Spruce Lake Elderhostel OBSERVING THE NIGHT SKY   Robert C. Newman

June 1-6, 1997                                    Biblical Seminary

                         1. EARTH AND SKY

 

Climate at Philadelphia, lat 39o56'58"N; long 75o09'21"W

Normal monthly temperature: 30-yr averages

 

1

month        1961-90   1951-80

 

January        30        31

February       33        33

March          42        42

April          52        53

May            63        63

June           72        72

July           77        77

August         76        75

September      68        68

October        56        57

November       46        46

December       36        36

(From 1997 World Almanac)

 

 

Sunrise/Sunset at Phila (40N, 75W)

Note: maxima and minima (bold) show earth's orbit not circular

 

date      sunrise   sunset

2

 

Jan 1     7:22      16:46

Jan 15    7:20      16:59

Feb 1     7:09      17:19

Feb 14    6:54      17:35

Mar 1     6:34      17:52

Mar 15    6:12      18:07

Apr 1     5:44      18:24

Apr 15    5:22      18:38

May 1     5:00      18:55

May 15    4:45      19:08

Jun 1     4:33      19:23

Jun 15    4:31      19:30

Jul 1     4:35      19:33

Jul 15    4:44      19:28

Aug 1     4:58      19:14

Aug 15    5:11      18:57

Why is the sky blue in the daytime and black at night?

 

Why is the sun red when it rises and sets?

1

Sep 1     5:28      18:32

Sep 15    5:41      18:09

Oct 1     5:56      17:42

Oct 15    6:10      17:21

Nov 1     6:29      16:58

Nov 15    6:46      16:43

Dec 1     7:03      16:35

Dec 15    7:15      16:36

(From 1997 World Almanac)


Horizon

 

Can you see farther in the day­time or at night?

 

How far can you see?

2

     On an ideal smooth, spherical earth, our ho­rizon is where a flat, broad cone with apex at our eye height tangen­tially touches the sur­face of the earth.

 

 

     The extremes:

          At eye height approaching infinity, cone becomes a cylinder, so we can see one full half of the earth; with earth's circum­ference c25 K mi, this means horizon is about 1/4 this distance, 6250 mi.

          At eye height approaching zero, cone becomes a flat plane, can see virtually none of earth, so horizon is basically zero.

 

     On the real earth, neither smooth not exactly spherical, horizon distance will vary in different directions due to details of relief and various obstacles (vegetation, build­ings, etc.).  If viewpoint is above local roughness, result is simpler, but will still depend on roughness near horizon in each direction.

 

     Ideal calculation:

          Let h = local ht of observer, R = radius of earth, D = distance to horizon; then since tangent point is a right angle, by Pythagoras' theorem:

 

 

 

 

 

 

     (h + R)2 = R2 + D2

 

     h2 + 2hR + R2 = R2 + D2

 

     h2 + 2hR = D2

 

     D = SQRT (h2 + 2 hR)

 

 

 

 

 

 

 

 

     Example:

          Let h = 5 ft, i.e., observer standing on surface.

               R = 4000 mi; h = .001 mi

          for h << R, equation simplifies to D = SQRT (2hR)

          D = SQRT (2x.001x4000) = SQRT (8) = 2.74 mi

             Table: Ideal Horizon for Various Heights

 

          R (earth) = 3963.2 mi; h (in miles)

          D = SQRT (7926.4h) = 89 SQRT(h)

 

          ht of observer (h)   horizon dist (D)

 

                5 ft                     2.7 mi

               10 ft                     3.9 mi

              100 ft               12.3 mi

             1000 ft               38.7 mi

                1 mi                     89 mi

               10 mi                    126 mi

              100 mi               890 mi

 

Earth's Rotation

 

     Earth rotates on its axis once in 24 hours.  A complete rotation is 360o, so rotation rate is 360o/24 hr = 15o/hr, which is 15o/hr/60 min/hr = 1/4 deg/min or 4 min/deg.

