SpruceLake Elderhostel OBSERVING THE NIGHT SKY   Robert C. Newman

June 1-6,1997                                    BiblicalSeminary

                         1.EARTH AND SKY

 

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

Normal monthlytemperature: 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 WorldAlmanac)

 

 

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

Note: maxima andminima (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 WorldAlmanac)


Horizon

 

Can you see farther in the day­time or at night?

 

How far can you see?

2

     Onan ideal smooth, spherical earth, our ho­rizon is where a flat, broad conewith apex at our eye height tangen­tially touches the sur­face of theearth.

 

 

     The extremes:

          Ateye height approaching infinity, cone becomes a cylinder, so we can see onefull half of the earth; with earth's circum­ference c25 K mi, this meanshorizon is about 1/4 this distance, 6250 mi.

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

 

     Onthe real earth, neither smooth not exactly spherical, horizon distance willvary 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 stilldepend on roughness near horizon in each direction.

 

     Ideal calculation:

          Let h = local ht ofobserver, R = radius of earth, D = distance to horizon; then since tangentpoint 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:

          Leth = 5 ft, i.e., observer standing on surface.

               R= 4000 mi; h = .001 mi

          forh << 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)

 

          htof observer (h)   horizon dist(D)

 

                5 ft                     2.7mi

               10 ft                     3.9mi

              100 ft               12.3 mi

             1000 ft               38.7 mi

                1 mi                     89mi

               10mi                    126 mi

              100 mi               890 mi

 

Earth'sRotation

 

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

 

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

 

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

 

     But the sun, etc. doesnot 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 zeroat the equator and 90o at the north pole, then our tilt at a givenlatitude will be equal to that of the latitude, so at Phila, tilt = 40deg.  This is fixed rela­tiveto the equator, as long as the earth does not shift its pole of rotation, or NoAmer continent move too far.

 

     Thesunset angle, however, varies with the season, since the earth's axis facestoward the sun in summer and away in winter.  The angle of the earth's axis is about 23o27' or232deg.  At the spring and fallequinoxes, the direction to the sun and the equator are aligned, so the sunsetangle (mea­sured from the vertical) will be the same, or measured from thehori­zontal, SS = 90 - lat. 


     ForPhila, this will be SS = 50o. The two extremes are the winter solstice and the summer solstice, whichare 232osmaller and larger than this.

 

 

                    Philadelphia,40 deg N lat

     Date      Angle sun makesw/ horizon at rising/setting

 

     Mar 21    50o

     Jun 21    732o

     Sep 21    50o

     Dec 21    262o

 

MeasuringAngles

 

     Since the distance tothe sky is indeterminate, distances on the celestial sphere are measured asangles 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 180ofrom one horizon to the horizon opposite.

 

     For smaller angles, itis convenient (if not terribly accurate) to use your anatomy for makingmeasurements.  Say the distancefrom your eye to your stretched out thumb is about 24" or two feet.  And that your spread-out hand (span) is9" from thumb to tip of small finger, that your palm width (withoutcounting thumb) is 3" and your thumb width is 3/4". 

 

     Then, since the anglemarked 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 youroutstretched thumb marks off about 4 times the width of the sun or moon, aboutthe distance (at the equator) that the celestial sphere turns in 8minutes.  You palm marks off thedis­tance 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 ofthe cross section of a pencil at arm's length.


                        2.MOON AND PLANETS

 

Our Moon:

 

Moon:

     Radius = 1738 km = 1080mi

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

     Orbit = Distance fromearth = 385,000 km = 239,000 mi

 

The Planets:

 

Earth:   

     Radius = 6378 km = 3963mi .4000 mi

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

     Gravity = 9.8 m/sec2= 32 ft/sec2

     Orbit = 1 AU = 149.6million 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                  +cpdensity of water

Source: David Morrison, ThePlanetary 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 hugeball of gas held together by its own gravity.  Our sun is a star, by far the nearest one to us.

 

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

 

The force ofgravity heats up the gas inside the star, until it reaches a temperature highenough to turn on a nuclear reaction by which hydrogen is converted tohelium.  Thereafter the starproduces light and heat from the energy produced by this reaction until thehydrogen 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 areestimates.

 

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 amuch larger collection of stars than an open or even a globular cluster, whichare parts of galax­ies. Galaxies were once called nebulae, then later, "islanduniverses."

 

Our galaxy hasbeen called "the Milky Way" since ancient times, long before we knewwhat it was.  It is shaped ratherlike two fried eggs laid back-to-back, or a pair of marching-band cymbals, thatis, a rather flat disk of stars with a flattened-roundish bulge of stars in thecenter.  It appears to be about100,000 ly across the disk, which is perhaps only 10,000 ly thick.  The bulge is perhaps 30,000 ly thick by40,000 wide.  The disk has veryprominent 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 theuniverse?  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 bemisleading.  We're inside, anddon't know how big it is.  Thevisible part apparently had a beginning at the big bang.

