ارقام فلكية

MEAN ORBITAL ELEMENTS OF THE PLANETS

 

Planet Mean Distance Mean Distance Period of Revolution Eccentricity Inclination Long. of Long. of Long. at
Name from Sun (AU) from Sun (Mkm) Sidereal
(a)
(e) ° Asc. Node Perihelion Epoch
Mercury 0.387 57.9 0.2408 0.206 7.0 48.3 77.5 252.3
Venus 0.723 108.2 0.6152 0.007 3.4 76.7 131.6 182.0
Earth 1.000 149.6 1.0000 0.017 0.0 —- 102.9 100.5
Mars 1.524 227.9 1.8808 0.093 1.8 49.6 336.1 355.4
Jupiter 5.203 778.3 11.86 0.048 1.3 100.5 14.3 34.4
Saturn 9.555 1429.4 29.42 0.056 2.5 113.7 93.1 50.1
Uranus 19.218 2875.0 83.75 0.046 0.8 74.0 173.0 314.1
Neptune 30.110 4504.4 163.73 0.009 1.8 131.8 48.1 304.3
Pluto 39.545 5915.8 248.03 0.249 17.1 110.3 224.1 238.7

These elements are referred to the mean equinox and ecliptic of J2000.0 = JD 245 1545.0 = 2000 January 1.5 .

PHYSICAL ELEMENTS OF THE PLANETS

 

 

Object Equat. Diam. Oblateness Mass Density Gravity Escape Speed Rot’n Period Incl. Albedo
Name km Earth=1 t/m3 Earth=1 km/s d °
Sun 1392000 0 332946.0 1.41 27.9 617.5 25-35* —- —-
Mercury 4879 0 0.055274 5.43 0.38 4.2 58.646 0.0 0.11
Venus 12104 0 0.815005 5.24 0.90 10.4 243.019 177.4 0.65
Earth 12756 1/298 1.000000 5.52 1.00 11.2 0.9973 23.4 0.37
Moon 3475 0 0.012300 3.34 0.17 2.4 27.3217 6.7 0.12
Mars 6794 1/154 0.107447 3.94 0.38 5.0 1.0260 25.2 0.15
Jupiter 142980## 1/15.4 317.833 1.33 2.53 59.5 0.4101# 3.1 0.52
Saturn 120540## 1/10.2 95.159 0.70 1.06 35.5 0.4440 25.3 0.47
Uranus 51120## 1/43.6 14.500 1.30 0.90 21.3 0.7183 97.9 0.51
Neptune 49530## 1/58.5 17.204 1.76 1.14 23.5 0.6712 28.3 0.41
Pluto 2300 0? 0.0025 1.1 0.08 1.3 6.3872 123. 0.3

– The table gives the mean density, the gravity and the escape speed at the equator, and the inclination of the equator to the orbital plane.
* Depending on latitude.
# For the most rapidly rotating part of Jupiter, the equatorial region.
## At 1 bar (101.325 kPa).

LENGTH

  • One astronomical unit (AU)……………..
= 1.49597870 * 1011 m.
  • One light-year (ly)………………………….
= 9.460536 * 1015 m.
  • …………………………………………………..
= 63239.8 AU.
  • One parsec (pc)…………………………….
= 3.261631 light-year = 206264.8 AU
  • …………………………………………………..
= 3.085678 * 1016 m.
  • One mile………………………………………
º 1.609344 km.

 

TIME

 

Day

 

  • Mean sidereal (equinox to equinox):…………..
= 86,164.093 S
  • Mean rotation (fixed star to fixed star):……….
= 86,164.101 S
  • Day (d):………………………………………………..
º 86,400 S
  • Mean solar:……………………………………………
= 86,400.002 S

 

Month

 

  • Draconic (node to node):………………………
= 27.21222 d
  • Tropical (equinox to equinox):………………..
= 27.32158 d
  • Sidereal (fixed star to fixed star):…………….
= 27.32166 d
  • Anomalistic (perigee to perigee):…………….
= 27.55455 d
  • Synodic (New Moon to New Moon):……..
= 29.53059 d

 

Year

  • Eclipse (lunar node to lunar node):……….
= 346.6201 d
  • Tropical (equinox to equinox) (a):………..
= 365.2422 d
  • Average Gregorian:…………………………..
º 365.2425 d
  • Average Julian:…………………………………
º 365.2500 d
  • Sidereal (fixed star to fixed star):………….
= 365.2564 d
  • Anomalistic (perihelion to perihelion):……
= 365.2596 d

EARTH

  • Mass = 5.974 * 1024 kg.
  • Radius:
    • Equatorial (a)
    = 6378.140 km.
    • Polar (b)
    = 6356.755 km.
    • Mean
    = 6371.004 km.

