provide plenty of food for thought for theorists.
On October 4th 1957 - 50 years ago today - the Soviet Union launched Sputnik 1, the first artificial satellite to orbit the earth.
It was 58 cm in diameter and weighed approximately 83.6 kg. It was placed in an elliptical orbit and took about 96 minutes to circle the Earth.
Sputnik 1 is shown in the photograph at right.
The launching of Sputnik caused great consternation amongst the Americans. They feared that it showed that the Soviets were technologically superior and also that the US might be within range of Soviet intercontinental rockets. That, of cause, was a real concern in those Cold War days.
The launching of sputnik led directly to the establishment of NASA in the US in the middle of 1958.
As a seven year old I remember watching Sputnik with my family. I remember being disappointed that it just looked like a star moving across the sky. I think I expected it to look bigger. Although the satellite was very shiny, as can be seen in the photograph, it was actually too small to see from the ground. What we really saw was the burnt out second stage of the rocket booster.
The equinoxes are around 21st of March and September respectively. I have always wondered about the vagueness of this description. Now I have found an answer - the date of equal day and night lengths varies with latitude. The following from the USNO site gives an explanation.
Day and night are not exactly of equal length at the time of the March and September equinoxes. The dates on which day and night are each 12 hours occur a few days before and after the equinoxes. The specific dates of this occurrence are different for different latitudes.
On the day of an equinox, the geometric center of the Sun's disk crosses the equator, and this point is above the horizon for 12 hours everywhere on the Earth. However, the Sun is not simply a geometric point. Sunrise is defined as the instant when the leading edge of the Sun's disk becomes visible on the horizon, whereas sunset is the instant when the trailing edge of the disk disappears below the horizon. These are the moments of first and last direct sunlight. At these times the center of the disk is below the horizon. Furthermore, atmospheric refraction causes the Sun's disk to appear higher in the sky than it would if the Earth had no atmosphere. Thus, in the morning the upper edge of the disk is visible for several minutes before the geometric edge of the disk reaches the horizon. Similarly, in the evening the upper edge of the disk disappears several minutes after the geometric disk has passed below the horizon. The times of sunrise and sunset in almanacs are calculated for the normal atmospheric refraction of 34 minutes of arc and a semidiameter of 16 minutes of arc for the disk. Therefore, at the tabulated time the geometric center of the Sun is actually 50 minutes of arc below a regular and unobstructed horizon for an observer on the surface of the Earth in a level region.
For observers within a couple of degrees of the equator, the period from sunrise to sunset is always several minutes longer than the night. At higher latitudes in the northern hemisphere, the date of equal day and night occurs before the March equinox. Daytime continues to be longer than nighttime until after the September equinox. In the southern hemisphere, the dates of equal day and night occur before the September equinox and after the March equinox.
Using this site I calculated that at the latitude and longitude of Melbourne 20 September had days and nights of equal length. At the top of Cape York Peninsular, at 10 degrees south, equal day and night occurred on 12th September.
The apparent magnitude (brightness) of a star can be easily measured, as it is just the brightness of the star as seen from Earth. The absolute magnitude is the brightness of the star as seen from 10 parsecs away. It is possible to determine the absolute magnitude of a star by determining its spectral type and then reading off the luminosity in a HR diagram. The luminosity can then be easily converted to absolute magnitude.
Once these two measures of brightness have been determined the distance to the star can be calculated by the formula: d = 10(m-M+5)/5 where d = distance (in parsecs), m = apparent magnitude and M = absolute magnitude.
Here are some sample calculations:
Proxima Centauri m = 11.01, M = 15.53 d= 10(11.01 -15.53 + 5) / 5 = 1.247 parsecs The distance determined from parallax is 1.3 parsecs so the Distance Modulus calculation is fairly accurate. The source for the parallax distance is Research Consortium on Nearby Stars (RECONS). Parallax = 0.76887 therefore distance = 1 / 0.76887 = 1.3 parsecs
Sirius m = -1.47, M = 1.48 d = 10(-1.47 - 1.48 + 5) /5 = 2.57 Paralax distance is 2.63 parsecs (1/0.38002) which is also reasonably accurate.
This is all well and good, but how was the Distance Modulus formula determined? The rest of the post attempts to answer this question. Warning: the following is fairly mathematical!
