Eratosthenes
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Eratosthenes was a Greek scholar who calculated the circumference of the Earth using shadows from sticks in Alexandria and Syene. He observed that on the summer solstice, a stick in Alexandria cast a shadow while a stick in Syene did not. Knowing the distance between the cities, he calculated the circumference of the Earth to within a few percent of the actual measurement. Eratosthenes made several other contributions including accurately calculating the tilt of the Earth's axis and inventing the leap day.
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Eratosthenes was a Greek mathematician who devised a simple method to measure the circumference of the Earth in the 3rd century BC. He noticed that on the summer solstice in Syene (now Aswan), Egypt, the sun was directly overhead at noon, casting no shadows, while in Alexandria shadows were cast. Using the known distance between the cities and basic geometry, he calculated the angle of the sun's rays and determined that this angle was approximately 1/50th of a full circle. Assuming the Earth was spherical, he estimated the circumference of the Earth to within a few percent of the actual measurement. The document describes replicating Eratosthenes' experiment to determine the circumference of the Earth by
Radio Astronomy and radio telescopes
This document defines and summarizes various units of measurement used in astronomy, including the astronomical unit (AU), light-year, and parsec. It describes coordinate systems like right ascension and declination that are used to specify positions of celestial objects. It also discusses magnitude scales used to measure the brightness of stars and other astronomical objects.
Tema 1 La tierra
This document provides an overview of geography and history concepts for 1st year secondary students in Spain. It covers topics like the universe, conditions for life, Earth's latitude and longitude, how to locate points on a map, time zones, Earth's rotation and revolution, axial tilt and seasons. It also discusses map projections, types of maps like physical, topographic, and thematic maps. Remote sensing images are briefly mentioned. The document is bilingual, providing definitions and explanations in both Spanish and English.
Origin of the earth
The document discusses the origin and evolution of models of the universe. It begins by describing early flat earth cosmologies from ancient civilizations like Egypt, India, and Mesopotamia. It then outlines the development of the spherical earth model in ancient Greece, including ideas proposed by Pythagoras, Plato, and calculations made by Eratosthenes to estimate the earth's circumference. The document also summarizes the geocentric model developed by the Greeks with the earth at the center, and revisions made by Aristotle and Ptolemy. Finally, it outlines the heliocentric model first proposed by Aristarchus, placing the sun at the center, and the further developments of this model by Copernicus.
choksilog.pptx
The document provides an overview of the history and development of astronomy. It discusses early astronomical observations dating back to 2000 BC and important discoveries by Galileo and Kepler. These include Galileo's observation of craters on the Moon and sunspots, and Kepler's laws of planetary motion. It also outlines several key concepts and tools in astronomy including light years, astronomical units, celestial coordinates, and telescopes. Finally, it provides a brief introduction to cosmology and the formation of the Milky Way galaxy in line with the two-stage collapse model.
Pr 1
A geographic coordinate system uses numbers to specify every location on Earth. Common coordinates are latitude, longitude, and elevation. Latitude is the angle between the equatorial plane and a line drawn from the Earth's center to the point, measured in degrees north or south. Longitude is the angle between the prime meridian and a line drawn to the point, measured in degrees east or west around the Earth's equator. Together, latitude and longitude uniquely identify any location on Earth.
earth as a sphere
This document provides information about latitude, longitude, and the coordinate system used to locate positions on Earth. It defines key terms like latitude, longitude, meridians, parallels, and the differences between them. Methods for calculating distances between points and angles subtended at the center of Earth are presented. Worked examples demonstrate how to find latitudes/longitudes of points, distances along meridians/parallels, and the shortest distance between two points on a great circle.
measuring the circumference ofmearth bye eratosthenes
Eratosthenes calculated the circumference of the Earth in the 3rd century BC using simple geometric principles. By measuring the shadows cast at two locations on the summer solstice, he deduced that the Earth must be curved. He then used trigonometry to calculate the circumference based on the angles of shadows and distance between the locations. His estimate of approximately 40,000 km was remarkably accurate given the simple methods used. This was a seminal early calculation that demonstrated humans' ability to measure the size of our planet through mathematical reasoning and observation.
