Physics research Safiyah Qureshi 12A An outlook into space Research by: Safiyah Qureshi Submitted to: Miss Sunaina Dessai Contents: 1. 2. 3. 4. 5. 6. 7. Introduction Luminosity and standard candles Stellar radii Practical activity- estimating diameter of sun Hubble’s law and doppler’s redshift The expanding universe Images and references An outlook into space Physics research Safiyah Qureshi 12A An outlook into space “That is one of the things I like most about going to space. You start thinking you belong to the earth rather than to a single country” -Anna Lee Fisher Introduction: My love of cosmology comes from a few recent years of pondering over the skies whenever I go out. After watching videos and reading articles out of pure interest, I have concluded that there is no better way to apply physics than to reach out to the unknown, the unpredictable and the unseeable. The beginning of all of us. When we exist on this earth, we take for granted that the whole universe started at a point. The beauty of this universe lies in the questions we ask, and have still been unable to answer: Was time relevant? Did it even exist? What existed, then, if we were not there. If none of our stars and none of our orbits were there? What was our beginning? What was the reason the earth became the homeland of life? Unlike any other planet. We could have been situated in Kepler planets, assumed to be more suitable for life than earth. Yet we exist here today, cheering over our successes to the moon. The universe is way beyond the earth and the moon, the solar system, the milky way. The universe continues, on and on, more than you will ever be able to imagine. And here is the catch. It continues to expand. Till today, it has not stopped expanding. Since its beginning? While no human is in the position to explain the full basis behind the universe, we can dive into the parts of cosmology that have physicists and cosmologists have evidently published papers on, astronomers have experienced. We can cover all we know… Although we should take a moment to appreciate that all we know is five percent of what is out there. Physics research Safiyah Qureshi 12A An outlook into space Luminosity and standard candles: In the basics of physics, it is usually easier to standardise values, to use constants; this makes the process of calculating values and deriving equations easier, as there are less factors to affect the variable. It makes it easier to understand a certain fact when comparing it with something comprehendible. This is where we apply relativity to the science we are studying. When I was going to school to school this morning, I narrowed my eyes to compete with the brightness of the sun. While at night, we can glare at the starry sky, with no harm in sight-seeing with the naked eye. This all extrapolates from the calculation of the luminosity of a star. How bright a star could be. Of course, we may see the star as a small twinkle in the sky, but there is a high likelihood that it is much brighter than our sun, the distance it is from the earth is what causes it to look like it has less luminosity. So, these factors are considered when calculating the luminosity of a star. In simple physics terms, luminosity of a star is the total radiant power emitted from a star. The sun has a luminosity LĘ= 3.83*1026 Watts. This means that the sun emits 3.83*1026 joules of energy in one second, self-explanatory as to why its bright enough to enlighten half the earth at once. When trying to study more about luminosity of different stars, scientists used standard candles, a celestial body with a known luminosity, to be able to calculate the distance of the galaxy in which this candle is located. This way they could tell how far the galaxy is from the earth, using the intensity by which its light arrived at earth. This observed intensity is known as radiant flux intensity, in simple words the brightness of the star from earth. Now as both the luminosity and distance affect the radiant flux intensity, an equation relating both can be determined. The equation used for this is: ðđ= ðŋ 4ðð2 Where F is the radiant flux intensity, L is the luminosity, and (4ðð2 ) is the area covered between the earth and the star (Fig 1.0) Radiant flux intensity is measured in watts per metre squared, however scientists do sometimes neglect the unit and focus on the magnitude of the intensity. As we can conclude from this equation, the observed brightness of a star is directly proportional to the intensity of the star, and inversely proportional to its distance from the