ASTR 103: Earth/Sky - Scale of the Universe

ASTR 103 - Astronomy

Earth/Sky - Scale of the Universe

Last Modified: January 19, 1998

And the earth is a particle of dust by sand-grain sun, lost in a nameless cove of shores of a continent.
Galaxy on Galaxy, innumerable swirls of unnumberable stars, endured as it were forever and humanity
Came into being, its two or three million years are a moment, in a moment it will certainly cease out from being
And galaxy on galaxy endure after that as it were forever....

Robinson Jeffers

Quantitative Nature of Science

Science is quantitative
Ordinary language is unable to capture either scale or precision necessary for scientific discourse
Numbers are essential to discussion and understanding
Units of measurement are also essential to discussion and understanding
Science uses a representation scheme called scientific notation

Scientific Notation

Scientific notation - is the expression of numbers as products of a number between 1 and 10 times a power of ten
Examples
- 123 = 1.23 x 100 = 1.23 x 10²
- 0.123 = 1.23 x 0.1 = 1.23 x 10^-1
- 86,400 = 8.64 x 10,000 = 8.64 x 10⁴
- 0.0000594 = 5.94 x 0.00001 = 5.94 x 10^-5

Powers of Ten
Word	Number	Power	Prefix	Symbol
trillion	1,000,000,000,000	10¹²	tera	T
billion	1,000,000,000	10⁹	giga	G
million	1,000,000	10⁶	mega	M
thousand	1,000	10³	kilo	k
hundred	100	10²	hecto	h
ten	10	10¹	deca	da
unit	1	10⁰	.	.
tenth	0.1	10^-1	deci	d
hundredth	0.01	10^-2	centi	c
thousandth	0.001	10^-3	milli	m
millionth	0.000,001	10^-6	micro	m
billionth	0.000,000,001	10^-9	nano	n
trillionth	0.000,000,000,001	10^-12	pico	p

Rules for Scientific Notation

Decimal point shift
- number of places the decimal point is shifted indicates the numerical value of the power of ten
- if the shift is to left, algebraic sign is positive,
- if the shift is to right, algebraic sign is negative
Multiplication and division
- powers of ten are added in multiplication,
- powers of ten are subtracted in division
Powers and roots
- to raise to a power, multiple the power of ten by the power,
- to find a root, multiple the power of ten by the root
Addition and/or subtraction
- power of ten must be the same for all numbers,
- which will also be the appropriate power of ten for the answer

Scales Size in the Universe

Nuclear scale	10^-12 cm
Atomic scale	10^-8 cm
Complex molecules	10^-6 cm
Human beings	10² cm
Earth	10⁹ cm
Solar System	10¹⁴ cm
Solar Neighborhood	10¹⁸ cm
Galaxy	10²² cm
Cluster of Galaxies	10²⁵ cm
Universe	10²⁸ cm
Total range	40 orders of magnitude

Model Universe

If one were to make a scale model of the universe in which one inch represents the mean Earth-Sun distance (1 AU), various other astronomical objects would have the distances in the model shown in the following table.

Earth-Sun distance (AU)	1 inch
Sun-Pluto distance	40 inches
Nearest Star (a Centauri)	4 miles
Radius of Our Galaxy	50,000 miles (12 times Earth's radius)
Andromeda galaxy	2,250,000 miles (10 times Moon's distance)
Most distant galaxy	6,000,000,000 miles (1.5 times Solar System)

Time Scale of the Universe

If one were to reduce the interval of time since the beginning of the universe to a mere 300 years, significant events in the history of human beings would have occurred as indicated in the following table.

Age of Universe	300 years
Age of Earth	100 years
Life began on Earth	70 years
First humanoid	25 days
Age of astronomical science	30 min
Age of telescopic astronomy	4.2 min
Age of radio astronomy	34 sec
Humans land on Moon	7.5 sec
Humans seek life on Mars	2.7 sec