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Basic tools
Expressing extreme quantities
Eg. Distance to nearest star is 120 trillion km (120×1012 km = 1.20×1014 km)
Diameter of Hydrogen nucleus is 53 trillionths of a meter (53×10-12 m = 5.3×10-11 m)
1) Scientific notation
Standard form of a number: number 10exponent
where: 1  number < 10
exponent is the number of powers (factors) of 10
10 is the base
Advantages for extreme quantities: compact
easier to compare numbers
information about size of number is mostly in
exponent
Examples:
1) 1300 = 1.3103
2) 58 billion = 58109  This is NOT in standard form: leading number >10
= 5.81010  This IS in standard form: leading number is  1 and < 10.
Special examples:
1) 10 = 1101
2) 1 = 1100
Caution: 3x105 is NOT the same as 35 !
3105 = 3 (10 10 10 10 10) = 300,000
35 = 3  3  3  3  3 = 243
Do not be confused by the way calculators display scientific notation!
Numbers smaller than one:
Exponent is number of powers (factors) of 1/10 (or 0.1)
Exponent is negative (< 0) to indicate division by 10
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Examples:
1) 0.00001 = 1.010-5
2) 0.00632 = 6.3210-3  Note standard form: mantissa is  1 and < 10.
2) Metric system
Simple: all conversion factors are powers of 10
Basic physical quantities:
Distance: meters (m)
Time: seconds (s)
Mass (not the same as weight!): kilograms (kg)
Energy: Joules (J)
Power (eg. Brightness): Energy/time = J/s = Watts (W)
Force: Newtons (N)
Related physical quantities expressed in terms of basic quantities:
Eg. Velocity: m/s
Units must be consistent when combining quantities:
- 100 g + 2 kg = 0.1 kg + 2 kg = 2.1 kg
Metric prefixes: way of expressing number of powers of 10
Prefix
Meaning Factor
Greater than one:
Terra (T) Trillion
1012
Giga (G) Billion
109
Mega (M) Million
106
Kilo (k) Thousand 103
Less than one:
Milli (m) Thousandth 10-3
Micro (μ) Millionth
10-6
Nano (n)
Billionth
10-9
Example
Terrawatt (TW) power
Gigayear (Gyr) age
Megaparsec (Mpc) distance
Kilograms (kg) mass, kilometers (km) distance
Milli-arc-seconds (mas) angular distance
Micrometers (“microns”, m) distance
Nanometers (nm) distance
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3) Special units used in Astronomy (not in MKS system!)
Astronomical Unit (AU):
Definition: Average distance from Earth to Sun, ie. average radius of Earth’s orbit
Value: 1.4961011 m
Use: Distances within solar system and within binary star systems
Eg. Distance of Pluto from Sun = 5.921012 m = 39.5 AU
- physical meaning: radius of Pluto’s orbit is about 40× larger than Earth’s
Light Year (LY):
Definition: Distance that light travels in one year in a vacuum
Value: 6.32104 AU = 9.461015 m
Use: Distances among stars in Milky Way galaxy
Eg. Distance of nearest star (Proxima Centauri) from Sun = 2.7105 AU= 4.2 LY
- physical meaning: the light we receive from Proxima Centauri now left the star 4.2
years ago
Parsec (pc):
Value: 1 pc = 3.26 LY = 3.091016 m
Use: kiloparsec (kpc): distances among stars in Milky Way galaxy; megaparsec (Mpc):
distances among galaxies
Angular distance
Use of angles in Astronomy to express difference in direction to two objects
Review of linear distance:
Linear distance (d): separation of two points in space
- an absolute quantity; ie. independent of observer’s position or motion
Eg.
Linear size of an object is the linear distance from one point on an object to another
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eg. linear diameter, D: linear distance from one edge of an object to another
linear radius, R: linear distance from center of objsect to edge
Related quantity: linear velocity (or rate or speed), v
- linear distance traversed by a moving object per unit time
Angular quantities:
Angular distance, : Separation in direction
- the angle between the line-of-sight from an observer to one object and the line-ofsight from that observer to another object
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- note 1: the two objects may have different linear distances
- note 2: angular distance, , is a relative quantity; ie. it depends on position of observer
(but in Astronomy position of Observer is ALWAYS Earth!)
Angular units:
Units of angular distance (or angular size): units of angle
- degrees (deg, o)
- Full circle = 360o
- therefore: maximum angular distance between any two points is 180 o
Eg. Angular distance between two stars:
1) Star 1 on horizon and Star 2 directly overhead:
 lines of sight to two stars form a right angle at the observer
 angular distance between star 1 & 2 is 90o or 270o
2) Star 1 on horizon at East point and Star 2 on horizon at West point:
 lines of sight to two stars form a straight line with observer at center
 angular distance between star 1 & 2 is 180o
- note: there is no ambiguity in this special case
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Angular size ,: the angular distance from one point of an extended object to the another
point
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eg. angular diameter, θD, of a spherical object: the angular distance from one
edge of sphere to the opposite edge
- eg. Angular diameter, D, of Sun and Moon is ~ 0.o5
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eg. angular radius, θR, of a spherical object: the angular distance from the center
the circular projection of the sphere to an edge
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Note: angular size depends on position of observer through distance, d
Eg.
d2 > d1, therefore, 1 > 2
Of course, angular size also depends on linear size:
D2 > D1, therefore, 2 > 1