Astronomy 161:
An Introduction to Solar System Astronomy Prof. Richard Pogge, MTWThF 2:30 |

- Express numbers using powers of 10
- Standard Prefixes (kilo-, mega-, etc.)

- Units of Length
- Units of Time
- Units of Mass
- Weight
*versus*Mass

Examples:

- Average distance of the Earth from the Sun: 149,597,900 kilometers
- Mass of the Sun: 1,989,000,000,000,000,000,000,000,000,000 kilograms
- Age of the Earth: 4,550,000,000 years (4.55 Billion years)

- Number of OREO cookies sold to date: 490,000,000,000
[source: Nabisco]
- US National Debt (public debt): $24,352,541,663,456.59 (as of 2022 Oct 31). [source: US Department of the Treasury, Debt to the Penny]

Because the numbers we will encounter in this course range from the very larger to the very small, we need a way of dealing with such numbers sensibly so we don't go crazy counting zero's, risking factor of 10 or greater mistakes at every turn.

Examples of Scientific Notation:

- The Mass of the Sun:
- 1,989,000,000,000,000,000,000,000,000,000 kilograms = 1.989x10
^{30}kilograms - The Size of a Hydrogen Atom:
- 0.0000000000106 meters = 1.06x10
^{-11}meters

- Length in Meters
- Mass in Kilograms
- Time in Seconds

^{3} |
kilo- |
kilogram, kilometer, kilobyte |

^{6} |
mega- |
megawatt, megayear, megabyte, megaton |

^{9} |
giga- |
gigayear, gigaton, gigabyte |

^{12} |
tera- |
terawatt, terabyte |

^{-2} |
centi- |
centimeter |

^{-3} |
milli- |
millimeter, millisecond, milliliter |

^{-6} |
micro- |
microsecond, micron |

^{-9} |
nano- |
nanosecond, nanometer |

Common Examples

- Length:
- 1 kilometer = 10
^{3}meters (1000 meters) - 1 centimeter = 10
^{-2}meters (1/100^{th}of a meter) - 1 millimeter = 10
^{-3}meters (1/1000^{th}of a meter) - 1 micron = 10
^{-6}meters (short for "micrometer") - Time:
- 1 nanosecond = 10
^{-9}s (1 billionth of a second) - 1 Gigayear = 10
^{9}years (1 Billion years) - 1 Megayear = 10
^{6}years (1 Million years)

__Traditional Definition__:- 1 ten-millionth the distance from the North Pole to the Equator of the
Earth.
__Modern Definition__:- The distance traveled by light in a vacuum
in 1/299792458
^{th}of a second.

The Astronomical Unit (AU):

1 AU is the Mean Distance from the Earth to the Sun:

- 1 AU = 1.496x10
^{8}kilometers

In round numbers, you can use "1 AU = 150 Million km" for the purposes of this class.

The Light Year (ly):

1 Light Year (ly) is the Distance Traveled by Light in 1 Year:

- 1 ly = 9.46x10
^{12}kilometers

- The Moon: 384,000 kilometers
- The Sun: 1 AU (149,600,000 km)
- Alpha Centauri (nearest star): 4.2 light years (266,000 AU)
- Center of the Milky Way Galaxy: 26,000 light years (1.65x10
^{9}AU)

__Traditional Definition__:- 1/86400
^{th}of the mean solar day. __Modern Definition__:- 9,192,631,770 oscillations of a
^{133}Cesium atomic clock.

__Traditional Definition__:- 1 kilogram is the mass of 1 liter of pure water.
__Modern Definition__:- 1 kilogram = mass of the international prototype of the kilogram.
- This is a piece of platinum-iridium alloy kept at the International Bureau of Weights & Measures in Sèvres, France.

Strictly speaking:

is the amount of matter in an object.__Mass__is the force of gravity on an object.__Weight__

- Mass is the same everywhere regardless of the strength of the local
gravitational field
- Weight depends on the strength of the local gravity field (i.e.,
it is different on the Earth and Moon for the
*same*mass.)

**Metric:**- Mass in kilograms
- Weight in Newtons
**English Units:**- Mass in slugs
- Weight in pounds

This double meaning often causes confusion: a subtlety not often appreciated is that the conversion between pounds (weight) and kilograms (mass) that you can find in tables of weights and measures is only strictly true at the surface of the earth (and then only for an assumed mean gravitational force at the sea-level)!

On the Moon or Mars, where the gravity is different at the surface, the conversion is also different!

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Updated: 2022 November 2

Copyright © Richard W. Pogge, All Rights Reserved.