Chapter 1
Chapter 1 of the History of Astronomy discusses prehistoric astronomy and early astronomical observations. It describes how early civilizations noticed the motions of the Sun, Moon, planets and stars and used them for timekeeping. It then discusses the development of models of the solar system from ancient Greek astronomers like Aristotle, Ptolemy and Copernicus to Renaissance scientists like Brahe, Kepler and Galileo. Key developments included determining the Earth and Moon's sizes, the heliocentric model of the solar system, and Kepler's laws of planetary motion. The growth of astrophysics in the 18th-19th centuries led to new discoveries and technologies.
Earth and sun relationships
1) The Earth revolves around the sun in an elliptical orbit over the course of 1 year, and its axial tilt of 23.5 degrees relative to the orbital plane causes the seasons.
2) As the Earth revolves, its hemispheres alternate between tilting towards and away from the sun, resulting in the summer and winter seasons in each hemisphere.
3) An analemma diagram can be used to determine the position of the subsolar point, solar noon time, and solar altitude for any location on Earth on any given date throughout the year.
6 latitude an longitude ..pptx
The document discusses key concepts related to globes and maps. It explains that a globe is a miniature model of the Earth that can be rotated to accurately show the sizes and positions of continents, oceans, and other geographic features. Parallels of latitude and meridians of longitude form a grid system on a globe, with the equator dividing it into northern and southern hemispheres. The Prime Meridian passes through Greenwich, England and longitude is measured in degrees east and west from there. The document also discusses time zones and how local times differ depending on a place's longitude.
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measuring the circumference ofmearth bye eratosthenes
measuring the circumference ofmearth bye eratosthenes
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Meet our Astronomers
This document introduces four astronomers from different countries: Pedro Nunes from Portugal, Kazimieras Simonavicius from Lithuania, Ali Qushji from Turkey, and Christian Doppler from Austria. It provides basic biographical information about each astronomer and their country of origin. Contact information is also listed for students from Portugal and Lithuania who are featured in the document.
Agrupamento de Escolas Gil Paes
The document provides demographic information about the city of Salzburg, Austria, which has a total area of 270km2 and around 36,500 inhabitants distributed across 17 small towns. It then lists information about the 12 academic units in Salzburg, including the number of operating assistants, teachers, childhood educators, and students at each unit. In total, there are 48 operating assistants, 125 teachers, and 573 students across the 12 academic units.
Cartoons about Deep Sky
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive function. Exercise causes chemical changes in the brain that may help protect against mental illness and improve symptoms.
Activities about light pollution
This document summarizes the activities of a Turkish school's Comenius team focused on raising awareness about light pollution. Some of the activities included student contests to design astronaut outfits, build 3D models of space, and construct balloon rocket experiments. Students collaborated with a local university and media outlets to measure and map light pollution in their city. They created educational materials like a dictionary and cartoon explanations of scientists. The goal was to engage students in learning about light pollution and space through hands-on projects and competitions.
Sun and the Solar System
O documento apresenta uma peça de teatro realizada por alunos sobre o Sistema Solar. A peça mostra os planetas representados como personagens discutindo sobre a destruição da Terra pelos humanos e o medo de outros planetas de sofrerem o mesmo destino. Os alunos também apresentam uma música e dança sobre o Sol.
Sun
This document appears to be a presentation about science and astronomy projects conducted by students in Turkey and Europe. It discusses students participating in a mobility program in Lithuania, then researching topics like the sun, solar and lunar eclipses, and making 3D models of the Earth, Moon, and Sun. The presentation continues describing how students studied sundials, making their own and researching famous sundials in Turkey. It concludes with students making experiments about day and night and constructing amateur telescopes.
The Moon
This lesson plan aims to teach primary school students about the phases of the Moon and its effect on tides. Key points include:
- The Moon orbits Earth approximately every 28 days, appearing in different phases as it circles the planet.
- The changing shapes of the Moon are caused by the varying angles between the Moon, Earth, and Sun as the Moon revolves.