Relating Flux to Distance Flux is the energy (light) passing through an area in an amount of time It is defined as: F = L / (4πD2) Note that 4πD2 is the surface area of a sphere. The observed brightness of a light source is related to its distance by the inverse square law - a source twice as far away appears to be on quarter as bright. For a single object or two objects of the same luminosity: The L terms cancel as do the 4π terms
Therefore F1 / F2 = (D2 / D1)2 - Equation 1
Converting Luminosity to Magnitude It is important to realise that luminosity is linear while magnitude is logarithmic. A difference of 5 magnitudes corresponds to a ratio of 100 in luminosity. L1 / L2 = xΔM ΔM is a change in M 100 = x5 5 M difference = 100 L difference 2.5118875 = 100.0001132 It is conventional to abbreviate this to 2.55 which equals 97.66 . Therefore: L1 / L2 = 2.5ΔM - Equation 2
Relating Luminosity to Distance We need to find the ratio of luminosity required to produce the same flux from different differences. F = L / (4πD2) L = F4πD2 L1 = F4πD12 L2 = F4πD22 Note: there is no F1 or F2 as we are looking for luminosity required to produce the same flux from different differences, ie F = F L1 / L2 = F4πD12 / F4πD22 = D12 / D22 = (D1 / D2) 2 - Equation 3 Note this is different to the flux / distance relationship.
ΔM = 2.5log10(D1 / D2) 2 = 5log10(D1 / D2) Note that ΔM = M2 - M1 therefore M2 - M1 = 5log10(D1 / D2) Note: absolute magnitude is defined as the apparent magnitude of an object when seen at a distance of 10 parsecs so the magnitude equation can be written as: m - M = 5log10(D/10) = 5(log10D - log1010) = 5(log10D - 1) = 5log10D -5
Solving for Distance if m - M = 5log10D -5 then m - M + 5 = 5log10D (m - M + 5)/5 = log10D Therefore D = 10(m - M + 5)/5 which is the relationship that we set out to prove!
During the last decade of the 19th century and the first decade of the 20th century, Henrietta Levitt studied variable stars at Harvard College Observatory. When she compared variables in the Small Magellanic Cloud SMC(a satellite galaxy of the Milky Way) she noted that there seemed to be a relationship between the period of variability and the luminosity (brightness) of the stars. As all of the stars in the SMC were basically the same distance away from Earth, the variations in luminosity were proportional to the intrinsic brightness of the stars. Meaning that it was not necessary to determine the distance of the individual stars to demonstrate that there was relationship between period and luminosity - period / luminosity relation (PL relation). The stars that Levitt studied were Cepheid variables. The diagram above shows the light curve of one of the Cepheids that Levitt studied.
This discovery indicated a method of measuring astronomical distances. Once the PL relation for Cepheids was established it would be possible to determine the absolute luminosity of a Cephid and by comparing absolute and apparent magnitudes to determine the distance to the star. Hubble used Cephids to show that there were many galaxies beyond our own and that the galaxies were moving away from each other ie that the universe was expanding. Eventually the Space Telescope that bears his name was able to determine the distances of galaxies as far away as 20 million light years using Cepheid variable stars.
There were many difficulties in calibrating the PL relation for Cepheids, and it was many decades before a reasonably accurate determination was made.
The rest of the post covers in some technical and mathematical detail the processes involved in determining a value for the PL relation, which enabled the modern measuring of distances in the millions of light year range.
The PL relation is usually written as: M = a + blog10P, where P is the period, M is the intrinsic magnitude (luminosity), a is a constant (the zero point) and b is the gradient of the relation.
The problem facing astronomers was to determine the values of the zero point and the gradient. One of the problems with the initial calibration attempts was that there are more than one variable star. The early calibrations included RR Lyrae stars, W Virginis stars as well as Cepheids. It took more that 20 years to clear up this confusion.
There were also difficulties with some of the techniques available. During Levitt's time and for many decades afterwards, photographic plates were used to measure the variations in the intensity of the stars. This was problematic for two reasons: 1) photographic plates are non linear and therefore produced incorrect measures of magnitude variation (fluxes), and 2) most of the light registered on photographic plates was from the blue wavelengths which is strongly absorbed by inter-stellar dust.
Measuring absolute distances to even close Cepheid variables was very difficult at they were too far away for accurate parallax measurements for much of the 20th Century.
