1

 A Little More about Scientific Notation, Units, and the Scale of the
Universe
 How we name and start to classify stars
 *Constellations*, Magnitudes
 How the stars move across the sky

2


3


4


5

 10^{1 }= 10
 10^{2 }= 100
 10^{3 }= 1,000 (one thousand)
 10^{6} = 1,000,000 (one
million )
 You can think of this as raising 10 to some power –
or just think of it as moving decimal place over some given
number of steps. Think of
computer speeds and disk space.
 10^{0} = 1
 10^{1 }= 0.1 = 1
/ 10
 10^{2 }= 0.01 = 1
/ 100
 10^{3} = 0.001 =
1 / 1,000
 10^{6} =
0.000001 = 1 / 1,000,000
 How to write numbers which are not powers of 10:
1 A.U. = 149,597,900 km = 1.496 ´ 10^{8}
km
= mantissa
´ 10^{exponent}

6

 Multiplication: Multiply the
mantissa
Add the exponents
 20 AU = (2 ´ 10^{1 })^{
}´ (1.496 ´10^{8} km)
= (2 ´ 1.496) ´ (10^{1} x 10^{8})
km
= 2.9992 ´ 10^{9 }km
 Division: Divide the
mantissa
Subtract the
exponents
 1 AU / 500 = (1.496 ´10^{8}
km) / (5 ´ 10^{2})
= (1.496 / 5 ) ´ (10^{8} / 10^{2}) km
= 0.2992 ´ 10^{6} km
= 2.992 ´ 10^{5} km
 Be careful when adding or subtracting:
 (2.0´10^{6) }+ (2.0´10^{3}) = 2,002,000 = 2.002´10^{6}
not 4. ´10^{6}

7


8


9

 speed of light = c = 3.0 ´ 10^{8}
m/s
 distance = speed ´ time
 d = c ´ t
 lightsecond = 3.0 ´ 10^{8} m/s ´ 1 s
= 3.0 ´ 10^{8} m
 lightminute = 3.0 ´ 10^{8} m/s ´ 60 s
= 180 ´ 10^{8} m
= 1.8 ´ 10^{10} m
 lightyear = 3.0 ´ 10^{8}
m/s ´
3.14 ´ 10^{7}
s (i.e. 31.4 million s) = 9.4 ´ 10^{15} m
= 9.5 ´ 10^{12} km
= 9.5 trillion km
= 9,500,000,000,000 km

10

 If someone says:
“The time it took me to walk to class today was 10 minutes.”
the number could possibly be wrong, but the statement at least
makes sense.
 If someone says:
“The time it took me to walk to class today was 10
kilograms.”
something is obviously wrong.
 When you use a formula to calculate some answer – you can treat units
just like numbers – multiplying and canceling them.
 The units you are left with MUST be those which match the ones expected
– or you have made some mistake.

11

 1 lightyear = c ´ t (where c is the
speed of light and t is one year)
= 3.0 ´ 10^{8}
m/s ´ 365 days
= 1.1 ´ 10^{11 } (m ´ days /s)
 but we know lightyears is a distance and must have “dimensions” of
distance. We should have units of
just meters. The fact that we
have this extra (days/s) means we have left something out.
 If we multiply by (24 hr/day ´ 60 min/hr ´
60 sec/min) the units will work out right and so will the
numerical answer
= 1.1 ´ 10^{11 }´ 24 ´ 60 ´
60 m
= 9.5 ´ 10^{15 }m
= 9.5 ´ 10^{12} km

12

 Chapter 2: The Sky
 Constellations:
 Originally vague
 Mostly Greek
 Now well defined
 Total of 88
 Asterisms:
 Less Formal Groups

13

 The stars in a constellation or asterism like the Big Dipper are NOT
necessarily at the same distances.
 These are just chance arrangements as seen from Earth.

