The Astronomical Units
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Quantity Symbol Value One Astronomical Unit 1 AU 1.50 × 10
Quantity Symbol Value One Astronomical Unit 1 AU 1:50 × 1011 m Speed of Light c 3:0 × 108 m=s One parsec 1 pc 3.26 Light Years One year 1 y ' π × 107 s One Light Year 1 ly 9:5 × 1015 m 6 Radius of Earth RE 6:4 × 10 m Radius of Sun R 6:95 × 108 m Gravitational Constant G 6:67 × 10−11m3=(kg s3) Part I. 1. Describe qualitatively the funny way that the planets move in the sky relative to the stars. Give a qualitative explanation as to why they move this way. 2. Draw a set of pictures approximately to scale showing the sun, the earth, the moon, α-centauri, and the milky way and the spacing between these objects. Give an ap- proximate size for all the objects you draw (for example example next to the moon put Rmoon ∼ 1700 km) and the distances between the objects that you draw. Indicate many times is one picture magnified relative to another. Important: More important than the size of these objects is the relative distance between these objects. Thus for instance you may wish to show the sun and the earth on the same graph, with the circles for the sun and the earth having the correct ratios relative to to the spacing between the sun and the earth. 3. A common unit of distance in Astronomy is a parsec. 1 pc ' 3:1 × 1016m ' 3:3 ly (a) Explain how such a curious unit of measure came to be defined. Why is it called parsec? (b) What is the distance to the nearest stars and how was this distance measured? 4. -
Units, Conversations, and Scaling Giving Numbers Meaning and Context Author: Meagan White; Sean S
Units, Conversations, and Scaling Giving numbers meaning and context Author: Meagan White; Sean S. Lindsay Version 1.3 created August 2019 Learning Goals In this lab, students will • Learn about the metric system • Learn about the units used in science and astronomy • Learn about the units used to measure angles • Learn the two sky coordinate systems used by astronomers • Learn how to perform unit conversions • Learn how to use a spreadsheet for repeated calculations • Measure lengths to collect data used in next week’s lab: Scienctific Measurement Materials • Calculator • Microsoft Excel • String as a crude length measurement tool Pre-lab Questions 1. What is the celestial analog of latitude and longitude? 2. What quantity do the following metric prefixes indicate: Giga-, Mega-, kilo-, centi-, milli-, µicro-, and nano? 3. How many degrees is a Right Ascension “hour”; How many degrees are in an arcmin? Arcsec? 4. Use the “train-track” method to convert 20 ft to inches. 1. Background In any science class, including astronomy, there are important skills and concepts that students will need to use and understand before engaging in experiments and other lab exercises. A broad list of fundamental skills developed in today’s exercise includes: • Scientific units used throughout the international science community, as well as units specific to astronomy. • Unit conversion methods to convert between units for calculations, communication, and conceptualization. • Angular measurements and their use in astronomy. How they are measured, and the angular measurements specific to astronomy. This is important for astronomers coordinate systems, i.e., equatorial coordinates on the celestial sphere. • Familiarity with spreadsheet programs, such as Microsoft Excel, Google Sheets, or OpenOffice. -
Distances in the Solar System Are Often Measured in Astronomical Units (AU). One Astronomical Unit Is Defined As the Distance from Earth to the Sun
Distances in the solar system are often measured in astronomical units (AU). One astronomical unit is defined as the distance from Earth to the Sun. 1 AU equals about 150 million km (93 million miles). Table below shows the distance from the Sun to each planet in AU. The table shows how long it takes each planet to spin on its axis. It also shows how long it takes each planet to complete an orbit. Notice how slowly Venus rotates! A day on Venus is actually longer than a year on Venus! Distances to the Planets and Properties of Orbits Relative to Earth's Orbit Average Distance Length of Day (In Earth Length of Year (In Earth Planet from Sun (AU) Days) Years) Mercury 0.39 AU 56.84 days 0.24 years Venus 0.72 243.02 0.62 Earth 1.00 1.00 1.00 Mars 1.52 1.03 1.88 Jupiter 5.20 0.41 11.86 Saturn 9.54 0.43 29.46 Uranus 19.22 0.72 84.01 Neptune 30.06 0.67 164.8 The Role of Gravity Planets are held in their orbits by the force of gravity. What would happen without gravity? Imagine that you are swinging a ball on a string in a circular motion. Now let go of the string. The ball will fly away from you in a straight line. It was the string pulling on the ball that kept the ball moving in a circle. The motion of a planet is very similar to the ball on a strong. -
Measuring the Astronomical Unit from Your Backyard Two Astronomers, Using Amateur Equipment, Determined the Scale of the Solar System to Better Than 1%