In recent decades improved techniques (such as charged coupled devices) have improved the measurement of fluxes. The Hipparcos satellite has allowed improved measurement of distances to Cepheids. These technical developments have made possible the reasonably accurate determination of the PL relation. The modern value is:
The next step for distances beyond trigonometric parallax is to use the brightness of start to determine their distance. There are enormous variations in the brightness of start so it is not possible to use brightness on its own to determine stellar distances. The light that we see is made op of "all of the colors of the rainbow" from dark blue to red. Taking the light of a star and breaking it up into its constituent colors is called taking the star's spectrum. Astronomers can determine the luminosity (brightness) of a star from the spectrum. If they know how bright a star is, astronomers can compare its brightness as seen from Earth and then determine how distant is is.
That simple description raises a number of questions. If you are interested in exploring these issues further click on the "Read the rest of the post" link.
1. How do astronomers determine the luminosity of a star from its spectrum? The first step is to determine the surface temperature. This can be done from the spectrum. A simplified version of a spectrum for a star like the sun is displayed below.
Note the colors range from dark blue to dark red. There are dark lines in the spectrum. Each line is caused by the absorption of light at that particular frequency by an element in the star's atmosphere. The electrons in the atoms of the elements have to be at particular energy levels to absorb the light. The energy levels of atoms are determined by temperature, so the temperature of the star can be determined. The next step is to use a Hertzsprung - Russell diagram (illustrated at right) to determine the luminosity of the star. The horizontal axis is the surface temperature and the vertical axis is the star's luminosity as a ratio of the luminosity of the sun. The calibration of the diagram has been improved by the large number of stars that have been studied by the Hipparcos satelite. Most stars are on the "main sequence" so to determine the luminosity from star temperature take a line up from the appropriate location on the horizontal axis to the main sequence and then read off the luminosity from the vertical axis. 2. How is distance determined from absolute luminosity? We can use the formula: D = 10(m-M+5)/5 where D = distance, m = apparent magnitude and M = absolute magnitude. Magnitude measure is an issue that I will not discuss in this post.
I will use Spica as an example: Apparent magnitude: m = 0.98 Spectral type is B1 From HR diagram this indicates an absolute magnitude, M, in the range: -3.2 to -5.0 For M = -3.2, D = 10(0.98 - (-3.2) + 5) / 5 = 68.54 parsecs (pc) For M = -5.0, D = 10(0.98 - (-5.0) + 5) /5 The Hipparcos measurements give D = 80.38 .
Spectroscopic Parallax provides a distance measurement to stars but is not particularly accurate.
In my post on Galaxies I noted the distance to the two galaxies concerned. This raises the issue of measuring astronomical distances. The first step is measuring distances to near by stars. This post considers how these measurements are done. It is possible to directly measure distances to stars that are relatively close to us by using trigonometry which is probably familiar from secondary school maths - eg COS, SIN, TAN, PI, radians and the like. Nearby stars appear to move with respect to more distant background stars due to the motion of the Earth around the Sun. This apparent motion (it is not "true" motion) is called Stellar Parallax. (Stellar means star). In the diagram at right , the line of sight to the star in December is different than that in June, when the Earth is on the other side of its orbit. As seen from the Earth, the nearby star appears to sweep through the angle shown. Half of this angle, is the parallax, p.
As even the closest stars are very far away the measured parallaxes are very small. Even the largest is less than an arcsecond.
If you are wondering what an arcsecond is, here is an explanation. A degree is 1/360 of a circle. An arcminute is 1/60 of a degree. An arcsecond is 1/60 of an arcminute. If you do the maths an arcsecond is 1/1296000 of a circle. For those with some maths background that is (π/648000) radians, which is approximately 1/206265 radian.
The closest star to the solar system, Proxima Centauri, has a parallax of 0.772-arcsec, which is the largest ever measured. (The closer a star is the larger its parallax). Incidentally the first parallax was measured in 1837 by Friedrich Bessel for the star 61 Cygni. We use photography and digital imaging techniques to measure parallaxes today. Increasingly, we measure parallaxes from space to avoid blurring due to the Earth's atmosphere.
The parallax relationship to distance can be expressed in a simple formula: d = 1/p , where p is the parallax measured in arcseconds and d is the distance measured in parscecs. So what is a parsec.