earth. At earth, we can measure the radiant flux intensity by calculating the intensity of the electromagnetic radiation arriving at the earth, but we do not know the distance of that body from the earth. This is why we must have knowledge of the luminosity of the object. Scientists found out that celestial bodies of various types had known luminosities, and naming them standard candles, they were able to use their values as constants. Physics research Safiyah Qureshi 12A An outlook into space You may have a question how the value of luminosity can be known to us. For that, let us dive into the types of standard candles. There are two types of standard candles: o o Cepheid variable stars Cepheid variable stars have a predictable luminosity. In 1908, Henrietta Leavitt discovered that the luminosity depended on the periodic brightness of the stars. This meant that the brightness of the star varied regularly with time, and the stars luminosity closely related to this change. Therefore, when astronomers calculated the brightness of the star in respect to time, they deduced the luminosity of the star. That made it possible to calculate the distance of the earth from the star, and hence the distance of the galaxy where that star is located from the earth. Type 1A supernovae As stars burn the fuel in their cores, they produce heat. This heat produces pressure that pushes outward against the forces of gravity that pull inward on the star. For most of the life of a star, inward gravity and outward pressure are in balance and the star is stable. But as a star burns through its fuel and begins to cool, the outward forces of pressure drop. When the pressure drops low enough in a massive star, gravity suddenly takes over and the star collapses in just seconds. This collapse produces the explosion we call a supernova. Type 1 and 2 supernova: There are two types of supernova. In a type 1 supernova, there is a binary system, where two stars orbit around a combined centre of mass. The white dwarf( hotter star) absorbs the energy from the red dwarf star, until a nuclear reaction causes it to burst. (Fig 1.1). The white dwarf absorbs energy until it is 1.4 times the mass of the sun. This value is constant, so no matter how large the dwarf may be, the supernova will only occur at that particular mass. Which means all the supernovas at the world occur at one mass, with one value of known luminosity. Type 2 supernovae occur with individual stars, not binary systems. The star loses its stability due to gravity and collapses, sending out emissions and leaving behind a black hole. The problem here is that all do not happen at a certain mass, which explains why they cannot be used as standard candles. Comparatively, cepheid variable stars are a more reliable standard candle because supernovas are short lasting, so it may not be as convenient. Physics research Safiyah Qureshi 12A An outlook into space Stellar radii: It may be pretty obvious by now that we would also want to determine the sizes of the stars, i.e., the radius of a star. For this, we will look at Wein’s displacement law and Stefan-Boltzmann law and combine them to come to an equation that can help us calculate the radius of a star, the stellar radii. o Wein’s displacement law Wien’s law or Wien’s displacement law, named after Wilhelm Wien, was derived in the year 1893 which states that black body radiation has different peaks of temperature at wavelengths that are inversely proportional to temperatures. Black bodies, like black holes are physical bodies that absorb all incident electromagnetic radiation, regardless of frequency or angle of incidence. It is important to note that it has a characteristic emission spectrum and intensity, which depends only on its thermodynamic temperature. So, the law is stating that for wavelengths that are inversely proportional to temperature, the black body radiation curve will peak at different temperatures(Fig 1.2). Even more simply, the wavelength peak( ððððĨ ) and temperature have an inverse relationship such that ððððĨ ð = ðððð ðĄðððĄ And the experimental value of the constant is 2.9 × 10−3 . The wavelengths then obviously respond to the colours of the stars (Fig 1.3) o Stefan-Boltzmann law This law relates the luminosity of the object to its radii. The law is ðŋ = 4ððð 2 ð 4 Where ð is the Stefan-Boltzmann constant 5.67 × 10−8 ðð −2 ðū −4 , r is the radius of the star and T is the thermodynamic temperature. So, to calculate the radius of the star, we can use the observed maximum wavelength from Wein’s displacement equation to calculate the