Measuring the Astronomical Unit from Your Backyard Two astronomers, using amateur equipment, determined the scale of the solar system to better than 1%. So can you. By Robert J. Vanderbei and Ruslan Belikov HERE ON EARTH we measure distances in millimeters and throughout the cosmos are based in some way on distances inches, kilometers and miles. In the wider solar system, to nearby stars. Determining the astronomical unit was as a more natural standard unit is the tUlronomical unit: the central an issue for astronomy in the 18th and 19th centu· mean distance from Earth to the Sun. The astronomical ries as determining the Hubble constant - a measure of unit (a.u.) equals 149,597,870.691 kilometers plus or minus the universe's expansion rate - was in the 20th. just 30 meters, or 92,955.807.267 international miles plus or Astronomers of a century and more ago devised various minus 100 feet, measuring from the Sun's center to Earth's ingenious methods for determining the a. u. In this article center. We have learned the a. u. so extraordinarily well by we'll describe a way to do it from your backyard - or more tracking spacecraft via radio as they traverse the solar sys precisely, from any place with a fairly unobstructed view tem, and by bouncing radar Signals off solar.system bodies toward the east and west horizons - using only amateur from Earth. But we used to know it much more poorly. equipment. The method repeats a historic experiment per This was a serious problem for many brancht:s of as formed by Scottish astronomer David Gill in the late 19th tronomy; the uncertain length of the astronomical unit led century. -
Guide for the Use of the International System of Units (SI)
Guide for the Use of the International System of Units (SI) m kg s cd SI mol K A NIST Special Publication 811 2008 Edition Ambler Thompson and Barry N. Taylor NIST Special Publication 811 2008 Edition Guide for the Use of the International System of Units (SI) Ambler Thompson Technology Services and Barry N. Taylor Physics Laboratory National Institute of Standards and Technology Gaithersburg, MD 20899 (Supersedes NIST Special Publication 811, 1995 Edition, April 1995) March 2008 U.S. Department of Commerce Carlos M. Gutierrez, Secretary National Institute of Standards and Technology James M. Turner, Acting Director National Institute of Standards and Technology Special Publication 811, 2008 Edition (Supersedes NIST Special Publication 811, April 1995 Edition) Natl. Inst. Stand. Technol. Spec. Publ. 811, 2008 Ed., 85 pages (March 2008; 2nd printing November 2008) CODEN: NSPUE3 Note on 2nd printing: This 2nd printing dated November 2008 of NIST SP811 corrects a number of minor typographical errors present in the 1st printing dated March 2008. Guide for the Use of the International System of Units (SI) Preface The International System of Units, universally abbreviated SI (from the French Le Système International d’Unités), is the modern metric system of measurement. Long the dominant measurement system used in science, the SI is becoming the dominant measurement system used in international commerce. The Omnibus Trade and Competitiveness Act of August 1988 [Public Law (PL) 100-418] changed the name of the National Bureau of Standards (NBS) to the National Institute of Standards and Technology (NIST) and gave to NIST the added task of helping U.S. -
Maths Objectives – Measurement
Maths Objectives – Measurement Key Stage Objective Child Speak Target KS 1 Y1 Compare, describe and solve practical problems for lengths and I use words such as long/short, longer/shorter, tall/short, double/half to heights [for example, long/short, longer/shorter, tall/short, describe my maths work when I am measuring. double/half]. KS 1 Y1 Compare, describe and solve practical problems for mass/weight When weighing, I use the words heavy/light, heavier than, lighter than [for example, heavy/light, heavier than, lighter than]. to explain my work. KS 1 Y1 Compare, describe and solve practical problems for capacity and When working with capacity, I use the words full/empty, more than, volume [for example, full/empty, more than, less than, half, half full, less than, half, half full and quarter to explain my work. quarter]. KS 1 Y1 Compare, describe and solve practical problems for time [for I can answer questions about time, such as Who is quicker? or What example, quicker, slower, earlier, later]. is earlier? KS 1 Y1 Measure and begin to record lengths and heights. I can measure the length or height of something and write down what measure. KS 1 Y1 Measure and begin to record mass/weight. I can measure how heavy an object is and write down what I find. KS 1 Y1 Measure and begin to record capacity and volume. I can measure the capacity of jugs of water and write down what I measure. KS 1 Y1 Measure and begin to record time (hours, minutes, seconds). I can measure how long something takes to happen - such as how long it takes me to run around the playground. -
