Astronomical Orientation of Caves in Ajantha and Ellora
|
|
- Edwina Barbra Hodge
- 5 years ago
- Views:
Transcription
1 Astrnmical Orientatin f Caves in Ajantha and Ellra M. N. Vahia 1, A. P. Jamkhedkar 2 and Parag Mahajani 3 1. Tata Institute f Fundamental Research, Mumbai, Maharashtra, India ( vahia@tifr.res.in) 2. Ananthacharya Indlgical Research Institute, Cuffe Parade, Mumbai, Maharashtra, India 3. DSK Vishwa, Rhini I 301, Simhagad Rad, Dhayari, Pune , Maharashtra, India Received: 09 July 2017; Revised: 01 September 2017; Accepted: 05 Nvember 2017 Heritage: Jurnal f Multidisciplinary Studies in Archaelgy 5 (2017): Abstract: Ajantha and Ellra Caves in Central India are examples f Buddhist cave art and architecture. The caves at Ajantha are frm 100 BC t 500 AD divided int tw perids, early (100 BC t 230 AD) and late ( AD) perid crrespnding t Satavahana and Vakataka perids (Jamkhedkar, 2009, 4). We have studied the directinal and astrnmical rientatin f the caves at these tw lcatins. The caves at Ajantha are built in a hrse she curve while thse at Ellra are built n a West facing muntain range. Hwever, ur studies shw that in cnnectin with the caves at Ajantha, the early perid caves pint t suth while the later Vakata perid caves pint t East and West with sme specific rientatin. In particular the caves 22 t 29 seem clustered twards summer slstice. The caves at Ellra, while largely facing west, have significant clustering in the directin f slstices. We suggest that rientatin t cardinal directins must have been an imprtant part f design and develpment f the caves. Keywrds: Astrnmy, Orientatin, Caves, Ajantha, Ellra, Tpgraphy, Summer Slstice Intrductin The caves at Ajantha (20 32 N; E) and Ellra (20 2 N; E) and amngst the mst exquisitely carved and painted caves in India. They were created in tw majr perids, the early perids made in Satavahana perid are dated t 100 BC t 230 AD while a majrity f caves were made during Sakataka perid ( ) AD (Jamkhedkar, 2009:4). They cnsist f an intermingling f Buddhist, Jain and Hindu caves. Architecturally these caves have been well studied (See Jamkhedkar, 2009 fr a cmprehensive review). Hwever, their rientatin with respect t slstices and astrnmical references has nt been well studied. In the present study, we reprt the measurement f the rientatin f caves in Ajantha and Ellra and discuss their pssible astrnmical relevance. We have lked at all the individual caves at Ajantha and Ellra and measured their rientatin with respect t magnetic nrth frm inside lking ut and frm utside lking in. Since the difference between the magnetic
2 Vahia et al. 2017: nrth and gegraphical nrth is less than 1 degree fr the subcntinent, we assume that the magnetic nrth represents the gegraphic nrth. Caves at Ajantha There are 29 caves in Ajantha (Latitude N and lngitude E) arranged alng a hrseshe bend in the Waghra river. The sharply curving inner mst part f the cave distributin faces rughly suth (Figure 1). Figure 1: Orientatin f Ajantha Caves Of these caves, the central cmplex f caves, cave numbers 1 t 7 are 460 t 500 AD, 8 is transitinal. Cave numbers 9, 10, 12, 13 and 15A belng t the first perid (1 st Century BC t 2 nd Cent AD), built in its early phase. Out f these, the caves 9 and 10 are prayer halls, rest are residential. Caves 11, 14, 15, are in the secnd phase f the secnd perid. We have measured their rientatin and the relevant data. The results are given in table 1. We have als pltted the rientatin f the caves in figure 2. Since the general curvature f the tpgraphy f the Ajantha regin is in the frm f a hrseshe, the fall in angle f rientatin (Measured clckwise frm Nrth is expected t shw a mntnic trend as can be seen frm figure 2. Hwever, there are sme 807
3 ISSN Heritage: Jurnal f Multidisciplinary Studies in Archaelgy 5: 2017 interesting features t this graph. The caves 1 t 6 seem t fllw a mntnic trend that is significantly different frm ther caves. Caves 8 t 20 seem t fllw a unifrm trend in line with the curvature f the regin. Hwever, caves 21 t 29 have a significant deviatin frm the general curvature f the regin. Table 1: Data f Orientatin f Ajanta Caves Cave Mean Perid Cmments frm Jamkhedkar (2009) number Angle Vakataka Rich in rck art and stne architecture Vakataka Rich in rck art and stne architecture with paintings n the ceiling Vakataka Mst delicate f all caves Vakataka Seems t have been made bttm up Transitin Several carvings f Buddha Satvhana Prayer hall with 18 painted inscriptins f the Sakata Perid Satvhana Prayer hall extensively decrated with paintinds Satvhana Stupa cnverted t image later Satvhana Mnastery Satvhana Mnastery Satvhana 15 A Satvhana Vakataka Shws evlutin f new expressive styles in Buddhist carving Vakataka Cntains paintings frm Jataka stries Vakataka Magnificent Prayer Hall Vakataka Tiny residential unit Vakataka Vakataka Vakataka Vakataka Mst mdern Mst mdern withut a dedicated Inscriptin In figure 2 we have marked ut the directins and drift f the Sun ver the slstices alng with the pinting directin f each cave. The vals alng the line mark ut the perid f cnstructin f these caves while the hrizntal shaded regins mark ut the drift in the Sunrise r Sunset pint frm Summer Slstice t Winter slstice. Based n this, the fllwing cnclusins can be made. There are 3 grups f caves. In general the caves fllw the curvature f the regin 808
