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1.1 ASTRONOMICAL MEASUREMENTS. Where Are You?. To find our place among the stars, we will zoom out from a familiar scene, to the largest scales of the universe. Each picture will widen your field of view , the region you can see in the image, by about a factor of 100.

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where are you
Where Are You?
  • To find our place among the stars, we will zoom out from a familiar scene, to the largest scales of the universe.
    • Each picture will widen your field of view, the region you can see in the image, by about a factor of 100.
      • This allows you to see an area 1 mile in diameter.

“The longest journey begins with a single step”

- Lao Tzu

where are you1
Where Are You?

Park Scene 16 x 16 m.

where are you2
Where Are You?

City Scene 1 mile x 1 mile

where are you3
Where Are You?

Pennsylvania Landscape 100 miles x 100 miles

where are you4
Where Are You?

Diameter of Earth 12,756 km.

where are you5
Where Are You?

Distance from Earth to Moon 384,000 km.

types of numbers
Types of Numbers
  • Before we look into complex details of astronomy, we must first study basic knowledge, such as numbers.
  • There are 2 kinds of numbers:
    • Exact
      • Example: There are 12 eggs in a dozen.
    • Inexact
      • Example: Measurement with some room for adjustment (paper thickness: 0.1 mm  0.089 mm)
accuracy vs precision
Accuracy vs. Precision
  • Another important detail when dealing with numbers is to understand values.
    • Do the words accuracy and precision sound familiar? What’s the difference?
  • Accuracy refers to how closely a measured value agrees with the correct value.
  • Precision refers to how closely individual measurements agree with each other.
significant figures
Significant Figures
  • When dealing with numerical values, it is imperative to focus on something probably familiar to many of you.
    • The number of significant figures(“sig figs”) is the number of digits believed to be correct by the person doing the measuring.
significant figures1
Significant Figures
  • Rules for calculating significant figures:
  • - Digits from 1-9 are always significant.
  • - Leading zeros are never significant.
  • - Imbedded zeros are always significant.
  • - Trailing zeros are only significant if the decimal point is specified.
significant figures2
Significant Figures
  • Further rules for calculating significant figures when performing mathematical operations:
  • Addition and Subtraction
  • The answer may only show as many significant decimal places as the measurement having the least number of significant decimal places.
  • Multiplication and Division
  • The answer may only show as many sig figs as the measurement having the least number of sig figs.
significant figures3
Significant Figures
  • Examples:
    • Using the correct number of sig figs and decimal places, solve the following:

5.26 + 1 + 29 – 3.74

2.3 x 4.28 x 6 x 1.05


Least significant decimal place

in measurements is located in

the ones position


Least number of sig figs

in measurements is 1

scientific notation
Scientific Notation
  • Often times in Astronomy, numbers are so large it is inconvenient to write them out.
  • Rather than writing large numbers out, it is easier to use scientific notation, a system used to express very large or very small numbers without using a lot of zeros.
    • Example: 384,000 becomes …

3.84 x 105

where are you6
Where Are You?

Distance from Sun to Earth 150,000,000 km.

astronomical unit au
Astronomical Unit (AU)
  • Another way astronomers simplify calculations using large numbers is to define larger units of measurement.
    • For example, the average distance from Earth to the Sun is a unit of distance called the astronomical unit (AU).
      • 1 AU = 1.5 x 108 km. = 93 million miles
astronomical unit au1
Astronomical Unit (AU)
  • Using AU’s, you can express the average distance from Venus to the Sun as about 0.72 AU, while the average distance from Mercury to the Sun is about 0.39 AU.
    • These distances are averages because the orbits of the planets are not perfect circles.

0.72 AU

0.39 AU

where are you7
Where Are You?

Diameter of Pluto’s Orbit Approx. 100 AU

where are you8
Where Are You?
  • When the field of view was allowing you to see the entire solar system, the Sun, Mercury, Venus, and Earth lie so close together and are so small you cannot see them separately at this scale.
  • You can only see the brighter, larger, more widely separated objects starting with Mars, a distance of 1.5 AU from the Sun.
  • You can remember the order of the planets using a simple sentence:

My Very Educated Mother Just Served Us Noodles

where are you9
Where Are You?

Empty space around solar system 10,000 AU

where are you10
Where Are You?

The solar neighborhood Approx. 17 light years

light years
Light Years
  • A light yearis the distance light travels in one year, which is equivalent to 9.46 trillion km.
    • A common misconception is when people think the word “year” is referring to a time measurement while it is actually a distance measurement.
  • The nearest star to our Sun is Proxima Centauri, a distance of 4.3 light years away.
where are you11
Where Are You?

The extended solar neighborhood Approx. 1,700 light years

where are you12
Where Are You?

Diameter of Milky Way Approx. 80,000 light years

where are you13
Where Are You?
  • Notice on the previous slide, we expanded our field of view yet again by a factor of 100 and saw our entire galaxy, the Milky Way.
  • A galaxy is a great cloud of stars, gas, and dust held together by the combined gravity of all its matter.
    • 3 different types: Spiral, Elliptical, Irregular
  • Galaxies range from 1500 to over 300 000 light years in diameter, and some contain over 100 billion stars.
where are you14
Where Are You?

Distance to the nearest large galaxies Several million light years

where are you15
Where Are You?

Clusters of galaxies are grouped into superclusters, which form filaments and walls around voids.

dimensional analysis
Dimensional Analysis
  • A mathematical technique allowing you to convert units to solve problems is called dimensional analysis.
    • When you want to use a conversion factor to change a unit in a problem, you can set up the problem in the following way:
      • Quantity sought (?) = quantity given x conversion factor
        • Example: How many quarters are in 12 dollars?
          • ? quarters = 12 dollars x conversion factor
          • ? quarters = 12 dollars x 4 quarters

1 dollar

48 quarters in 12 dollars

dimensional analysis1
Dimensional Analysis
  • Example: I am having a party this weekend and inviting 15 people, anticipating each person will eat 8 pieces of pizza. Knowing each pizza has 12 slices, how many total pizzas will I need in order to have enough for everyone at the party?
    • ? pizzas = 15 persons x conversion factor
    • ? pizzas = 15 persons x 8 slices x 1 pizza

1 person 12 slices

10 pizzas for my party