Standard Caption Abberaviation
TECHNICAL SHEET Page 1 of 2 STANDARD CAPTION ABBREVIATIONS Ref: T120 – Rev 10 – March 02 The abbreviated captions listed are used on all instruments except those made to ANSI C39. 1-19. Captions for special scales to customers’ requirements must comply with BS EN 60051, unless otherwise specified at time of ordering. * DENOTES captions applied at no extra cost. Other captions on request. ELECTRICAL UNITS UNIT SYMBOL UNIT SYMBOL Direct Current dc Watt W * Alternating current ac Milliwatts mW * Amps A * Kilowatts kW * Microamps µA * Megawatts MW * Milliamps mA * Vars VAr * Kiloamps kA * Kilovars kVAr * Millivolts mV * Voltamperes VA * Kilovolts kV * Kilovoltamperes kVA * Cycles Hz * Megavoltamperes MVA * Power factor cos∅ * Ohms Ω * Synchroscope SYNCHROSCOPE * Siemens S Micromhos µmho MECHANICAL UNITS Inches in Micrometre (micron) µm Square inches in2 Millimetre mm Cubic inches in3 Square millimetres mm2 Inches per second in/s * Cubic millimetres mm3 Inches per minute in/min * Millimetres per second mm/s * Inches per hour in/h * Millimetres per minute mm/min * Inches of mercury in hg Millimetres per hour mm/h * Feet ft Millimetres of mercury mm Hg Square feet ft2 Centimetre cm Cubic feet ft3 Square centimetres cm2 Feet per second ft/s * Cubic centimetres cm3 Feet per minute ft/min * Cubic centimetres per min cm3/min Feet per hour ft/h * Centimetres per second cm/s * Foot pound ft lb Centimetres per minute cm/min * Foot pound force ft lbf Centimetres per hour cm/h * Hours h Decimetre dm Yards yd Square decimetre dm2 Square yards yd2 Cubic -
Lesson 3 – Understanding Distance in Space (Optional)
Lesson 3 – Understanding Distance in Space (optional) Background The distance between objects in space is vast and very difficult for most children to grasp. The values for these distances are cumbersome for astronomers and scientists to manipulate. Therefore, scientists use a unit of measurement called an astronomical unit. An astronomical unit is the average distance between the Earth and the Sun – 150 million kilometers. Using a scale model to portray the distances of the planets will help the students begin to understand the vastness of space. Astronomers soon found that even the astronomical unit was not large enough to measure the distance of objects outside of our solar system. For these distances, the parsec is used. A parsec is a unit of light-years. A parsec equals approximately 3.3 light-years. (Keep in mind that a light-year is the distance light travels in one year – 9.5 trillion km – and that light travels 300,000 km per second!) Teacher Notes and Hints Prior to lesson • Discuss and review measuring length or distance. How far is one meter? • Discuss the use of prefixes that add or subtract to “basic” units of length. Example: meter is the basic metric unit for length “kilo” means 1000 – kilometer is 1000 meters “centi” means 1/100 – centimeter is 1/100 of a meter Adapt the discussion for grade level. For example, fifth graders can learn the metric prefixes for more “lengths” and may add to decimal work in math class: Kilo – 1000 Hecto – 100 Deka – 10 Deci – 1/10 (0.1) Centi – 1/100 (0.01) Milli – 1/1000 (0.001) • When discussing kilometers, it is helpful to know the number of km’s to local places (for example, kilometers to the Mall). -
Using Mathematical Operations to Convert Metric Linear Units
Converting Metric Linear Units Using Mathematical Operations to Convert Metric Linear Units Converting Larger to Smaller Units To convert from larger to smaller metric linear units, multiply by 10 for each step downward on the metric staircase. Metric Staircase Use this ACRONYM to help you remember the kilo King order of the units: hecto Henry’s King Henry’s deca Daughter Daughter base unit Betty Betty deci Detested Detested centi Counting Counting milli Money Money Examples A) How many cm in 1 m? m to cm is 2 steps Metric Staircase 1 m = 10 × 10 = 100 cm There are 100 cm in 1 m. m dm B) How many mm in 1 m? cm m to mm is 3 steps mm 1 m = 10 × 10 × 10 = 1000 mm There are 1000 mm in 1 m. Remember that 10 × 10 × 10 = 1000 10 × 10 = 100 C) How many mm in 4.2 m? 4.2 × 10 × 10 × 10 = 4200 mm OR 4.2 × 1000 = 4200 mm There are 4200 mm in 4.2 m. Knowledge and Employability Studio Shape and Space: Measurement: Mathematics Linear Measurement: ©Alberta Education, Alberta, Canada (www.LearnAlberta.ca) Converting Metric Linear Units 1/12 D) For every kilometre you travel in a car or school bus, you are travelling 1000 metres. How many metres in 69.7 kilometres? km to m is 3 steps Metric Staircase 10 × 10 × 10 = 1000 m There are 1000 m in 1 km. km 69.7 × 10 × 10 × 10 = 69 700 m hm OR dam 69.7 × 1000 = 69 700 m m There are 69 700 m in 69.7 km. -
The International System of Units (SI)