4 Vahia et al. 2017: Grups 2 and 3 seem t be largely aligned t the curvature f the regin Grup 1 seems t have tried hard t maintain East alignment. They seem t have wrked hard t break away frm curvature t maintain astrnmical directins. Grup 2 facing suth seems t g entirely with curvature. Grup 3 seems t be later due t precessinal ffset f abut 3 degree indicating a delay f abut 200 years in making them. Caves 1, 26 and 29 are aligned t Summer Slstice. They shuld be studied in detail. Cave n 21 is artificially riented t exact East and shuld als be studied Other caves in grup 1 shuld als be studied fr alignment n a specific day. Figure 2: Cave rientatins and details f directins and sunrise sunset pints. The shaded bands arund East and West mark the maximum drift f the Sun due t its annual mvement. The blue val marks the caves f the early perid while the ther circles mark caves f the later perid. Ellra Caves Ellra is cnstructed n a muntain range with a natural nrth suth rientatin. Hence nrmally caves are expected t pen t West. In table 2 belw we give the data fr select Ellra caves. We have measured the cave angle inwards frm the entrance. The layut f the Ellra caves (taken frm in.pinterest.cm/pin/ /) is given in figure 3. The results f these measurements are given in figure
5 ISSN Heritage: Jurnal f Multidisciplinary Studies in Archaelgy 5: Figure 3: Layut f Ellra Caves, (Nrth Twards Tp)
6 Vahia et al. 2017: Table 2: Orientatin f Caves in Ellra Cave N Cave Angle Cmments Grund flr Grund flr Devi temple Kailash Shaiva Cave Shaiva Cave Pashupati Cave 30 A 270 Chta Kailash Jain Jain Aurangabad Caves Figure 4: Orientatin f Ellra Caves. The shaded Regin Shws the Maximum Excursin f the Sun during Slstices. 811
7 ISSN Heritage: Jurnal f Multidisciplinary Studies in Archaelgy 5: 2017 Frm this, we can make the fllwing deductins. Out f the 18 caves studied: 4 caves (number 14, 21, 22, 29) are aligned t Summer Slstice sunset. Of these, 14 is Devi cave. 21, 22 and 29 are all Shaiva Cave (Pashupata) 4 caves (number 1, 2, 3, 4) Aurangabad Caves are aligned 30 exactly east f Suth. These are Buddhist caves facing suth is expected 3 caves (number 16, 23, 30) are aligned t exact West. Of these, 16 is Kailash, 23 is Shaiva and 30 is Rushabhnatha (Jain) 2 caves (number 5, and pssibly 26) t winter slstice sunset, Cave 4 is similar t cave 10 at Kanheri 1 cave (number 34) t exact East. Caves 30 and 34 are ppsite these are Jain Caves. 1 cave (number 8) is aligned t Nrth. This is a transitin phase cave. 1 cave (number 32) is aligned t Suth. These are Jain caves Samavsarna is held and is expected t face Suth Cave numbered 11, 12 and 26 are within the winter sunset shadw and may be aligned t sme specific dates Cnclusin The caves at Ajantha, fllw the general curvature. Hwever, within these limitatins, attempts seem t have been made t rient them t imprtant directins. The caves Ellra, while generally created n the west facing muntain, d have specific directinal rientatin with summer slstice sunset directin particularly well marked ut. Reference Jamkhedkar, A. P Ajanta: A mnumental Legacy. Oxfrd University Press. New Delhi. 812
14. Which shows the direction of the centripetal force acting on a mass spun in a vertical circle?
Physics 0 Public Exam Questins Unit 1: Circular Mtin NAME: August 009---------------------------------------------------------------------------------------------------------------------- 1. Which describes
More information14. Which shows the direction of the centripetal force acting on a mass spun in a vertical circle?
Physics 3204 Public Exam Questins Unit 1: Circular Mtin NAME: August 2009---------------------------------------------------------------------------------------------------------------------- 12. Which
More information37 Maxwell s Equations
37 Maxwell s quatins In this chapter, the plan is t summarize much f what we knw abut electricity and magnetism in a manner similar t the way in which James Clerk Maxwell summarized what was knwn abut
More informationPlate Tectonics and the Fossil Record
Plate Tectnics and the Fssil Recrd Accrding t the thery f plate tectnics, the earth's surface is dynamic. The current cnfiguratin f its land and cean masses is the result f mtins that have ccurred ver
More informationPhys101 First Major-131 Zero Version Coordinator: Dr. A. A. Naqvi Wednesday, September 25, 2013 Page: 1
Phys11 First Majr-11 Zer Versin Crdinatr: Dr. A. A. Naqvi Wednesday, September 5, 1 Page: 1 Q1. Cnsider tw unifrm slid spheres A and B made f the same material and having radii r A and r B, respectively.