- Gravity from the Moon and Sun causes ocean tides on Earth to regularly rise and fall, with stronger tides occurring during full and new Moons.
Light pollution
This document discusses light pollution, which is excessive or inappropriate artificial light that harms human health and wildlife. It defines light pollution and describes its causes such as inadequate lighting design and incorrect installation. The consequences of light pollution include wasted energy, air and light pollution, and negative impacts on living beings. Wildlife like birds and sea turtles are especially harmed by light pollution disrupting natural behaviors and attracting animals to light sources where they can get injured or die. Prevention methods aim to direct light downward and use efficient bulbs to reduce impacts.
Exoplanets
An exoplanet is a planet that orbits a star other than the Sun. Nearly 2000 exoplanets have been discovered orbiting other stars by detecting their gravitational influence or observing dimming of the star's light as the planet passes in front. The Kepler space telescope has been instrumental in discovering many new exoplanets using the transit method of detection, including some that may be capable of hosting life such as Gliese 581g. As exoplanet discoveries increase, interest in finding signs of life on other worlds outside our solar system continues to grow.
Nebula
Nebulae are giant clouds of dust and gas found in space where stars are formed. They can be light years across and look fuzzy in appearance. When the gas and dust in a nebula collapses under its own gravity, it forms hot, dense cores where stars ignite and shine. Some nebulae glow due to radiation from young stars, called emission nebulae. Others reflect the light of stars, known as reflection nebulae. Planetary nebulae are formed when aging stars blow off their outer layers.
Sun - Our friend or foe
The document discusses the sun's positive and negative effects on humans. Positively, the sun provides warmth, energy through photosynthesis, boosts serotonin levels and immunity. However, ultraviolet radiation from the sun can cause skin cancer, sunburns, weaken the immune system, lead to heat stroke and damage eyes and skin over time. While the sun has benefits, prolonged unprotected exposure to its UV rays poses health risks like skin cancer, so protection is recommended to harness its energy safely.
Sun
The document summarizes information about the Sun, including:
1) It is an average star that produces energy through nuclear fusion in its core and contains over 99% of the mass in the Solar System.
2) Significant variations in solar activity like sunspots and solar flares can be seen from day to day and year to year, arising from the bending and twisting of magnetic fields in the Sun's atmosphere.
3) Coronal mass ejections are powerful explosions that can eject large amounts of plasma from the Sun's corona and impact Earth's environment and technology.
Solar system
The Solar System is comprised of the Sun and objects that orbit it. It formed 4.6 billion years ago from a giant cloud. The inner terrestrial planets like Earth are rocky, while the outer giant planets like Jupiter are much larger and gaseous. The asteroid belt lies between Mars and Jupiter, containing millions of objects but only about 1% of the mass of Earth. Ceres is the largest asteroid in the belt.
Life without the Moon
If the Moon suddenly vanished:
- Earth's axis would lose stability and wobble dramatically, causing extreme temperature changes and unpredictable seasons.
- Tides would be much smaller, caused only by the Sun, disrupting marine life and coastal ecosystems.
- Earth's rotation would speed up, with day lengths shortening to 8-10 hours and winds of 160-200 km/h sweeping the surface.
- Life on Earth would struggle to adapt to the entirely different environmental conditions without the stabilizing influence of the Moon.
Dive in the Sky story
Vasco tells his mother about a dream where he and his friend Claudia took a rocket trip through space. During their journey to the moon, Claudia points out light pollution on Earth which obscures the night sky in some areas. Light pollution is harmful to animals like turtles and birds. At school, Vasco's class is working on a project about light pollution called "Dive into the Sky" which aims to reduce artificial light at night to see more stars. Vasco is enjoying learning new things through the project.
Space lesson (8 - 10 grade)
The document outlines an integrated English/Astronomy lesson plan for secondary school students about space exploration. It includes vocabulary building, a timeline fill-in-the-blank exercise about major space events, dividing students into groups to write questions about the timeline, and a question/answer activity where students test each other's knowledge in a game format. The lesson aims to teach students about space topics while practicing English vocabulary and questioning skills.
