University of Michigan - Department of Astronomy

Version: worksheet

Units and Conversions

Abreviations: a nm is a nanometer (look carefully, nm looks a lot like mm); pc is a parsec; M is mega or million; G is giga or billion. Rsubscript stands for the radius of the object named in the subscript; AU is astronomical unit, the average distance between the Earth and Sun (aka the semi-major axis of Earth's orbit); ly is light year.

Part 1: Conversion Factors

  1. Length conversion factors: fill in the blanks.  The first one has been done for you. Use scientific notation wherever it makes more sense to use it (e.g. if you have to write more than 3 or 4 zeros). You may need your book or another refrence. Checking your answers with another group is highly recommended, since this will be a good refrence for the rest of this activity (and maube homework too.)
    1. ________100____________cm = 1 m
    2. _______________________nm = 1 m
    3. _______________________cm = 1 nm
    4. _______________________m = 1 nm
    5. _______________________km = 1 m
    6. _______________________m = 1 km
    7. _______________________miles = 1 m
    8. _______________________km = 1 mile
    9. _______________________km = 1 ly
    10. _______________________km = 1 AU
    11. _______________________AU = 1 m
    12. _______________________Mpc = 1 pc
    13. _______________________ly = 1 Mpc
    14. _______________________m = 1 pc
    15. _______________________pc = 1 ly
    16. _______________________AU = 1 pc
    17. _______________________m = 1 Rsun
  2. Place the following in order from smallest to largest using the abbreviation of the names:
    1. kilometer
    2. foot
    3. meter
    4. astronomical unit
    5. centimeter
    6. mile
    7. parsec
    8. light year
    9. nanometer
    10. solar radius
  3. Compare your list from number 2 to the conversion factors in number 1.  Do all your answers to number 1 still make sense? How can you tell?

  4. Below is a list of objects with units. Decide if it is sensible to use those units when talking about the size of the object. explain your reasoning, and if you don't think the unit is right, give a better unit to use.
    1. a notebook; inches

    2. the Moon; km

    3. the distnace to the nearest star; km

    4. a building; m

    5. an atom; inches

Conversions and Calculations

You must show all your work (i.e. you cannot just use an online conversion calculator or the conversion function in your calculator!). 

  1. A standard size piece of paper is 8.5 x 11 inches.
    1. Convert the length and width to cm.

    2. convert the length and width to feet.

    3. find the area in square inches from the original measurements

    4. find the area in square cm from your answer to a.

    5. Convert the area in square inches you found in c to square cm.

    6. Do your answers to e and f match?  Why would there be any differences?

  2. A basket ball is about 1 foot in diameter
    1. Find its volume in feet3

    2. Convert its volume in inches3

    3. Convert its diameter to cm

    4. Find its volume in cm3

    5. Find its volume in m3

    6. Find its volume in R3Earth

  3. The magnification of a telescope is the effective focal length (efl) of the telelscope optics divided by the focal length of the eyepiece, and the results should be unitless (ie magnification does not have things like mm or inches in it). Calculate the magnification of the following systems. Show your work. (note eyepieces are interchangeable, so astronomers generally don't care about the magnification - if it doesn't look good, we just change the eyepiece.)
    1. efl: 80 inches; eyepiece: 40 mm

    2. efl: 80 inches; eyepiece 25 mm

    3. efl: 325 cm; eyepiece 35 mm

  4. The semi-major axis (average distance from the planet) of each of the Galilean moons are given in km in the table below. Convert each of these distances to AU, miles, and light seconds and fill in the rest of the table.  Show your work for Io.


























Last updated: 2/10/12 by SAM

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