 

     Since the apparent diameter of both the sun and moon as viewed from the earth is about 1/2 degree, the sun and moon appear to move across the sky at about about one diameter every two minutes.

 

     If the sun or moon sets vertically compared to the horizon, then (ignoring effects of refraction by the atmosphere), the time of setting from when the lower edge first touches the horizon until the upper edge disappears would be about 2 minutes.

 

     But the sun, etc. does not set vertically as far north as we are.  Have to calculate the tilt of our horizon and such.  If we take the horizon tilt to be zero at the equator and 90o at the north pole, then our tilt at a given latitude will be equal to that of the latitude, so at Phila, tilt = 40 deg.  This is fixed rela­tive to the equator, as long as the earth does not shift its pole of rotation, or No Amer continent move too far.

 

     The sunset angle, however, varies with the season, since the earth's axis faces toward the sun in summer and away in winter.  The angle of the earth's axis is about 23o27' or 232 deg.  At the spring and fall equinoxes, the direction to the sun and the equator are aligned, so the sunset angle (mea­sured from the vertical) will be the same, or measured from the hori­zontal, SS = 90 - lat. 


     For Phila, this will be SS = 50o.  The two extremes are the winter solstice and the summer solstice, which are 232o smaller and larger than this.

 

 

                    Philadelphia, 40 deg N lat

     Date      Angle sun makes w/ horizon at rising/setting

 

     Mar 21    50o

     Jun 21    732o

     Sep 21    50o

     Dec 21    262o

 

Measuring Angles

 

     Since the distance to the sky is indeterminate, distances on the celestial sphere are measured as angles rather than miles (or whatever).  Standing on the surface of the earth, with no high hills or such around, it is about 90o from the horizon to the zenith, or 180o from one horizon to the horizon opposite.

 

     For smaller angles, it is convenient (if not terribly accurate) to use your anatomy for making measurements.  Say the distance from your eye to your stretched out thumb is about 24" or two feet.  And that your spread-out hand (span) is 9" from thumb to tip of small finger, that your palm width (without counting thumb) is 3" and your thumb width is 3/4". 

 

     Then, since the angle marked out by an object of length L at length L away is about 70o, then 

Rules of Thumb

 

Span              26o

Palm               9o

Thumb           2o

3

 

3

 

 

 

 

 

 

 

 

 

 

 

So your outstretched thumb marks off about 4 times the width of the sun or moon, about the distance (at the equator) that the celestial sphere turns in 8 minutes.  You palm marks off the dis­tance it turns in about half an hour (actually 36 min).  Two spans mark off a 45o angle.  The sun or moon is about the size of the cross section of a pencil at arm's length.


                        2. MOON AND PLANETS

 

Our Moon:

 

Moon:

     Radius = 1738 km = 1080 mi

     Mass = 7.32 x 1025 g = 7 x 1019 mT = 80 quintillion tons

     Orbit = Distance from earth = 385,000 km = 239,000 mi

 

The Planets:

 

Earth:   

     Radius = 6378 km = 3963 mi . 4000 mi

     Mass = 5.997 x 1027 g . 6 x 1021 mT = 6.6 sextillion tons

     Gravity = 9.8 m/sec2 = 32 ft/sec2

     Orbit = 1 AU = 149.6 million km . 93 million mi

 

Planet

a

(AU)

Or­bit. Peri­od

Rot.

Peri­od

Mass*

 

Radi­us*

 

Densi­ty+

Surface

Gravity*

Known

Moons

Mercury

0.39

88d

58.7d

.055

.382

5.4

.377

0

Venus

0.72

225d

243d

.815

.949

5.3

.905

0

Earth

1.00

365d

23.9h

1.00

1.00

5.5

1.00

1

Mars

1.52

1.88y

24.6h

.107

.533

3.9

.377

2

Juptier

5.20

11.9y

9.92h

318

11.2

1.3

2.54

16+

Saturn

9.54

29.5y

10.7h

95.2

9.45

0.7

1.07

19+

Uranus

19.2

84y

17.3h

14.5

4.10

1.2

.869

15

Neptune

30.1

165y

16.1h

17.0

3.90

1.7

1.14

8

Pluto

39.4

248y

6.4d

.003

.18

2.0

.07

1

 