Bulgaria bilateral meeting
This document outlines the program for a bilateral meeting between schools in Bulgaria and Lithuania from July 6-10, 2015. The theme of the visit was to develop integrated astronomy and English lessons for primary and secondary schools. The schedule included a guided visit to Vasil Aprilov Primary School in Ruse, Bulgaria, a workshop for teachers to prepare lesson plans, astronomy lessons for different grade levels, visits to local museums, and an excursion to the Rock Monastery of St. Dimitar Basarbovski.
Evaluation of the project
1. Students and teachers from several European countries participated in a survey to evaluate the Comenius Multilateral Project "Dive in the Sky".
2. The results showed that students found sharing the European project, learning about partner countries, exchanging experiences with foreign students, practicing astronomy and foreign languages to be mostly good or excellent.
3. Teachers rated their relationships with partners, communication, sharing tasks and organizing visits as excellent and found the support from administrators, colleagues and students to be good.
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Immersive Learning That Works: Research Grounding and Paths Forward
We will metaverse into the essence of immersive learning, into its three dimensions and conceptual models. This approach encompasses elements from teaching methodologies to social involvement, through organizational concerns and technologies. Challenging the perception of learning as knowledge transfer, we introduce a 'Uses, Practices & Strategies' model operationalized by the 'Immersive Learning Brain' and ‘Immersion Cube’ frameworks. This approach offers a comprehensive guide through the intricacies of immersive educational experiences and spotlighting research frontiers, along the immersion dimensions of system, narrative, and agency. Our discourse extends to stakeholders beyond the academic sphere, addressing the interests of technologists, instructional designers, and policymakers. We span various contexts, from formal education to organizational transformation to the new horizon of an AI-pervasive society. This keynote aims to unite the iLRN community in a collaborative journey towards a future where immersive learning research and practice coalesce, paving the way for innovative educational research and practice landscapes.
Mending Clothing to Support Sustainable Fashion_CIMaR 2024.pdf
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JAMES WEBB STUDY THE MASSIVE BLACK HOLE SEEDS
The pathway(s) to seeding the massive black holes (MBHs) that exist at the heart of galaxies in the present and distant Universe remains an unsolved problem. Here we categorise, describe and quantitatively discuss the formation pathways of both light and heavy seeds. We emphasise that the most recent computational models suggest that rather than a bimodal-like mass spectrum between light and heavy seeds with light at one end and heavy at the other that instead a continuum exists. Light seeds being more ubiquitous and the heavier seeds becoming less and less abundant due the rarer environmental conditions required for their formation. We therefore examine the different mechanisms that give rise to different seed mass spectrums. We show how and why the mechanisms that produce the heaviest seeds are also among the rarest events in the Universe and are hence extremely unlikely to be the seeds for the vast majority of the MBH population. We quantify, within the limits of the current large uncertainties in the seeding processes, the expected number densities of the seed mass spectrum. We argue that light seeds must be at least 103 to 105 times more numerous than heavy seeds to explain the MBH population as a whole. Based on our current understanding of the seed population this makes heavy seeds (Mseed > 103 M⊙) a significantly more likely pathway given that heavy seeds have an abundance pattern than is close to and likely in excess of 10−4 compared to light seeds. Finally, we examine the current state-of-the-art in numerical calculations and recent observations and plot a path forward for near-future advances in both domains.