thermodynamic temperature, and then substitute in StefanBoltzmann’s equation to calculate the radius of the star. Physics research Safiyah Qureshi 12A An outlook into space Practical activity- estimating the radius of the sun: ï· ï· ï· ï· ï· ï· ï· Construct a solar pinhole projector like the one shown in Fig 1.4 . You will need heavy cardboard or cardstock, aluminium foil, and a sheet of white paper on a clipboard to use as a projection screen. The larger the piece holding the pin holed aluminium foil the better; it will cast a darker shadow on your drawing surface, making it easier to sketch the Sun. The hole in the cardboard, which is covered by the aluminium foil, should be only an inch or two across. You may try different pinhole sizes. Small holes, made with a single pinprick, work for short projections (a meter or so), while larger pinholes work for larger project ions (images have been projected over 20 meters!). In general, smaller pinholes are better. Make your observations on a cloudless day when the Sun is reasonably high in the sky. Rigidly support the pinhole device on a ladder, chair back, camera tripod or post (for example). The observations will work best if the screens are all perpendicular to the direction to the Sun (especially the drawing screen). Use the pinhole to cast an image of the Sun on your screen. Make sure that the projected image is several times larger than the pinhole itself; if it is not, move the screen farther back. Outline the image with a pencil, then measure its diameter and its distance from the pinhole. Repeat this procedure at different distances (and with different pinhole sizes if you wish) to collect at least five measurements. One way to make accurate measurements is to pre-draw precise circles of varied sizes on your drawing screen, then adjust the distance to the pinhole so the Sun's image exactly fills each circle. This reduces your field measurements to only the distance between the screens. If you have trouble seeing the projected image of the Sun at a great enough distance, try setting up your viewing screen so it is mostly shaded from the sky. It is actually best to make your measurements indoors, with the sun shining in a south-facing window. To then calculate the diameter, use a ratio: ððððððĄðð ðð ððððð ððððððĄðð ðð ð ðĒð = ððð ðĄðððð ðð ððððð ððð ðĄðððð ðð ð ðĒð As we have learnt how to determine the distance of a star from earth, and we can measure the diameter of image formed and its distance from the pinhole, this experiment is a straightforward way to calculate the suns diameter, and with all accuracy measures, quite precise as well. Physics research Safiyah Qureshi 12A An outlook into space Hubble’s law and Doppler redshift Hubble’s experiments lead to an overwhelming discovery that the universe was expanding. We said recently that we can measure the radiant flux intensity of a body by collecting the electromagnetic radiation that reach the earth. We do this by taking absorption spectrums, as shown in Fig 1.5. It is visible that although the same pattern is observed, there is a slight shift of it. Astro scientist Edward Hubble noticed that as the galaxy gets further away, the absorption lines, shown by black, are moved further to the red end of the spectrum. And as physics goes, he reached a conclusion as to why. In a simple doppler effect, waves are seen to be of larger wavelengths as they move further away from the observer. Similarly, as the galaxies move away from us, the wavelengths they emit become larger and closer to the redder spectrum area as they reach us. (Fig 1.6) . So why are galaxies redshifted? Well, think of light waves with a particular wavelength emitted by a remote galaxy. It may take many millions of years for these light waves to reach Earth. During this time empty space is expanding, stretching the light waves along with it, so they arrive at Earth with a longer, redder wavelength. This type of redshift is called the cosmological redshift. A longer light travel time means more cosmic expansion, more wavelength stretching and thus a higher redshift. Doppler shift from the galaxy’s motion through space may slightly adjust this cosmological redshift, but this is a minor effect for remote objects, so a galaxy’s observed redshift is usually a reliable indicator of its distance. Doppler redshift can be represented using ratios: âð âð ðĢ = = ð ð ð Where v is the recession speed, and c is the speed of light. This calculation can only be used for nonrelativistic galaxies, those that have speeds much smaller than that of light. Vesto Slipher