*cp earth's                  +cp density of water

Source: David Morrison, The Planetary System (Astronomical Society of the Pacific, 1989)


Other Moons (Satellites):

 

Planet

Moon

a (km)

period (days)

mass*

radius (km)

Earth

Moon

385,000

27.3

1.00

1738

Mars

Phobos

9,380

0.319

1.3 [-7]

12i

 

Deimos

23,500

1.26

2.7 [-8]

7.5i

Jupiter

Io

422,000

1.77

1.2

1816

 

Europa

671,000

3.55

0.66

1569

 

Ganymede

1,070,000

7.16

2.0

2631

 

Callisto

1,883,000

16.7

1.5

2400

Saturn

Mimas

186,000

0.942

.0005

197

 

Enceladus

238,000

1.37

.001

251

 

Tethys

295,000

1.89

.01

524

 

Dione

377,000

2.74

.014

560

 

Rhea

527,000

4.52

.034

765

 

Titan

1,220,000

16.0

1.8

2575

 

Hyperion

1,481,000

21.3

?

135i

 

Iapetus

3,561,000

79.3

.026

718

 

Phoebe

12,950,000

550r

?

110

Uranus

Miranda

130,000

1.41

.001

243

 

Ariel

191,000

2.52

.02

580

 

Umbriel

266,000

4.14

.02

600

 

Titania

436,000

8.71

.05

805

 

Oberon

583,000

13.5

.04

775

Neptune

Triton

354,600

5.88r

0.8

1430

 

Nereid

5,510,700

359

2 [-8]

470

Pluto

Charon

19,700

6.39

.02

600

 

*cp our moon's           [-n] means times -n powers of 10                 r = retrograde             i = irregular

Source: Morrison, Planetary System

 


                         3. SUN AND STARS

 

A star is a huge ball of gas held together by its own gravity.  Our sun is a star, by far the nearest one to us.

 

Because gravity is a spherically symmetric force, a star is spherical, except for a larger or smaller bulge at its equator, depending on how fast it is spinning.

 

The force of gravity heats up the gas inside the star, until it reaches a temperature high enough to turn on a nuclear reaction by which hydrogen is converted to helium.  Thereafter the star produces light and heat from the energy produced by this reaction until the hydrogen in its core is exhausted.  Stars getting their energy from hydrogen are called Main Sequence stars.

 

                                                                  Principal Stellar Classes of Stars

Type

Class

Surface Temp (deg K)

Example

Hottest, bluest

O

40,000

Alnitak (zeta Orionis)

Bluish

B

18,000

Spica (alpha Virginis)

Bluish-white

A

10,000

Sirius (alpha Can Maj)

White

F

7,000

Procyon (alpha Can Min)

Yellowish-white

G

5,500

Sun

Orangish

K

4,000

Arcturus (alpha Bootes)

Coolest, reddest

M

3,000

Antares (alpha Scorpii)

 

Source: Wm K Hartmann, Astronomy: the Cosmic Journey (Wadsworth, 1989)

 

File written with CompuPic(R) - Photodex Corporation (http://www.photodex.com)

4

 

The (17) Brightest Stars as Seen from Earth

Star Name

(Constellation)

Apparent

Magnitude

Luminosi­ty

(cp sun)

Type

Radius

(cp sun)

Distance

(light yr)

Sun

-26.7

1.0

Main seq

1.0

0.0

Sirius (Can Maj)

-1.4

23

Main seq

1.8

8.8

Canopus (Cari­na)

-0.7

(1400)

Supergiant

30

110

Arcturus (Bootes)

-0.1

115

Red giant

(25)

36

Rigel Kent (Centaurus)

