Basic Astronomy Math Review
Dr. Niescja E. Turner, University of Colorado
Cube
Roots To take a cube root on your calculator, you have
a few options. The first option is to use the cube root key. If your
calculator does not have one of these, then you can use the generic
root key (looks like a square root but has a variable -- usually y --
where the 3 would go in a cube root sign). Then you would type in the
number you want the root of, and hit the root key, followed by a
3. Another option is to use the xy key, and take the
number to the 1/3 power.
Scientific Notation.
To put a number from standard notation into scientific notation,
move the decimal point so that exactly one digit is to the left
of it. The number of places you moved the decimal is the power
of ten. This power is negative if you move the decimal to the
right, and positive if you move it to the left. It's EASY. If
you can count, you can do scientific notation. Examples:
2,378,000 = 2.378 x 106
71,100 = 7.1 x 104
.000352 = 3.52 x 10-4
.000000078 = 7.8 x 10-8
Scientific Notation on a Calculator.
Most calculators have a button labeled "EXP" (or "EE"). "EXP"
means 10n where n is the next number you punch in. For example,
to put 3.43 x 107 into your calculator you punch in: "3.43 EXP
7". Another Example: multiply 2.13 x 1012 by 1.52 x 105. Punch
in "2.13 EXP 12 X 1.52 EXP 5". The display will read:
"3.2376E+17" or "3.2376 17" depending on the type of calculator.
Both of these mean 3.2376 x 1017.
ALWAYS check your answer to see if it makes sense. A calculator
is an aid for your brain - not a replacement.
Math with Units:
Treat Units as numbers or as algebraic symbols - they obey the
same rules. Examples:
3m * 7m = 21m2
12m3 / 3m = 4m2
49m / 7s = 7m/s
(20m/s) / (4s) = 5m/s2
Converting units:
An object travels 146,880 meters in 1 day. (Velocity = 146,880
meters / day.) How many meters per hour does it travel? We need
to convert from days to hours. One day is equal to 24 hours, so
the quantity "1 day" divided by "24 hours" must equal 1: (1 day /
24 hours = 1). Since we can always multiply by 1 without
changing anything, we multiply (146,880 m/day) by (1 day / 24
hours):
146,880 m/day * (1 day / 24 hours) = 6120 m/hour.
Notice that the unit "day" cancelled since it occurred in both a
numerator and a denominator. We are left with meters per hour -
which is what we wanted. The final answer does make sense -
clearly the object will travel fewer meters in an hour than it
will in a day.
How many meters per minute?
6120 m/hour * (1 hour / 60 minutes) = 102 m/minute
How many meters per second?
102 m/minute * (1 minute / 60 seconds) = 1.7 m/second
Units
| name | abbreviation | dimension |
| meter | m | distance, length |
| second | s | time |
| kilogram | kg | mass |
| newton | N = kg*m/s2 | force |
| joule | J = N*m | energy |
| watt | W = J/s | power |
| parsec | pc | distance |
| light year | ly | distance |
| astronomical unit | A.U. | distance |
| kelvin | K | temperature |
1 pc = 3.09 x 1016 m
1 ly = 9.46 x 1015 m
1 A.U. = 1.496 x 1011 m
Combined units:
| m/s | velocity |
| m/s2 | acceleration |
| kg/m3 | density |
| m2 | area |
| m3 | volume |
Unit prefixes
| n | nano | 10-9 |
| µ | micro | 10-6 |
| m | milli | 10-3 |
| c | centi | 10-2 |
| k | kilo | 103 |
| M | mega | 106 |
| G | giga | 109 |
Example: 3 nm = 3 nanometers = 3 x 10-9 meters
Always keep track of your units and use them to check your
answer. For example, if you're trying to calculate a velocity,
but your units end up as m/s2, you've messed up since these are
the units for acceleration.