14

 Proper names mostly from Arabic
 Astronomers use
(a, b, d, e, ...
) + Constellation
in approximate order of brightness
 Alpha Orionis = Betelgeuse
 Beta Orionis = Rigel
 Alpha Tauri = Aldebaran
 Numbers and other schemes for fainter stars. (About 6000 stars are visible to naked
eye.)

15

 Ancient system created by Hipparchus
 1^{st} magnitude = brightest stars in sky
 6^{th} magnitude = faintest visible to naked eye
 Confusing because smaller number implies brighter
 (Think of first magnitude as “first in class”)
 Astronomers want a numerical measure of
Intensity (I) which is proportional to energy per
unit time received from the star.
 Relationship between I and m turns out to be “logarithmic” (result of properties of human eye)

16

 Every increase in m by 1 is a drop in brightness by a factor of 2.512
 We receive 2.512 times less power from a 2^{nd} magnitude star
than from a 1^{st} magnitude one.
 We receive 2.512 ´2.512 =
6.310 times less from a 3^{rd} magnitude than a 1^{st}
magnitude
 We receive (2.512)^{5} times less from a 6^{th}
magnitude star than a 1^{st} magnitude. The 5 comes from 61.
 Because (2.512)^{5} = 100 (not by accident) the faintest stars
we can see are 100 times fainter than the brightest.

17

 From our Text, Horizons by Seeds

18


19

 Imagine being being in a rotating restaurant on top of a tall building.
All the outside objects are very far away – much farther than the
distance across the room.
 Paint the view on the windows – and keep the people near the center of
the room – away from the windows themselves.
 Can the people tell if the room is rotating, or if the painted windows
are just moving around the room?
 Which is more reasonable – a rotating room or rotating painted windows?

20

 If you “paint” the stars on a sphere much bigger than the earth, then
you can obtain the motion of the stars by pretending that sphere
rotates, rather than the earth.
For most people that motion is easier to “see”.
 The sphere rotates once every day (actually once every 23^{h} 56^{m}
for reasons we’ll see later)
 We will see later that the sun, moon, and planets move slowly along the
sphere relative to the stars. You
can think of them (for a night or so) as “stars” which move almost with
the other fixed – but drift relative to them from night to night.
 The celestial sphere will also have marked on it a projection of the
earth’s latitude and longitude system, as well as a few other special
points and circles.

21


22

 HORIZON: The horizontal circle
which separates the part of the sky visible to you and the part of the
sky hidden by the earth.
 ZENITH: The point on the sky
directly overhead.
 MERIDIAN: The circle which
starts on the northern horizon, runs through the zenith, continuing on
to the southern horizon. It
separates the eastern half of the sky from the western half.
 CELESTIAL POLES: The points where
the extension of the rotation axis of the earth would intersect the
celestial sphere.
 CELESTIAL EQUATOR: The circle
around the sky which would be a projection of the earth’s equator.

23

 At the Earth’s north pole, looking overhead all stars appear to circle
around the north celestial pole.
 At the equator:
 Stars on the celestial equator rise in the east, move overhead, then
set in the west
 The N and S celestial poles are just on your N and S horizons, and
stars near those points still circle around them. But those stars are only visible for
the upper half of their circles.

24

 Stars close enough to the north celestial pole are always above the
horizon, and just circle the pole star.
(CIRCUMPOLAR STARS)
 Stars on the celestial equator rise in the east, move higher along a
slanted path which crosses the “meridian” to the south of the zenith,
then descend and set due west.
 Stars far enough to the south never make it above the horizon.

25


26

 The earth’s axis of rotation is tilted 23.5^{0} relative to the
plane containing the sun and other planets.
 The gravity from the Sun and moon is trying to tip the earth just like
gravity is trying to tip a spinning top.
 As with the top, the axis of the earth wobbles or PRECESSES in space,
with a 26,000 year period.
 Because the directions to the celestial poles are defined by the spin
axis – those poles move with time.
 It isn’t that the stars move – it is that the grid we paint on the
celestial sphere has to be redrawn from timetotime.
 Eventually Polaris will not be the “pole” star.

27