More informationChapter 1 Notes Using Geography Skills
Chapter 1 Ntes Using Gegraphy Skills Sectin 1: Thinking Like a Gegrapher Gegraphy is used t interpret the past, understand the present, and plan fr the future. Gegraphy is the study f the Earth. It is
More informationEmpiricism, objectivity and falsifiability are important scientific tenets. Together they tell us that
Hmewrk 1! This is a preview f the draft versin f the quiz Started: Jan 27 at 9:12am Quiz Instruc!ns Questin 1 Empiricism, bjectivity and falsifiability are imprtant scientific tenets. Tgether they tell
More informationQ1. In figure 1, Q = 60 µc, q = 20 µc, a = 3.0 m, and b = 4.0 m. Calculate the total electric force on q due to the other 2 charges.
Phys10 Secnd Majr-08 Zer Versin Crdinatr: Dr. I. M. Nasser Saturday, May 3, 009 Page: 1 Q1. In figure 1, Q = 60 µc, q = 0 µc, a = 3.0 m, and b = 4.0 m. Calculate the ttal electric frce n q due t the ther
More informationASTRODYNAMICS. o o o. Early Space Exploration. Kepler's Laws. Nicolaus Copernicus ( ) Placed Sun at center of solar system
ASTRODYNAMICS Early Space Explratin Niclaus Cpernicus (1473-1543) Placed Sun at center f slar system Shwed Earth rtates n its axis nce a day Thught planets rbit in unifrm circles (wrng!) Jhannes Kepler
More informationSunrise and Sunset Times for the 22 nd of each month of 2012 in New York City
Sunrise and Sunset Times fr the nd f each mnth f 01 in New Yrk City January 01 Sunrise: 7:14am Sunset: 5:00pm February 01 Sunrise: 6:51am Sunset: 5:38pm March 01 Sunrise: 6:45am Sunset: 7:09pm April 01
More informationUsing GPS with Students High Tech Hide & Seek!
Using GPS with Students High Tech Hide & Seek! Intrductin: As we cntinue int the twenty-first century, we are cntinuusly being challenged by new technlgies. As teachers, we try t use technlgy effectively
More informationProject CONVERGE 1/13/15. How to Read CONVERGE CODAR Imagery Data Primer
Hw t Read CONVERGE CODAR Imagery Data Primer Overall Ntes abut the data: Everything is in Greenwich Mean Time (GMT), which is 5 hurs ahead f the east cst. All time is presented in military time, which
More informationDifferentiation Applications 1: Related Rates
Differentiatin Applicatins 1: Related Rates 151 Differentiatin Applicatins 1: Related Rates Mdel 1: Sliding Ladder 10 ladder y 10 ladder 10 ladder A 10 ft ladder is leaning against a wall when the bttm
More informationIntroduction to Smith Charts
Intrductin t Smith Charts Dr. Russell P. Jedlicka Klipsch Schl f Electrical and Cmputer Engineering New Mexic State University as Cruces, NM 88003 September 2002 EE521 ecture 3 08/22/02 Smith Chart Summary
More informationCONSTRUCTING STATECHART DIAGRAMS
CONSTRUCTING STATECHART DIAGRAMS The fllwing checklist shws the necessary steps fr cnstructing the statechart diagrams f a class. Subsequently, we will explain the individual steps further. Checklist 4.6
More informationmaking triangle (ie same reference angle) ). This is a standard form that will allow us all to have the X= y=
Intrductin t Vectrs I 21 Intrductin t Vectrs I 22 I. Determine the hrizntal and vertical cmpnents f the resultant vectr by cunting n the grid. X= y= J. Draw a mangle with hrizntal and vertical cmpnents
More informationSPH3U1 Lesson 06 Kinematics
PROJECTILE MOTION LEARNING GOALS Students will: Describe the mtin f an bject thrwn at arbitrary angles thrugh the air. Describe the hrizntal and vertical mtins f a prjectile. Slve prjectile mtin prblems.
More informationCESAR Science Case The differential rotation of the Sun and its Chromosphere. Introduction. Material that is necessary during the laboratory
Teacher s guide CESAR Science Case The differential rtatin f the Sun and its Chrmsphere Material that is necessary during the labratry CESAR Astrnmical wrd list CESAR Bklet CESAR Frmula sheet CESAR Student
More informationChemistry 20 Lesson 11 Electronegativity, Polarity and Shapes
Chemistry 20 Lessn 11 Electrnegativity, Plarity and Shapes In ur previus wrk we learned why atms frm cvalent bnds and hw t draw the resulting rganizatin f atms. In this lessn we will learn (a) hw the cmbinatin
More informationAP Statistics Notes Unit Two: The Normal Distributions
AP Statistics Ntes Unit Tw: The Nrmal Distributins Syllabus Objectives: 1.5 The student will summarize distributins f data measuring the psitin using quartiles, percentiles, and standardized scres (z-scres).
