Transcript Math in astronomy

Some math for astronomy
Astronomy 115, Spring 2013
Scientific Notation:
Scientific notation is a shorthand way of writing and multiplying
large (and small) numbers.
1,000,000,000,000
1012
terra (T)
(trillions)
1,000,000,000
109
giga (G)
(billions)
1,000,000
106
mega (M)
(millions)
1000
103
kilo (k)
(thousands)
1
100
unity
0.01
0.001
10-2
10-3
centi (c)
milli (m)
(hundredth)
(thousandth)
0.000001
10-6
micro ()
(millionth)
0.000000001
10-9
nano (n)
(billionth)
Using Scientific Notation:
To do numbers that are not divisible by ten, we multiply by an
exponential number.
4,275,000,000 = 4.275 x 1,000,000,000 = 4.275 x 109
0.000374 = 3.74 x 0.0001 = 3.74 x 10-4
Using Scientific Notation:
To multiply numbers using scientific notation, we add the
exponents.
103 x 10-9
= 10(3) + (- 9)
= 10-6
102 x 105
= 10(2) + (5)
= 107
To divide numbers using scientific notation, we subtract the
exponents.
10 3
10 9
= 10(3) - (- 9)
= 1012
10 2
105
= 10(2) - (5)
= 10-3
Using Scientific Notation:
To raise a number to a power, we multiply the exponents
10 
3 2
 10
3*2 
 10
6
To changing from division to multiplication, we change the
sign of the exponent
5
-2
= 5 ´ 10
2
10
Using Scientific Notation:
To add or subtract numbers using scientific notation, we work in
front of the exponents, but they must have the same exponent.
3.0 x102 + 2.6 x 105
= 0.003 x 105 + 2.6 x 105
= 2.603 x105
1.0 x105 - 7.0 x 102= 1.0 x105 -
= 0.993 x105
0.007 x105
Scientific Notation /Units Example 1
How long does light take to travel from the visible surface of the Sun to the
Earth?
Distance from Sun to Earth D = 150,000,000 km
This is also known as one astronomical unit (AU)
In scientific notation D = 1.5  108 km
Scientific Notation /Units Example 1
How long does light take to travel from the visible surface of the Sun to the
Earth?
There are 1000 m = 103 m = 1 km:
 103 m 
1 
 km 



Hence, in meters:
æ 1.5 ´ 108 km ö æ 10 3 m ö
D =ç
֍
÷
1
è
ø è km ø
= 1.5 ´ 10 (
8+3)
= 1.5 ´ 10 m
11
m
Scientific Notation/Units Example 1
How long does light take to travel from the visible surface of the Sun to the
Earth?
The speed of light c = 3 x 108 m/s
distance
speed 
time
OR
distance
time 
speed
Scientific Notation/Units Example 1
How long does light take to travel from the visible surface of the Sun to the
Earth?
distance 1.5 ´ 1011 m
time =
=
speed
3 ´ 108 m / s
1.5
s
(11-8)
= ´ 10
m = 0.5 ´ 103 s
3
m
2
= 5 ´ 10 s = 500 s
 1 min 
 500 s

 60s 
 8.33 min
Scientific Notation/Units Example 2
Density of Water
Density is mass per volume
For water: 1 gram / centimeter3 (1g/cm3)
What is this in kilograms / meters3 ?
3
 1g  1kg  10 cm 
0 3 2*3  kg
  10
 3  3 
3
m
 cm  10 g  m 
3 kg
 10 3
m
2