"A star with a parallax of 1 arcsecond has a distance of 1 Parsec."
1 parsec (pc) is equivalent to:
* 206,265 AU (and AU is the distance between the Earth and the Sun about 149,598,000 Kms)
* 3.26 Light Years
* 3.086x1013 km
It can be argued that the parsec measure of distance is probably more "natural" than the light year as the latter is dependent on the length of one year (revolution of the Earth around the Sun) where as a parsec relates to a fraction of a circle. On the other hand the fraction of a circle used to define a parsec is pretty unusual, and relates to the realatively arbitrary decision to define degrees as 1/360 of a circle, and arcminute as 1/60 of a degree and arcsecond as 1/60 of an arcminute. Parsec as a "natural" measure is not in the same class as radian measure.
Here is an example of the calculation of parallax distances:
Alpha Centauri has a parallax of p=0.742-arcsec.
d = 1/p = 1/0.742 = 1.35 parsecs (pc)
There are serious limitations to this method: If the stars are too far away, the parallax can be too small to measure accurately. In general, the greater the distance, the smaller the parallax, and so the less precise the distance measurement will be. The smallest parallax measurable from the ground is about 0.01-arcsec. This means that from the ground, the method of Trigonometric Parallaxes has the following limitations: * good out to 100 pc * only get 10% distances out to a few parsecs. * only a few hundred stars are this close
The blurring of stars caused by the atmosphere makes it difficult to measure parallaxes to high precisions. Consequently the Hipparcos satellite was launched by the European Space Agency in 1989 with the aim of more precisely measuring stellar parallaxes. It can measure parallaxes to an accuracy of about 0.001-arcsec. *Hiparcos has measured parallaxes for about 100,000 stars *It can get a 10% accuracy for distances out to about 100 pc *It can measure good distances for bright stars out to 1000 pc
Hiparcos represented a great leap in our knowledge of the distances (and motions) of nearby stars. For more information on Hiparcos visit the web site.
I was browsing through the Hubble Space Telescope site today and came across many beautiful images of astronomical objects taken with the space telescope. Among them were the two galaxies displayed in this post.
The one at rightis M 101. It is a spiral galaxy that is about 25 Million Light Years away. It is nicknamed the "Pinwheel Galaxy" for obvious reasons. It was first discovered by Pierre Mechain in 1871 and was included by Charles Messier in his catalog. It is relatively large with a diameter of 170.000 light years. Our galaxy, the Milky Way has a diameter of about 100,000 light years. The Pinwheel is quite asymetrical (compare left and right sides in the picture). This asymetry is thought to have been caused by a close encounter with another galaxy in the relatively recent past. Galactic collisions are not particularly rare, photographs have been taken of galactic collisions. Our galaxy would look something like M 101 from the outside. We see it as a band across the sky as we are inside the Milky Way Galaxy. The galaxy at left is also a spiral but with quite a different appearance. Its designation is NGC 1300. It type is called a "Barred Spiral" as the spiral arms are connected by a large bar rather than spiral in to the centre as in M 101. It is approximately 70 million light years away and about 100,00 light years across. It was discovered by John Herschel in 1835. His father was the more famous William Herschel.
A light year is the distance that light travels in one year, so the pictures show the galaxies as they were 25 and 70 million years ago respectively. The distance of a light year can be easily calculated by multiplying seconds in a minute X minutes in a hour X hours in a day X days in a year X distance light travels in one second. As light travels very close to 300,000 Kms in a second the calculation becomes 60 X 60 X 24 X 365 X 300,000. The answer is 9,460,000,000,000 Kms.
That means that M 101 is 236,000,000,000,000,000,000 Kms away and NGC 1300, 66,20,00,000,000,000,000,000 Kms away. These are large distances in anyone's estimation - except maybe for astronomers. Compared to the most distant galaxies known M 101 and NGC 1300 are just in our back yard. The most distant galaxies are of the order of 13 billion light years distant from us. I won't even bother with the kilometer distance which would be meaningless and silly. Galaxies much older than 13 billion years old are unlikely to be found as the universe is about 13.7 billion years old.
This post raises many questions, in particular, how are astronomical distances measured and how do we know that the universe is about 13.7 billion years old? They are obvious topics for later posts.