More informationFinding the Earth s magnetic field
Labratry #6 Name: Phys 1402 - Dr. Cristian Bahrim Finding the Earth s magnetic field The thery accepted tday fr the rigin f the Earth s magnetic field is based n the mtin f the plasma (a miture f electrns
More informationWriting Guidelines. (Updated: November 25, 2009) Forwards
Writing Guidelines (Updated: Nvember 25, 2009) Frwards I have fund in my review f the manuscripts frm ur students and research assciates, as well as thse submitted t varius jurnals by thers that the majr
More informationGAUSS' LAW E. A. surface
Prf. Dr. I. M. A. Nasser GAUSS' LAW 08.11.017 GAUSS' LAW Intrductin: The electric field f a given charge distributin can in principle be calculated using Culmb's law. The examples discussed in electric
More informationMatter & Interactions Chapter 17 Solutions
Matter & Interactins Chapter 7 Slutins are int the page ( z directin, and and 6 are ut f the page (+z directin. Due t symmetry, 3 6 4. µ q v ˆr sin θ 4π r 2 T ( m 0 7 A (.6 0 9 C(5 0 6 m/s( sin 25 (0.08
More informationPopulation Structure and Migration Patterns of Atlantic Cod (Gadus morhua) in West Greenland Waters Based on Tagging Experiments from 1946 to 1964
NAFO Sci. Cun. Studies, : - Ppulatin Structure and Migratin Patterns f Atlantic Cd (Gadus mrhua) in West Greenland Waters Based n Tagging Experiments frm t Hlger Hvgard Greenland Fisheries Research Institute
More information= m. Suppose the speed of a wave on a string is given by v = Κ τμ
Phys101 First Majr-11 Zer Versin Sunday, Octber 07, 01 Page: 1 Q1. Find the mass f a slid cylinder f cpper with a radius f 5.00 cm and a height f 10.0 inches if the density f cpper is 8.90 g/cm 3 (1 inch
More informationA Polarimetric Survey of Radio Frequency Interference in C- and X-Bands in the Continental United States using WindSat Radiometry
A Plarimetric Survey f Radi Frequency Interference in C- and X-Bands in the Cntinental United States using WindSat Radimetry Steven W. Ellingsn Octber, Cntents Intrductin WindSat Methdlgy Analysis f RFI
More informationPhysics 212. Lecture 12. Today's Concept: Magnetic Force on moving charges. Physics 212 Lecture 12, Slide 1
Physics 1 Lecture 1 Tday's Cncept: Magnetic Frce n mving charges F qv Physics 1 Lecture 1, Slide 1 Music Wh is the Artist? A) The Meters ) The Neville rthers C) Trmbne Shrty D) Michael Franti E) Radiatrs
More informationA study on GPS PDOP and its impact on position error
IndianJurnalfRadi& SpacePhysics V1.26,April1997,pp. 107-111 A study n GPS and its impact n psitin errr P Banerjee,AnindyaBse& B SMathur TimeandFrequencySectin,NatinalPhysicalLabratry,NewDelhi110012 Received19June
More informationPlate 5. Giovanni Paolo Panini, The Interior of the Pantheon, Oil on canvas. Detroit Museum of Art
The Rman Panthen One f the mst impressive structures f Rman antiquity is the Panthen (never t be cnfused with the Parthenn in Athens). Its supervising architect was the Rman emperr Hadrian. It was built
More informationPrecalculus A. Semester Exam Review
Precalculus A 015-016 MCPS 015 016 1 The semester A eaminatin fr Precalculus cnsists f tw parts. Part 1 is selected respnse n which a calculatr will NOT be allwed. Part is shrt answer n which a calculatr
More informationWeathering. Title: Chemical and Mechanical Weathering. Grade Level: Subject/Content: Earth and Space Science
Weathering Title: Chemical and Mechanical Weathering Grade Level: 9-12 Subject/Cntent: Earth and Space Science Summary f Lessn: Students will test hw chemical and mechanical weathering can affect a rck
More informationAstro 102 Lab #2. 1) Learning the user interface and setting up your home location
Name: Astr 102 Lab #2 Lab bjectives 1) Learn hw t use the Stellarium planetarium prgram by becming familiar with the user interface and cnfiguring the planetarium t yur present lcatin n Earth 2) Learn
More informationROUNDING ERRORS IN BEAM-TRACKING CALCULATIONS
Particle Acceleratrs, 1986, Vl. 19, pp. 99-105 0031-2460/86/1904-0099/$15.00/0 1986 Grdn and Breach, Science Publishers, S.A. Printed in the United States f America ROUNDING ERRORS IN BEAM-TRACKING CALCULATIONS
More information, which yields. where z1. and z2
The Gaussian r Nrmal PDF, Page 1 The Gaussian r Nrmal Prbability Density Functin Authr: Jhn M Cimbala, Penn State University Latest revisin: 11 September 13 The Gaussian r Nrmal Prbability Density Functin
More informationPages with the symbol indicate that a student should be prepared to complete items like these with or without a calculator. tan 2.
Semester Eam Review The semester A eaminatin fr Hnrs Precalculus cnsists f tw parts. Part 1 is selected respnse n which a calculatr will NOT be allwed. Part is shrt answer n which a calculatr will be allwed.