0.0

1.5

Main seq

1.1

4.3

Vega (Lyra)

0.0

(58)

Main seq

(3)

27

Capella (Auriga)

0.1

(90)

Red giant

13

46

Rigel (Orion)

0.1

(60,000)

Supergiant

(40)

(910)

Procyon (Can Min)

0.4

6

Main seq

2.2

11

Archernar (Eridanus)

0.5

(650)

Main seq

(7)

120

Hadar (Centaurus)

0.7

(10,000)

Supergiant

(10)

490

Betelgeuse (Ori­on)

0.7

10,000

Supergiant

800

520

Altair (Aquila)

0.8

(9)

Main seq

1.5

16

Aldebaran (Tau­rus)

0.9

125

Red giant

(40)

68

Acrux (So Cross)

0.9

(2500)

Main seq

(3)

(360)

Antares (Scorpius)

0.9

(9000)

Supergiant

(600)

(520)

Spica (Virgo)

1.0

(2300)

Main seq

8

274

Source: Hartmann, Astronomy; numbers in parentheses are estimates.

 

Some Prominent Star Clusters

 

Name

Distance (ly)

Diameter (ly)

Mass (sun = 1)

Age (yr)

Open Clusters

Ursa Major

68

23

300

200M

 

Hyades

137

16

300

500M

 

Pleiades

415

13

350

100M

 

Beehive (M44)

518

13

300

400M

Globular Clusters

M4

6500

30

150,000

1.4B

 

M13

21500

35

660,000

1.4B

 

M5

25000

40

850,000

1.4B

 

M3

32500

42

1,100,000

1.4B

 

Source: Hartmann, Astronomy


                          4. THE GALAXIES

 

A galaxy is a much larger collection of stars than an open or even a globular cluster, which are parts of galax­ies.  Galaxies were once called nebulae, then later, "island universes."

 

Our galaxy has been called "the Milky Way" since ancient times, long before we knew what it was.  It is shaped rather like two fried eggs laid back-to-back, or a pair of marching-band cymbals, that is, a rather flat disk of stars with a flattened-roundish bulge of stars in the center.  It appears to be about 100,000 ly across the disk, which is perhaps only 10,000 ly thick.  The bulge is perhaps 30,000 ly thick by 40,000 wide.  The disk has very prominent spiral arms characterized by dust clouds and young, bright stars.

               Distances to Objects in the Milky Way Galaxy

Destination

Distance (ly)

Nearest star beyond Sun

4.2

Sirius

8.8

Vega

26

Hyades cluster

137

Pleiades cluster

415

Central part of our spiral arm (Orion)

1300

Orion nebula

1500

Vertical distance to leave disk

3300

Next-nearest spiral arm (Sagittarius)

3900

Center of galaxy

30,000

M13 globular cluster

36,000

Far edge of galaxy

78,000

Source: Hartmann, Astronomy

 

                                                                                    Types of Galaxies

Name

Sym­bol

Shapes

Subclasses

Frequency

Elliptical

E

spherical to flat disk;

both giant and dwarf

E0 -> E7+S0: less -> more

flat­tened

giant 5%

dwarf 50%

Spiral

S

disk w/ spiral arms

Sa -> Sc: smaller center,

more open arms

20%

Barred spiral

SB

bar connects center

and arms

SBa -> SBc: same tendencies

as regular spirals

 

Irregular

Irr

no standard shape

none

25%


                          5. THE UNIVERSE

 

What is the universe?  Is it "all that is, or ever was, or ever will be" (Carl Sagan)?  We don't know.  We could define it by Sagan's definition, but that might be misleading.  We're inside, and don't know how big it is.  The visible part apparently had a beginning at the big bang.

 

What we do know:

 

1. The universe is big.  The distances to stars are measured in light years (6 trillion miles each) or parsecs (3.26 ly).  The distan­ces to globular clusters in thousands of light years (or kiloparsecs), to galaxies in millions of light years (or megapar­secs), the distances to the most distant observable objects (galaxies and quasars) in billions of light years (or gigapar­secs).  Thus the universe is at least billions of trillions (i.e., quintillions) of miles in radius.