Pests of Storage_Identification_Dr.UPR.pdf
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Graininfestation
Directdamage
Indirectly
•theexuviae,skin,deadinsects
•theirexcretawhichmakefoodunfitforhumanconsumption
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Hello Everyone Here We are Sharing You with The process of protien Synthesis in very short points you will be Able to understand It Very well
在线办理(salfor毕业证书)索尔福德大学毕业证毕业完成信一模一样
学校原件一模一样【微信：741003700 】《(salfor毕业证书)索尔福德大学毕业证》【微信：741003700 】学位证，留信认证（真实可查，永久存档）原件一模一样纸张工艺/offer、雅思、外壳等材料/诚信可靠,可直接看成品样本，帮您解决无法毕业带来的各种难题！外壳，原版制作，诚信可靠，可直接看成品样本。行业标杆！精益求精，诚心合作，真诚制作！多年品质 ,按需精细制作，24小时接单,全套进口原装设备。十五年致力于帮助留学生解决难题，包您满意。
本公司拥有海外各大学样板无数，能完美还原。
1:1完美还原海外各大学毕业材料上的工艺：水印，阴影底纹，钢印LOGO烫金烫银，LOGO烫金烫银复合重叠。文字图案浮雕、激光镭射、紫外荧光、温感、复印防伪等防伪工艺。材料咨询办理、认证咨询办理请加学历顾问Q/微741003700
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留信网认证的作用:
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6:个人职称评审加20分
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Applied Science: Thermodynamics, Laws & Methodology.pdf
When I was asked to give a companion lecture in support of ‘The Philosophy of Science’ (https://shorturl.at/4pUXz) I decided not to walk through the detail of the many methodologies in order of use. Instead, I chose to employ a long standing, and ongoing, scientific development as an exemplar. And so, I chose the ever evolving story of Thermodynamics as a scientific investigation at its best.
Conducted over a period of >200 years, Thermodynamics R&D, and application, benefitted from the highest levels of professionalism, collaboration, and technical thoroughness. New layers of application, methodology, and practice were made possible by the progressive advance of technology. In turn, this has seen measurement and modelling accuracy continually improved at a micro and macro level.
Perhaps most importantly, Thermodynamics rapidly became a primary tool in the advance of applied science/engineering/technology, spanning micro-tech, to aerospace and cosmology. I can think of no better a story to illustrate the breadth of scientific methodologies and applications at their best.
Evidence of Jet Activity from the Secondary Black Hole in the OJ 287 Binary S...
Wereport the study of a huge optical intraday flare on 2021 November 12 at 2 a.m. UT in the blazar OJ287. In the binary black hole model, it is associated with an impact of the secondary black hole on the accretion disk of the primary. Our multifrequency observing campaign was set up to search for such a signature of the impact based on a prediction made 8 yr earlier. The first I-band results of the flare have already been reported by Kishore et al. (2024). Here we combine these data with our monitoring in the R-band. There is a big change in the R–I spectral index by 1.0 ±0.1 between the normal background and the flare, suggesting a new component of radiation. The polarization variation during the rise of the flare suggests the same. The limits on the source size place it most reasonably in the jet of the secondary BH. We then ask why we have not seen this phenomenon before. We show that OJ287 was never before observed with sufficient sensitivity on the night when the flare should have happened according to the binary model. We also study the probability that this flare is just an oversized example of intraday variability using the Krakow data set of intense monitoring between 2015 and 2023. We find that the occurrence of a flare of this size and rapidity is unlikely. In machine-readable Tables 1 and 2, we give the full orbit-linked historical light curve of OJ287 as well as the dense monitoring sample of Krakow.
Compexometric titration/Chelatorphy titration/chelating titration
Classification
Metal ion ion indicators
Masking and demasking reagents
Estimation of Magnisium sulphate
Calcium gluconate
Complexometric Titration/ chelatometry titration/chelating titration, introduction, Types-
1.Direct Titration
2.Back Titration
3.Replacement Titration
4.Indirect Titration
Masking agent, Demasking agents
formation of complex
comparition between masking and demasking agents,
Indicators/Metal ion indicators/ Metallochromic indicators/pM indicators,
Visual Technique,PM indicators (metallochromic), Indicators of pH, Redox Indicators
Instrumental Techniques-Photometry
Potentiometry
Miscellaneous methods.
Complex titration with EDTA.
Farming systems analysis: what have we learnt?.pptx
Presentation given at the official farewell of Prof Ken Gillet at Wageningen on 13 June 2024
Sexuality - Issues, Attitude and Behaviour - Applied Social Psychology - Psyc...
A proprietary approach developed by bringing together the best of learning theories from Psychology, design principles from the world of visualization, and pedagogical methods from over a decade of training experience, that enables you to: Learn better, faster!