More informationOverview of the Molecule:
Prtein Mdeling Event Guide t Scring the Invitatinal Pre-Build Mdel Fr Science Olympiad 2016 Invitatinal Cmpetitin These instructins are t help the event supervisr and scring judges use the rubric develped
More informationPhysics 2010 Motion with Constant Acceleration Experiment 1
. Physics 00 Mtin with Cnstant Acceleratin Experiment In this lab, we will study the mtin f a glider as it accelerates dwnhill n a tilted air track. The glider is supprted ver the air track by a cushin
More informationQUIZ Fundamentals of Daylighting 1h30
MIT Architecture Fall 6 Curse 4.4 Daylighting M. Andersen Octber 17, 6 QUIZ Fundamentals f Daylighting 1h Questins pts 3 pts a. Hw wuld yu describe the greenhuse effect bserved inside a glazed space? Hw
More information1.2.1 Vectors. 1 P age. Examples What is the reference vector angle for a vector that points 50 degrees east of south?
1.2.1 Vectrs Definitins Vectrs are represented n paper by arrws directin = magnitude = Examples f vectrs: Examples What is the reference vectr angle fr a vectr that pints 50 degrees east f suth? What is
More informationFlipping Physics Lecture Notes: Simple Harmonic Motion Introduction via a Horizontal Mass-Spring System
Flipping Physics Lecture Ntes: Simple Harmnic Mtin Intrductin via a Hrizntal Mass-Spring System A Hrizntal Mass-Spring System is where a mass is attached t a spring, riented hrizntally, and then placed
More informationFlipping Physics Lecture Notes: Simple Harmonic Motion Introduction via a Horizontal Mass-Spring System
Flipping Physics Lecture Ntes: Simple Harmnic Mtin Intrductin via a Hrizntal Mass-Spring System A Hrizntal Mass-Spring System is where a mass is attached t a spring, riented hrizntally, and then placed
More informationLECTURE From Measurement of Pressure and Quantity of Air in. 7.2 From Measurement of Pressure and Quantities in the
LECTURE 1 THE CONTENTS OF THIS LECTURE ARE AS FOLLOWS: 1.0 NATURAL VENTILATION.0 PRODUCTION OF NATURAL VENTILATION 3.0 DENSITY DIFFERENCE BETWEEN THE AIR OF TWO SHAFTS 4.0 DEFINITION OF NATURAL VENTILATING
More informationChapter 2 GAUSS LAW Recommended Problems:
Chapter GAUSS LAW Recmmended Prblems: 1,4,5,6,7,9,11,13,15,18,19,1,7,9,31,35,37,39,41,43,45,47,49,51,55,57,61,6,69. LCTRIC FLUX lectric flux is a measure f the number f electric filed lines penetrating
More informationThis project has received funding from the European Union s Horizon 2020 research and innovation programme under grant agreement number
This prject has received funding frm the Eurpean Unin s Hrizn 2020 research and innvatin prgramme under grant agreement number 727524. Credit t & http://www.h3uni.rg/ https://ec.eurpa.eu/jrc/en/publicatin/eur-scientific-andtechnical-research-reprts/behaviural-insights-appliedplicy-eurpean-reprt-2016
More information(s6 ~lj t') >~.'c;. .. ' ' 9adanki ( N, E)',- !2!!!m'!!.y~ation-6fhorizont~~cb' in the ~()wert.~2qq~~hereover --:!"
t (s6 ~lj t') \ >""\., ~hysia Indian Jurnal f 11adi&Sp8Ce V~3.February 1994,pp. ~::4().,I\' :!",,,. 'I\.J \ '0f"'~ r't t ~.'c;. ~~ \,!2!!!m'!!.y~atin6fhriznt~~cb' in the ~()wert.~2qq~~herever.. '
More informationRegents Chemistry Period Unit 3: Atomic Structure. Unit 3 Vocabulary..Due: Test Day
Name Skills: 1. Interpreting Mdels f the Atm 2. Determining the number f subatmic particles 3. Determine P, e-, n fr ins 4. Distinguish istpes frm ther atms/ins Regents Chemistry Perid Unit 3: Atmic Structure
More informationEvaluation of the outdoor thermal environment in redevelopment buildings in front of Osaka Station based on observations
Academic Article Jurnal f Heat Island Institute Internatinal Vl. 9-2 (2014) Evaluatin f the utdr thermal envirnment in redevelpment buildings in frnt f Osaka Statin based n bservatins Kentar Ayama *1 Sae
More informationMAJOR 40,000m GOLD EXPLORATION DRILLING PROGRAM COMMENCES
2 Nvember 2016 MAJOR 40,000m GOLD EXPLORATION DRILLING PROGRAM COMMENCES Highlights A majr explratin drilling prgram has cmmenced n the Tampia Gld Prject t scpe the extent f the knwn gld resurce thrugh
More informationPhys101 Final Code: 1 Term: 132 Wednesday, May 21, 2014 Page: 1
Phys101 Final Cde: 1 Term: 1 Wednesday, May 1, 014 Page: 1 Q1. A car accelerates at.0 m/s alng a straight rad. It passes tw marks that are 0 m apart at times t = 4.0 s and t = 5.0 s. Find the car s velcity
More informationSIZE BIAS IN LINE TRANSECT SAMPLING: A FIELD TEST. Mark C. Otto Statistics Research Division, Bureau of the Census Washington, D.C , U.S.A.