NAT'L INST. OF STAND & TECH NIST National Institute of Standards and Technology Technology Administration, U.S. Department of Commerce NIST Special Publication 330 2001 Edition The International System of Units (SI) 4. Barry N. Taylor, Editor r A o o L57 330 2oOI rhe National Institute of Standards and Technology was established in 1988 by Congress to "assist industry in the development of technology . needed to improve product quality, to modernize manufacturing processes, to ensure product reliability . and to facilitate rapid commercialization ... of products based on new scientific discoveries." NIST, originally founded as the National Bureau of Standards in 1901, works to strengthen U.S. industry's competitiveness; advance science and engineering; and improve public health, safety, and the environment. One of the agency's basic functions is to develop, maintain, and retain custody of the national standards of measurement, and provide the means and methods for comparing standards used in science, engineering, manufacturing, commerce, industry, and education with the standards adopted or recognized by the Federal Government. As an agency of the U.S. Commerce Department's Technology Administration, NIST conducts basic and applied research in the physical sciences and engineering, and develops measurement techniques, test methods, standards, and related services. The Institute does generic and precompetitive work on new and advanced technologies. NIST's research facilities are located at Gaithersburg, MD 20899, and at Boulder, CO 80303. -
Introducyon to the Metric System Bemeasurement, Provips0.Nformal, 'Hands-On Experiences For.The Stud4tts
'DOCUMENT RESUME ED 13A 755 084 CE 009 744 AUTHOR Cáoper, Gloria S., Ed.; Mag4,sos Joel B., Ed. TITLE q Met,rits for.Theatrical COstum g: ° INSTITUTION Ohio State Univ., Columbus. enter for Vocational Education. SPONS AGENCY Ohio State Univ., Columbus. Center for.Vocational Education. PUB DATE 76 4. CONTRACT - OEC-0-74-9335 NOTE 59p.1 For a. related docuMent see CE 009 736-790 EDRS PRICE 10-$0.8.3 C-$3.50 Plus Pdstage: DESCRIPTORS *Curriculu; Fine Arts; Instructional Materials; Learning. ctivities;xMeasurement.Instrnments; *Metric, System; S condary Education; Teaching Technigue8; *Theater AttS; Units of Sttidy (Subject Fields) ; , *Vocational Eiducation- IDENTIFIERS Costumes (Theatrical) AESTRACT . Desigliedto meet tbe job-related m4triceasgrement needs of theatrical costuming students,'thiS instructio11 alpickage is one of live-for the arts and-huminities occupations cluster, part of aset b*: 55 packages for:metric instrection in diftepent occupations.. .The package is in'tended for students who already knovthe occupaiiOnal terminology, measurement terms, and tools currently in use. Each of the five units in this instructional package.contains performance' objectiveS, learning:Activities, and'supporting information in-the form of text,.exertises,- ard tabled. In. add±tion, Suggested teaching technigueS are included. At the'back of the package*are objective-base'd:e"luation items, a-page of answers to' the exercises,and tests, a list of metric materials ,needed for the ,activities4 references,- and a/list of supPliers.t The_material is Y- designed. to accVmodate awariety of.individual teacting,:and learning k. styles, e.g., in,dependent:study, small group, or whole-class Setivity. -
IAU 2012 Resolution B2
RESOLUTION B2 on the re-definition of the astronomical unit of length. Proposed by the IAU Division I Working Group Numerical Standards and supported by Division I The XXVIII General Assembly of International Astronomical Union, noting 1. that the International Astronomical Union (IAU) 1976 System of Astronomical Constants specifies the units for the dynamics of the solar system, including the day (D=86400 s), the mass of the Sun, MS, and the astronomical unit of length or simply the astronomical unit whose definitioni is based on the value of the Gaussian gravitational constant, 2. that the intention of the above definition of the astronomical unit was to provide accurate distance ratios in the solar system when distances could not be estimated with high accuracy, 3. that, to calculate the solar mass parameter, GMS, previously known as the heliocentric gravitation constant, in Système International (SI) unitsii,the Gaussian gravitational constant k, is used, along with an astronomical unit determined observationally, 4. that the IAU 2009 System of astronomical constants (IAU 2009 Resolution B2) retains the IAU 1976 definition of the astronomical unit, by specifying k as an “auxiliary defining constant” with the numerical value given in the IAU 1976 System of Astronomical Constants, 5. that the value of the astronomical unit compatible with Barycentric Dynamical Time (TDB) in Table 1 of the IAU 2009 System (149 597 870 700 m 3 m), is an average (Pitjeva and Standish 2009) of recent estimates for the astronomical unit defined by k, 6. that the TDB-compatible value for GMS listed in Table 1 of the IAU 2009 System, derived by using the astronomical unit fit to the DE421 ephemerides (Folkner et al.