 

2. The visible universe cannot be both infinitely large and infinitely old.  Because the sky is dark at night!  The so-called Olbers' Paradox shows that if the universe is infinitely old and infinitely large (with a reasonably uniform distribution of stars) the light from the stars falling on the earth ought to be infinite or (at least) very bright.  Because the sky (ignoring city lights, etc.) is instead rather dark, the stars must come to an end before their images cover every speck of the sky (so the universe is not infinite), OR the really distant stars whose images would cover every speck of the sky have not been burning long enough for their light to get here yet (so the universe hasn't always existed).

 

3. The visible universe is probably only some 10-20 billion years old.  This appears to be the case for several reasons:

a. The most distant objects we can see are only about 10 billion ly away;

b. The age of the globular clusters is some 10-15 billion years;

c. The expansion rate of the universe would suggest that it was once very hot and compact some 10-20 billion years ago;

d. The age of the earth and sun is some 5 billion years, and the sun does not appear to be a first generation star.


4. The universe shows every evidence of being very carefully designed to be able to support life.

 

                                                                                         The "Fine Tuned" Universe

Item

Consequences if larger

Consequences if smaller

Strong nuclear force constant

no hydrogen

nothing but hydrogen

Weak nuclear force constant

too much He; no heavy elements*

too little He; no heavy elements*

Gravitational force constant

stars too hot, burn too fast

stars too cool, no heavy elements

Electromagnetic force constant

insufficient chemical bonding

insufficient chemical bonding

Ratio of e-m to gravity

no stars less than 1.4 solar masses

no stars more than .8 solar masses

Ratio of electron to proton mass

insufficient chemical bonding

insufficient chemical bonding

Ratio of ## of protons to electrons

e-m dominates grav; no stars

e-m dominates grav; no stars

Expansion rate of universe

no galaxy formation

univ collapses quickly

Entropy level of universe

no proto-galaxy formation

no star formation

Mass density of universe

too much H-2, stars burn too fast

too little He & heavy elements

Velocity of light

stars too luminous

stars not luminous enough

Age of universe

no solar-type stars in right places

solar-type stars not yet formed

Initial uniformity of radiation

stars, clusters, galaxies not formed

universe mostly black holes

Fine structure constant

DNA doesn't work; stars too small

DNA doesn't work; stars too large

Average distance betw galaxies

insuff gas to continue star formation

sun's orbit too disturbed

Average distance betw stars

too few heavy elements for planets

planetary orbits unstable

Decay rate of proton

life exterminated by decay radiation

insuff matter for life

Energy level ratio C-12 to O-16

insufficient oxygen

insufficient carbon

Ground state energy level of He-4

insufficient O and C

insufficient O and C

Decay rate of Beryllium-8

stars explode catastrophically

no elements heavier than Be

Mass excess: neutron over proton

n's decay, too few heavy ele­ments

p's decay, stars collapse

Initial excess nucleons to anti-nuc

too much rad for planet formation

not enough matter for stars

Polarity of water molecule

heat of fusion, vap too gt for life

heats too small; ice won't float

Ratio of exotic to ordinary matter

univ collapse before solar-type stars

no galaxies formed

*outside stars; source:  Ross, Creator and Cosmos, 118-121.

 

 

5. Our earth-sun environment appears to be unique and even designed.  The following characteristics of a planet, its moon, its star, its galaxy, must have values falling within narrowly defined ranges for life of any kind to exist.