found that most galaxies displayed large redshifts, meaning they were receding at hundreds or even thousands of kilometres per second. Hubble added to his finding by creating what is known as Hubble’s law. Fig 1.7 demonstrates this effect. As the galaxy moves further away, its speed increases, and hence its emissions are received with the largest wavelengths. Hubble confirmed this by plotting a V/d graph(Fig 1.8), and being able to reach this conclusion: ðĢ∝ð Therefore: ðĢ = ðŧ0 ð Where ðŧ0 is the Hubble’s constant, at a value of 2.4 × 10−18 Physics research Safiyah Qureshi 12A An outlook into space The expanding universe: The universe is such an abstract piece of art that its origin was obviously researched by various scientists, and still some questions remain unanswered. An effective way to help visualise the expanding universe is to compare space with the surface of an expanding balloon. This analogy was used by Arthur Eddington as early as 1933 in his book The Expanding Universe. It was also used by Fred Hoyle in the 1960 edition of his popular book The Nature of the Universe. Take a moment to think, that if the universe is still expanding, there must have been a time it began. History goes that in 1927, George Lemaitre published a paper on the theory that the universe started with a single primeval atom, but it went completely unnoticed as he had no evidence. Until then, the basic belief was of an eternal and static universe. But years later, with Lemaitre still researching, scientists such as Einstein and Willem de Sitter had considered this theory unsatisfactory. On the other hand, Hubble discovered the continuous expansion of the universe. This gave Lemaitre the courage to, this time, boldly propose the idea that the universe started from a dense centre. Scientists have now concluded that what we call Big Bang Theory is the most astronomically appropriate explanation for the existence of the universe. Fred Hoyle was the man who named the theory while talking on a BBC radio, thinking of it as illogical. However, the big bang theory is the worldwide accepted theory nowadays. So, what was the big bang? In the first 10−43 seconds of its existence, the universe was very compact, less than a million billion billionth the size of a single atom. It is thought that at such an incomprehensibly dense, energetic state, the four fundamental forces—gravity, electromagnetism, and the strong and weak nuclear forces—were forged into a single force. The universe cooled, and as it cooled, the four forces divided, the quarks became protons and the protons became atoms, atoms became molecules, and so it went on and on, until stars became galaxies and galaxies make up our current universe. Even though this may be a fairly simple theory to understand, taking it back in time to ask why it began in the first place is the question no physicist has yet answered. There is still no explanation as to what forced the existence of this dense matter. Scientists believe gravity has a role there, but we are yet to comprehend gravity at a microscopic scale, and with all due efforts, are still unsure as to what the dense matter was before it was dense matter. Although many theories have suggested that the inflation of the universe means it was a cold, empty, matterless medium before the Big Bang, nothing has yet proven it, but you never know, after all Lemaitre’s paper went overlooked for years before scientists returned to it. Maybe the answer to our question is lying in the future generation’s George Lemaitre. Physics research Images and references : Fig 1.0- equation of radiant flux intensity Fig 1.3- black body radiation peaks Safiyah Qureshi 12A Fig 1.1- supernova types An outlook into space Physics research Fig 1.4practical setup Fig 1.5- EM spectra for redshifted waves Fig 1.6- doppler redshift Fig 1.7- Hubble’s law examples Safiyah Qureshi 12A An outlook into space Fig 1.8Hubble’s law graph Physics research Safiyah Qureshi 12A An outlook into space References: ï· ï· ï· ï· ï· ï· http://www.astro.ex.ac.uk/people/hatchell/rinr/candles.pdf https://phys.libretexts.org/Bookshelves/Astronomy__Cosmology/Big_Ideas_in_Cosmology_(Cob le_et_al.)/06%3A_Measuring_Cosmic_Distances/6.03%3A_Standard_Candle https://exoplanets.nasa.gov/resources/2172/type-ia-supernova/ https://physics.weber.edu/schroeder/astro/sizeofsun.html https://www.skyatnightmagazine.com/space-science/galaxies-redshift https://www.amnh.org/learn-teach/curriculum-collections/cosmic-horizons-book/georgeslemaitre-big-bang Only 12% of this research is plagiarised from internet sources.