SIZE BIAS IN LINE TRANSECT SAMPLING: A FIELD TEST Mark C. Ott Statistics Research Divisin, Bureau f the Census Washingtn, D.C. 20233, U.S.A. and Kenneth H. Pllck Department f Statistics, Nrth Carlina State
More informationUnit Project Descriptio
Unit Prject Descriptin: Using Newtn s Laws f Mtin and the scientific methd, create a catapult r trebuchet that will sht a marshmallw at least eight feet. After building and testing yur machine at hme,
More informationBOUNDED UNCERTAINTY AND CLIMATE CHANGE ECONOMICS. Christopher Costello, Andrew Solow, Michael Neubert, and Stephen Polasky
BOUNDED UNCERTAINTY AND CLIMATE CHANGE ECONOMICS Christpher Cstell, Andrew Slw, Michael Neubert, and Stephen Plasky Intrductin The central questin in the ecnmic analysis f climate change plicy cncerns
More informationTo get you thinking...
T get yu thinking... 1.) What is an element? Give at least 4 examples f elements. 2.) What is the atmic number f hydrgen? What des a neutral hydrgen atm cnsist f? Describe its "mtin". 3.) Hw des an atm
More informationCLASS. Fractions and Angles. Teacher Report. No. of test takers: 25. School Name: EI School. City: Ahmedabad CLASS 6 B 8709
SEPTEMBER 07 Math Fractins and Angles CLASS 6 Teacher Reprt Test Taken 4 5 6 7 8 Schl Name: EI Schl City: Ahmedabad CLASS SECTION EXAM CODE 6 B 8709 N. f test takers: 5 6.5 Average.5 9.0 Range (Scres are
More informationQ1. A string of length L is fixed at both ends. Which one of the following is NOT a possible wavelength for standing waves on this string?
Term: 111 Thursday, January 05, 2012 Page: 1 Q1. A string f length L is fixed at bth ends. Which ne f the fllwing is NOT a pssible wavelength fr standing waves n this string? Q2. λ n = 2L n = A) 4L B)
More informationName: Period: Date: PERIODIC TABLE NOTES ADVANCED CHEMISTRY
Name: Perid: Date: PERIODIC TABLE NOTES ADVANCED CHEMISTRY Directins: This packet will serve as yur ntes fr this chapter. Fllw alng with the PwerPint presentatin and fill in the missing infrmatin. Imprtant
More informationSurface and Contact Stress
Surface and Cntact Stress The cncept f the frce is fundamental t mechanics and many imprtant prblems can be cast in terms f frces nly, fr example the prblems cnsidered in Chapter. Hwever, mre sphisticated
More informationSYNTHESIS OF TWO MECHANISMS WHICH GENERATE LUNULES OVER AN EQUILATERAL TRIANGLE S SIDES
SYNTHESIS OF TWO MECHANISMS WHICH GENERATE LUNULES OVER AN EQUILATERAL TRIANGLE S SIDES Assciate Prfessr PhD Ludmila SASS, University f Craiva, Faculty f Mechanics, ludmila_sass@yah.cm Prfessr Iulian POPESCU,
More informationName: Period: Date: PERIODIC TABLE NOTES HONORS CHEMISTRY
Name: Perid: Date: PERIODIC TABLE NOTES HONORS CHEMISTRY Directins: This packet will serve as yur ntes fr this chapter. Fllw alng with the PwerPint presentatin and fill in the missing infrmatin. Imprtant
More informationCESAR Science Case Rotation period of the Sun and the sunspot activity
Teacher s guide CESAR Science Case Rtatin perid f the Sun and the sunspt activity The students can use different ways during the labratry and there are diverse methds t use. Material that is necessary
More informationHigher Mathematics Booklet CONTENTS
Higher Mathematics Bklet CONTENTS Frmula List Item Pages The Straight Line Hmewrk The Straight Line Hmewrk Functins Hmewrk 3 Functins Hmewrk 4 Recurrence Relatins Hmewrk 5 Differentiatin Hmewrk 6 Differentiatin
More informationTHE LIFE OF AN OBJECT IT SYSTEMS
THE LIFE OF AN OBJECT IT SYSTEMS Persns, bjects, r cncepts frm the real wrld, which we mdel as bjects in the IT system, have "lives". Actually, they have tw lives; the riginal in the real wrld has a life,
More informationConcept Category 2. Trigonometry & The Unit Circle
Cncept Categry 2 Trignmetry & The Unit Circle Skill Checklist Use special right triangles t express values f fr the six trig functins Evaluate sine csine and tangent using the unit circle Slve tw-step
More informationPhys102 Second Major-102 Zero Version Coordinator: Al-Shukri Thursday, May 05, 2011 Page: 1
Crdinatr: Al-Shukri Thursday, May 05, 2011 Page: 1 1. Particles A and B are electrically neutral and are separated by 5.0 μm. If 5.0 x 10 6 electrns are transferred frm particle A t particle B, the magnitude
More informationThe Legacy of Ancient Greece
The Legacy f Ancient Greece 31.1 Intrductin (p.297) Stry f Archimedes ( Eureka! ) Curisity and careful bservatin are imprtant parts f science This way f thinking is just ne f the gifts we have received
More information1. Introduction. Lab 4 - Geophysics 424, October 29, One-dimensional Interpretation of Magnetotelluric Data
Lab 4 - Gephysics 424, Octber 29, 2018 One-dimensinal Interpretatin f Magnettelluric Data Lab reprt is due by 5 p.m. Nvember 5, 2018 All late reprts require a valid reasn t be accepted. Include answers
More informationM thematics. National 5 Practice Paper E. Paper 1. Duration 1 hour. Total marks 40
N5 M thematics Natinal 5 Practice Paper E Paper 1 Duratin 1 hur Ttal marks 40 Yu may NOT use a calculatr Attempt all the questins. Use blue r black ink. Full credit will nly be given t slutins which cntain
More informationPhys102 Final-061 Zero Version Coordinator: Nasser Wednesday, January 24, 2007 Page: 1
Crdinatr: Nasser Wednesday, January 4, 007 Page: 1 Q1. Tw transmitters, S 1 and S shwn in the figure, emit identical sund waves f wavelength λ. The transmitters are separated by a distance λ /. Cnsider
More informationWe can see from the graph above that the intersection is, i.e., [ ).