Direct Seeded Rice - Climate Smart Agriculture
Direct Seeded Rice - Climate Smart AgricultureInternational Food Policy Research Institute- South Asia Office
PPT on Direct Seeded Rice presented at the three-day 'Training and Validation Workshop on Modules of Climate Smart Agriculture (CSA) Technologies in South Asia' workshop on April 22, 2024.
The binding of cosmological structures by massless topological defects
Assuming spherical symmetry and weak field, it is shown that if one solves the Poisson equation or the Einstein field
equations sourced by a topological defect, i.e. a singularity of a very specific form, the result is a localized gravitational
field capable of driving flat rotation (i.e. Keplerian circular orbits at a constant speed for all radii) of test masses on a thin
spherical shell without any underlying mass. Moreover, a large-scale structure which exploits this solution by assembling
concentrically a number of such topological defects can establish a flat stellar or galactic rotation curve, and can also deflect
light in the same manner as an equipotential (isothermal) sphere. Thus, the need for dark matter or modified gravity theory is
mitigated, at least in part.
MICROBIAL INTERACTION PPT/ MICROBIAL INTERACTION AND THEIR TYPES // PLANT MIC...
MICROBIAL INTERACTION PPT/ MICROBIAL INTERACTION AND THEIR TYPES // PLANT MIC...ABHISHEK SONI NIMT INSTITUTE OF MEDICAL AND PARAMEDCIAL SCIENCES , GOVT PG COLLEGE NOIDA
Microbial interaction
Microorganisms interacts with each other and can be physically associated with another organisms in a variety of ways.
One organism can be located on the surface of another organism as an ectobiont or located within another organism as endobiont.
Microbial interaction may be positive such as mutualism, proto-cooperation, commensalism or may be negative such as parasitism, predation or competition
Types of microbial interaction
Positive interaction: mutualism, proto-cooperation, commensalism
Negative interaction: Ammensalism (antagonism), parasitism, predation, competition
I. Mutualism:
It is defined as the relationship in which each organism in interaction gets benefits from association. It is an obligatory relationship in which mutualist and host are metabolically dependent on each other.
Mutualistic relationship is very specific where one member of association cannot be replaced by another species.
Mutualism require close physical contact between interacting organisms.
Relationship of mutualism allows organisms to exist in habitat that could not occupied by either species alone.
Mutualistic relationship between organisms allows them to act as a single organism.
Examples of mutualism:
i. Lichens:
Lichens are excellent example of mutualism.
They are the association of specific fungi and certain genus of algae. In lichen, fungal partner is called mycobiont and algal partner is called
II. Syntrophism:
It is an association in which the growth of one organism either depends on or improved by the substrate provided by another organism.
In syntrophism both organism in association gets benefits.
Compound A
Utilized by population 1
Compound B
Utilized by population 2
Compound C
utilized by both Population 1+2
Products
In this theoretical example of syntrophism, population 1 is able to utilize and metabolize compound A, forming compound B but cannot metabolize beyond compound B without co-operation of population 2. Population 2is unable to utilize compound A but it can metabolize compound B forming compound C. Then both population 1 and 2 are able to carry out metabolic reaction which leads to formation of end product that neither population could produce alone.
Examples of syntrophism:
i. Methanogenic ecosystem in sludge digester
Methane produced by methanogenic bacteria depends upon interspecies hydrogen transfer by other fermentative bacteria.
Anaerobic fermentative bacteria generate CO2 and H2 utilizing carbohydrates which is then utilized by methanogenic bacteria (Methanobacter) to produce methane.
ii. Lactobacillus arobinosus and Enterococcus faecalis:
In the minimal media, Lactobacillus arobinosus and Enterococcus faecalis are able to grow together but not alone.
The synergistic relationship between E. faecalis and L. arobinosus occurs in which E. faecalis require folic acid
11.1 Role of physical biological in deterioration of grains.pdf
Storagedeteriorationisanyformoflossinquantityandqualityofbio-materials.