 

1. galaxy type

too elliptical: star formation ends before enough heavy elements for life chemistry

too irregular: radiation exposure too high on occasion, heavy elements for life chem not available

 

2. supernova eruptions

too close: life on planet exterminated

too far: not enough heavy elements to form rocky planets

too frequent: life on planet exterminated

too infrequent: not enough heavy elements to form rocky planets

     too late: life on planet exterminated

too soon: not enough heavy elements to form rocky planets

 

3. white dwarf binaries

too few: insuff fluorine for life chemistry to proceed

too many: planetary orbits disrupted

too soon: not enough heavy elements to make fluorine

too late: flourine formed too late to be incorporated into planet

 

4. parent star distance from center of galaxy

farther: heavy elements insuff for rocky planets

closer: too much galactic radiation; planetary orbits dis­turbed by large number of stars

 

5. number of stars in planetary system

more than one: plantary orbits disrupted

less than one: not enough heat for life

 

6. parent star birth date

more recent: star not yet in stable-burning phase; too many heavy elements

less recent: not enough heavy elements

 

7. parent star age

older: luminosity would change too quickly

younger: luminosity would change too quickly

 

8. parent star mass

greater: luminosity too variable; star burns too rapidly

less: life zone too narrow; tides slow rotation too much; uv radiation insufficient for photosynthesis

 

9. parent star color

redder: photosynthesis too weak

bluer: photosynthesis too weak

 

10. parent star luminosity change

increases too soon: runaway greenhouse effect

increases too late: runaway glaciation

 

11. planet's surface gravity

larger: atm retains too much ammonia, methane

smaller: atm loses too much water

 

12. planet's distance from parent star

further: too cool for stable water cycle

closer: too warm for stable water cycle

 

13. inclination of planetary orbit

too great: temperature differences too extreme

 

14. eccentricity of planetary orbit

too great: seasonal temperature differences too extreme

 

15. axial tilt of planet

greater: surface temperature differences too great

less: surface temperature differences too great

 

16. rotation period of planet

longer: diurnal temperature differences too great

shorter: wind velocities too great

 

17. rate of change in rotation period

larger: surface temperature range necessary for life not sustained

smaller: surface temperature range necessary for life not sustained

 

18. age of planet

too young: planet would rotate too rapidly

too old: planet would rotate too slowly

 

19. magnetic field of planet

stronger: electromagnetic storms too severe

weaker: insuff protection for land life from hard radiation from sun and stars

 

20. thickness of planet's crust

thicker: too much oxygen lost to crust

thinner: too much volcanic & tectonic activity

 

21. reflectivity of planet

greater: runaway glaciation

less: runaway greenhouse

 

22. collision rate with asteriods and comets

greater: too many species wiped out

less: too few minerals needed for life in crust

 

23. ratio of oxygen to nitrogen in atmosphere

larger: advanced life functions proceed too quickly

smaller: advanced life functions proceed too slowly

 

24. carbon dioxide level in atmosphere

greater: runaway greenhouse effect

less: plant photosynthesis too low

 

25. water vapor level in atmosphere

greater: runaway greenhouse effect

less: too little rainfall for advanced land life

 

26. atmospheric electric discharge rate

greater: too much destruction from fire

less: too little nitrogen fixed in soil

 

27. ozone level in atmosphere

greater: surface temperatures too low

less: surface temps too high; too much uv at surface

 

28. quanity of oxygen in atmosphere

greater: plants, hydrocarbons burn too easily

less: too little for advanced animals to breathe

 

29. activity of tectonic plates

greater: too many life forms destroyed

less: nutrients lost by river runoff not recycled

 

30. ratio of oceans to continents

greater: diversity, complexity of life forms limited

smaller: diversity, complexity of life forms limited

 

31. global distribution of continents (for Earth)

too much in So hemisphere: seasonal temperature differences would be too severe for advanced life

 

32. soil mineralization

too nutrient poor: diversity, complexity of life forms limited

too nutrient rich: diversity, complexity of life forms limited

 

33. gravitational interaction of planet with moon

greater: tidal effects on oceans, atmosphere and rotation period would be too severe

less: climatic instability; movement of nutrients betw continents and oceans restricted; magnetic field too weak

 

Probability of getting all these in right range for a given planet is 1 in 10 to 53rd power!

 

Source: Ross, Creator and Cosmos, 131-145.