MTH 111 Cllege Algebra Lecture Ntes July 2, 2014 Functin Arithmetic: With nt t much difficulty, we ntice that inputs f functins are numbers, and utputs f functins are numbers. S whatever we can d with
More informationBuilding to Transformations on Coordinate Axis Grade 5: Geometry Graph points on the coordinate plane to solve real-world and mathematical problems.
Building t Transfrmatins n Crdinate Axis Grade 5: Gemetry Graph pints n the crdinate plane t slve real-wrld and mathematical prblems. 5.G.1. Use a pair f perpendicular number lines, called axes, t define
More informationo Land and water both are heated by solar radiation, but land
Benchmark: SC.D.l.4.1 The student knws hw climatic patterns n Earth result frm an interplay f many factrs (Earth's tpgraphy, its rtatin'tn its axis, slar radiatin, the transfer f heat energy where the
More informationEFFECTS OF FLOWERING ON SUCROSE CONTENT AND SUCROSE YIELD IN FIVE SUGARCANE VARIETIES
EECTS O LOWERING ON SUCROSE CONTENT AND SUCROSE YIELD IN IVE SUGARCANE VARIETIES By K. J. NUSS Suth African Sugar Assciatin Experiment Statin, Munt Edgecmbe 43 Abstract The yield and quality traits f flwered
More informationSOIL PROPERTIES STUDY NOTES
SOIL PROPERTIES STUDY NOTES UNIT I SOIL PROPERTIES Objectives and Values f Getechnical Engineering Physical prperties f sil Phase relatins, Grain size distributin, Atterberg Limits, Sil descriptin and
More informationHow do scientists measure trees? What is DBH?
Hw d scientists measure trees? What is DBH? Purpse Students develp an understanding f tree size and hw scientists measure trees. Students bserve and measure tree ckies and explre the relatinship between
More informationREADING STATECHART DIAGRAMS
READING STATECHART DIAGRAMS Figure 4.48 A Statechart diagram with events The diagram in Figure 4.48 shws all states that the bject plane can be in during the curse f its life. Furthermre, it shws the pssible
More information4 electron domains: 3 bonding and 1 non-bonding. 2 electron domains: 2 bonding and 0 non-bonding. 3 electron domains: 2 bonding and 1 non-bonding
[4.3D VSEPR] pg. 1 f 7 Curriculum The use f VSEPR thery t predict the electrn dmain gemetry and the mlecular gemetry fr species with tw, three and fur electrn dmains. Shapes f species are determined by
More informationAP Physics Kinematic Wrap Up
AP Physics Kinematic Wrap Up S what d yu need t knw abut this mtin in tw-dimensin stuff t get a gd scre n the ld AP Physics Test? First ff, here are the equatins that yu ll have t wrk with: v v at x x
More informationPreparation work for A2 Mathematics [2017]
Preparatin wrk fr A2 Mathematics [2017] The wrk studied in Y12 after the return frm study leave is frm the Cre 3 mdule f the A2 Mathematics curse. This wrk will nly be reviewed during Year 13, it will
More informationLab #3: Pendulum Period and Proportionalities
Physics 144 Chwdary Hw Things Wrk Spring 2006 Name: Partners Name(s): Intrductin Lab #3: Pendulum Perid and Prprtinalities Smetimes, it is useful t knw the dependence f ne quantity n anther, like hw the
More information1 Course Notes in Introductory Physics Jeffrey Seguritan
Intrductin & Kinematics I Intrductin Quickie Cncepts Units SI is standard system f units used t measure physical quantities. Base units that we use: meter (m) is standard unit f length kilgram (kg) is
More informationMultipole Vortices in an ECR Plasma
J. Plasma Fusin Res. SERIES, Vl. 4 (2001) 363-36'l Multiple Vrtices in an ECR Plasma OKAMOTO Atsushi*, ISHIHARA Tatsuz, NAGAOKA Kenichi, YOSHIMURA Shinjit and TANAKA Masayshi y.r Nagya University, Nagya
More informationFractal dimensions of convective clouds around Delhi
, j Indian Jurnal f Radi & Space Physics Vl. 27, February 1998, pp.i-6 Fractal dimensins f cnvective cluds arund Delhi Kaushar AIi, R N Chatterjee, Prem Prakash & P C S Devara Indian Institute f Trpical
More informationDetermination of Static Orientation Using IMU Data Revision 1
Determinatin f Static Orientatin Usin IMU Data Revisin 1 Determinatin f Static Orientatin frm IMU Accelermeter and Manetmeter Data Intrductin An imprtant applicatin f inertial data is the rientatin determinatin
More informationPhy 213: General Physics III 6/14/2007 Chapter 28 Worksheet 1
Ph 13: General Phsics III 6/14/007 Chapter 8 Wrksheet 1 Magnetic Fields & Frce 1. A pint charge, q= 510 C and m=110-3 m kg, travels with a velcit f: v = 30 ˆ s i then enters a magnetic field: = 110 T ˆj.