Themajorcausesofdeteriorationinstorage
•Physical
•Biological
•Mechanical
•Chemical
Storageonlypreservesquality.Itneverimprovesquality.
Itisadvisabletostartstoragewithqualityfoodproduct.Productwithinitialpoorqualityquicklydepreciates
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Juaristi, Jon. - El canon espanol. El legado de la cultura española a la civi...
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11.1 Role of physical biological in deterioration of grains.pdf
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Eratosthenes
- 1. PRIMARY SCHOOL "VASIL APRILOV" - RUSE DIVE IN THE SKY
- 2. Eratosthenes of Cyrene was a Greek mathematician, geographer, poet, astronomer, and music theorist. He was a man of learning, becoming the chief librarian at the Library of Alexandria. He invented the discipline of geography, including the terminology used today. He is best known for being the first person to calculate the circumference of the Earth, which he did by applying a measuring system using stadia, a standard unit of measure during that time period. His calculation was remarkably accurate. He was also the first to calculate the tilt of the Earth's axis (again with remarkable accuracy). Additionally, he may have accurately calculated the distance from the Earth to the Sun and invented the leap day (February 29).
- 4. Eratosthenes' model depends on the assumption that the earth is a globe and that the sun is far away and therefore produces parallel rays of light all over the earth. If the sun is nearby, then shadows will change length even for a flat earth. A flat earth model is sketched below. The vertical stick casts shadows that grow longer as the stick moves to the left, away from the closest point to the sun. (The sun is at height h above the earth.)
- 7. Using the values 50 degrees and 60 degrees as measured on the trip, with b=1000 miles, we find that h is approximately 2000 miles. This relatively clos sun would have been quite plausible to the ancients. Continuing the calculation, we find that a is approximately 2400 miles and the two distances R1 and R2 are approximately 3000 and 3900 miles, respectively.
- 8. USING MATH TO FIND THE CIRCUMFERENCE OF THE EARTH
- 9. USING MATH TO FIND THE CIRCUMFERENCE OF THE EARTH A denotes the base of the pole in Alexandria; S the base of a pole in Syrene; T the tip of the shadow cast by the pole in Alexandria; P the top of the same pole; E the center of the Earth. Angle APT was measured to be 7o, so by Euclidean geometry interior angles and are equal, thus angle There are 360o in a complete circle, so the portion of the circumference of the Earth between A and S is which is approximately or is 50. The distance from Alexandria to Syrene is 800 km, so he concluded that the circumference of the Earth must be
- 10. March, 22
- 12. On March 21-22 the sun is directly overhead at the equator and appears 45 degrees above the horizon at 45 degrees north and south latitude. As the angle of sun above the earth at the equator is 90 degrees while it is 45 degrees at 45 degrees north or south latitude, it follows that the angle at the sun between the vertical from the horizon and the line from the observers at 45 degrees north and south must also be 45 degrees. The result is two right angled triangles with legs of equal length. The distance between the equator and the points at 45 degrees north or south is approximately 3,000 miles. Ergo, the sun would be an equal distance above the equator.
- 13. Bulgaria Location: 0°00'00.0", 0°00'00.0", 0m (Longitude referred to Greenwich meridian) Time Zone: Greenwich Date Begin Rise Az. Transit Alt. Set Az. End (Zone) Civil Civil Twilight Twilight h m h m ° h m ° h m ° h m 2015 Mar 22 (Sun) 05:43 06:04 89 12:07 89N 18:10 271 18:31 2015 Mar 23 (Mon) 05:43 06:03 89 12:07 89N 18:10 271 18:31 2015 Mar 24 (Tue) 05:42 06:03 89 12:06 89N 18:10 272 18:30 2015 Mar 25 (Wed) 05:42 06:03 88 12:06 88N 18:09 272 18:30 2015 Mar 26 (Thu) 05:42 06:03 88 12:06 88N 18:09 272 18:30
- 17. There is no other way to get a distance for the sun. Just looking at it from a single point on earth will not tell you its distance, you must look at it from several points and account for the curvature or non-curvature of the distance between those points.