 

What we doknow:

 

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

 

2. The visibleuniverse 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 infinitelyold and infinitely large (with a reasonably uniform distribution of stars) thelight 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 anend before their images cover every speck of the sky (so the universe is notinfinite), OR the really distant stars whose images would cover every speck ofthe sky have not been burning long enough for their light to get here yet (sothe universe hasn't always existed).

 

3. The visibleuniverse is probably only some 10-20 billion years old.  Thisappears to be the case for several reasons:

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

b. The age of the globular clusters is some10-15 billion years;

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

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


4. Theuniverse shows every evidence of being very carefully designed to be able tosupport 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. Ourearth-sun environment appears to be unique and even designed.  Thefollowing characteristics of a planet, its moon, its star, its galaxy, musthave values falling within narrowly defined ranges for life of any kind toexist.

 

1. galaxy type

too elliptical: star formation ends beforeenough heavy elements for life chemistry

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

 

2. supernovaeruptions

too close: life on planet exterminated

too far: not enough heavy elements to formrocky planets

too frequent: life on planet exterminated

too infrequent: not enough heavy elements toform rocky planets

     too late: life onplanet exterminated

too soon: not enough heavy elements to formrocky planets

 

3. white dwarfbinaries

too few: insuff fluorine for life chemistry toproceed

too many: planetary orbits disrupted

too soon: not enough heavy elements to makefluorine

too late: flourine formed too late to beincorporated into planet

 

4. parent stardistance from center of galaxy

farther: heavy elements insuff for rockyplanets

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

 

5. number ofstars in planetary system

more than one: plantary orbits disrupted

less than one: not enough heat for life

 

6. parent starbirth date

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

less recent: not enough heavy elements

 

7. parent starage

older: luminosity would change too quickly

younger: luminosity would change too quickly

 

8. parent starmass

greater: luminosity too variable; star burnstoo rapidly

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

 

9. parent starcolor

redder: photosynthesis too weak

bluer: photosynthesis too weak

 

10. parent starluminosity change

increases too soon: runaway greenhouse effect

increases too late: runaway glaciation

 

11. planet'ssurface gravity

larger: atm retains too much ammonia, methane

smaller: atm loses too much water

 

12. planet'sdistance from parent star

further: too cool for stable water cycle

closer: too warm for stable water cycle

 

13. inclinationof planetary orbit

too great: temperature differences too extreme

 

14. eccentricityof planetary orbit

too great: seasonal temperature differencestoo extreme

 

15. axial tilt ofplanet

greater: surface temperature differences toogreat

less: surface temperature differences toogreat

 

16. rotationperiod of planet

longer: diurnal temperature differences toogreat

shorter: wind velocities too great

 

17. rate ofchange in rotation period

larger: surface temperature range necessaryfor life not sustained

smaller: surface temperature range necessaryfor life not sustained

 

18. age of planet

too young: planet would rotate too rapidly

too old: planet would rotate too slowly

 

19. magneticfield of planet

stronger: electromagnetic storms too severe

weaker: insuff protection for land life from hardradiation from sun and stars

 

20. thickness ofplanet's crust

thicker: too much oxygen lost to crust

thinner: too much volcanic & tectonicactivity

 

21. reflectivityof planet

greater: runaway glaciation

less: runaway greenhouse

 

22. collisionrate with asteriods and comets

greater: too many species wiped out

less: too few minerals needed for life incrust

 

23. ratio ofoxygen to nitrogen in atmosphere

larger: advanced life functions proceed tooquickly

smaller: advanced life functions proceed tooslowly

 

24. carbondioxide level in atmosphere

greater: runaway greenhouse effect

less: plant photosynthesis too low

 

25. water vaporlevel in atmosphere

greater: runaway greenhouse effect

less: too little rainfall for advanced landlife

 

26. atmosphericelectric discharge rate

greater: too much destruction from fire

less: too little nitrogen fixed in soil

 

27. ozone levelin atmosphere

greater: surface temperatures too low

less: surface temps too high; too much uv atsurface

 

28. quanity ofoxygen in atmosphere

greater: plants, hydrocarbons burn too easily

less: too little for advanced animals tobreathe

 

29. activity oftectonic plates

greater: too many life forms destroyed

less: nutrients lost by river runoff notrecycled

 

30. ratio ofoceans to continents

greater: diversity, complexity of life formslimited

smaller: diversity, complexity of life formslimited

 

31. globaldistribution of continents (for Earth)

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

 

32. soilmineralization

too nutrient poor: diversity, complexity oflife forms limited

too nutrient rich: diversity, complexity oflife forms limited

 

33. gravitationalinteraction of planet with moon

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

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

 

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

 

Source: Ross, Creatorand Cosmos, 131-145.