More informationName Honors Chemistry / /
Name Hnrs Chemistry / / Beynd Lewis Structures Exceptins t the Octet Rule Mdel Hydrgen is an exceptin t the ctet rule because it fills its uter energy level with nly 2 electrns. The secnd rw elements B
More informationACCELEROGRAPH RECORDINGS OF THE M USA EARTHQUAKE 16 SEPTEMBER, 1972
115 ACCELEROGRAPH RECORDINGS OF THE M USA EARTHQUAKE 16 SEPTEMBER, 1972 B.Gauir SUMMARY On 16 September, 1972 at 04 15 09.8 UT an earthquake f magnitude ML 5.0 ccurred in sutheast Papua within abut 20
More informationLesson Plan. Recode: They will do a graphic organizer to sequence the steps of scientific method.
Lessn Plan Reach: Ask the students if they ever ppped a bag f micrwave ppcrn and nticed hw many kernels were unppped at the bttm f the bag which made yu wnder if ther brands pp better than the ne yu are
More informationTrigonometry, 8th ed; Lial, Hornsby, Schneider
Trignmetry, 8th ed; Lial, Hrnsby, Schneider Trignmetry Final Exam Review: Chapters 7, 8, 9 Nte: A prtin f Exam will cver Chapters 1 6, s be sure yu rewrk prblems frm the first and secnd exams and frm the
More informationCHAPTER 3 INEQUALITIES. Copyright -The Institute of Chartered Accountants of India
CHAPTER 3 INEQUALITIES Cpyright -The Institute f Chartered Accuntants f India INEQUALITIES LEARNING OBJECTIVES One f the widely used decisin making prblems, nwadays, is t decide n the ptimal mix f scarce
More informationHomology groups of disks with holes
Hmlgy grups f disks with hles THEOREM. Let p 1,, p k } be a sequence f distinct pints in the interir unit disk D n where n 2, and suppse that fr all j the sets E j Int D n are clsed, pairwise disjint subdisks.
More informationMatter Content from State Frameworks and Other State Documents
Atms and Mlecules Mlecules are made f smaller entities (atms) which are bnded tgether. Therefre mlecules are divisible. Miscnceptin: Element and atm are synnyms. Prper cnceptin: Elements are atms with
More informationM thematics. National 5 Practice Paper D. Paper 1. Duration 1 hour. Total marks 40
N5 M thematics Natinal 5 Practice Paper D Paper 1 Duratin 1 hur Ttal marks 40 Yu may NOT use a calculatr Attempt all the questins. Use blue r black ink. Full credit will nly be given t slutins which cntain
More informationLESSON 10: NEITHER PLANT NOR ANIMAL
L I F E I N G E N E R A L LESSON 10: NEITHER PLANT NOR ANIMAL READING & RESEARCH Read KSE Fungi and Lichens, p. 55. Read USE Fungi, pp. 284-285. Read DSE Fungi, p. 315. DEFINITIONS Define the fllwing terms,
More informationCorrections for the textbook answers: Sec 6.1 #8h)covert angle to a positive by adding period #9b) # rad/sec
U n i t 6 AdvF Date: Name: Trignmetric Functins Unit 6 Tentative TEST date Big idea/learning Gals In this unit yu will study trignmetric functins frm grade, hwever everything will be dne in radian measure.
More informationPhysics 101 Math Review. Solutions
Physics 0 Math eview Slutins . The fllwing are rdinary physics prblems. Place the answer in scientific ntatin when apprpriate and simplify the units (Scientific ntatin is used when it takes less time t
More informationKepler's Laws of Planetary Motion
Writing Assignment Essay n Kepler s Laws. Yu have been prvided tw shrt articles n Kepler s Three Laws f Planetary Mtin. Yu are t first read the articles t better understand what these laws are, what they
More informationSection 6-2: Simplex Method: Maximization with Problem Constraints of the Form ~
Sectin 6-2: Simplex Methd: Maximizatin with Prblem Cnstraints f the Frm ~ Nte: This methd was develped by Gerge B. Dantzig in 1947 while n assignment t the U.S. Department f the Air Frce. Definitin: Standard
More informationAP Statistics Practice Test Unit Three Exploring Relationships Between Variables. Name Period Date
AP Statistics Practice Test Unit Three Explring Relatinships Between Variables Name Perid Date True r False: 1. Crrelatin and regressin require explanatry and respnse variables. 1. 2. Every least squares
More informationChapter 6 Fingerprints By the end of this chapter you will be able to:
Chapter 6 Fingerprints By the end f this chapter yu will be able t: Discuss the histry f fingerprinting Describe the characteristics f fingerprints and fingerprinting minutiae Explain when and hw fingerprints
More information