  • One degree of latitude = 111.133 – 0.559 cos 2f km (at latitude f).
  • One degree of longitude = 111.413 cosf – 0.094 cos 3f km.
  • Dip of horizon in degrees for eye h meters above sea-level » 0.0293*Sqr(h).
  • Standard atmospheric pressure º 101.325 kPa (» 1 kg above cm2)
  • Speed of sound in standard atmosphere = 331 m/s.
  • Magnetic field at surface » 5 * 10-5 T.
  • Standard acceleration of gravity º 9.80665 m/s2
  • Age » 4.6 Ga
  • Solar parallax = 8².794148
  • Constant of aberration = 20².49552
  • Annual general precession = 50².29 (2000.0); Precession period = 25,800 a
  • Orbital speed = 29.8 km/s

    SUN

     

     

     

    • Mass = 1.9891 * 1030 kg.
    • Radius = 696,265 km.
    • Surface temperature = 5,780 K.
    • Inclination of the solar equator on the ecliptic of date = 7°.25
    • Longitude of the ascending node of the solar equator on the ecliptic of date = 76°
    • Period of rotation at equator:
      • Sidereal = 25.38 d
      • Mean synodic = 27.275 d
    • Solar wind speed near Earth » 450 km/s (travel time, Sun to Earth » 4 d).
    • Solar velocity = 19.75 km/s toward a = 18.07 h, d = +30° (solar apex).

     

    MILKY WAY GALAXY

     

    • Mass = 1012 solar masses.
    • Center: a = 17 h 45.7 min, d = -29°00¢ (2000).
    • Distance to center » 9 kpc
    • Diameter » 100 kpc
    • North pole: a = 12h 51 min, d = 27°08¢ (2000).
    • Rotational speed (at Sun) » 250 km/s
    • Rotational period (at Sun) » 220 Ma
    • Velocity relative to the 3 K background » 600 km/s toward a » 10 h, d » -20°

     

    MAGNITUDE OF STARS

     

    Magnitude Class Range Included Number of Stars Cumulative Total
    -1 -1.50 to -0.51 2 2
    0 -0.50 to +0.49 6 8
    +1 +0.50 to +1.49 14 22
    +2 +1.50 to +2.49 68 90
    +3 +2.50 to +3.49 197 287
    +4 +3.50 to +4.49 599 886
    +5 +4.50 to +5.49 1,976 2,862
    +6 +5.50 to +6.49 5,830 8,692
    +7 +6.50 to +7.49 16,726 25,418
    +8 +7.50 to +8.01 24,653 50,071

    GREEK ALPHABET

     

    # C. Letter S. Letter Name # C. Letter S. Letter Name
    1 A a Alpha 13 N n Nu
    2 B b Beta 14 X x Xi
    3 G g Gamma 15 O o Omicron
    4 D d Delta 16 P p Pi
    5 E e Epsilon 17 R r Rho
    6 Z z Zeta 18 S s , V Sigma
    7 H h Eta 19 T t Tau
    8 Q q , J Theta 20 U u Upsilon
    9 I i Iota 21 F f Phi
    10 K k Kappa 22 C c Chi
    11 L l Lambda 23 Y y Psi
    12 M m Mu 24 W w Omega

    LIMITING MAGNITUDES AND SEPARATIONS FOR VARIOUS APERTURES

     

    D (mm) 60 100 125 150 200 250 330 444
    LG 73 200 320 460 820 1300 2200 4000
    Lm 11.6 12.7 13.2 13.6 14.2 14.7 15.3 15.9
    a (²) 2.0 1.2 1.0 0.80 0.60 0.48 0.36 0.27
    0.2D (x) 12 20 25 30 40 50 66 89
    2D (x) 120 200 250 300 400 500 660 890

     

    • D: The diameter of the objective in mm.
    • LG (Light Grasp): The ratio of the light flux intercepted by a telescope’s objective lens or mirror to that intercepted by a human eye having a 7 mm diameter entrance pupil.
    • Lm: Limiting visual magnitude, where Lm » 2.7 + 5 log D, assuming transparent, dark-sky conditions and magnification M ³ 1D.
    • a: The smallest resolvable angle, where a » 120/D seconds of arc. However, atmospheric conditions seldom permit values less than 0.5².
    • Useful magnification range » 0.2D to 2D. The lower limit may be a little less, but depends upon the maximum diameter of the entrance pupil of the individual observer’s eye. The upper limit is determined by the wave nature of the light and the optical limitations of the eye, although atmospheric turbulence usually limits the maximum magnification to 400x or less. For examination of double stars, detection of faint stars, and studying structure in bright nebulae, magnification of up to 4D are sometimes useful. Note that the reciprocal of the coefficient to D is the diameter (in mm) of the telescope’s exit pupil.

    LIMITING LUNAR DETAILS

    The following table (based upon work by E.A. Whitaker) gives the approximate diameters of the smallest crater half-filled with shadow, and of the narrowest black line certainly distinguishable. Perfect seeing conditions and optical equipment are assumed. Observationally, different observers will have different limits.

     

    Aperture Smallest crater Narrowest rill
    (Inches) (Km/m) (m)
    1 14.5 Km 805
    2 7.2 Km 402
    3 4.8 Km 257
    4 3.6 Km 201
    6 2.4 Km 137
    8 1.8 Km 101
    10 1.5 Km 82
    12 1.2 Km 64
    15 1.0 Km 55
    18 805 m 46
    33 457 m 27

    SPECTRAL TYPES

     

    Spectral type Notes Temperature (K) Star example
    WR Rare, very luminous » 50,000 g2 Vel
    O Extremely hot, blue 28,000-50,000 Alnitak (z Ori)
    B Hot, blue stars 10,000-28,000 Regulus (a Leo)
    A Blue-white stars 7,500-10,000 Vega (a Lyr)
    F White stars 6,000-7,500 Procyone (a CMi)
    G Yellow stars 5,000-6,000 Capella (a Aur)
    K Orange stars 3,500-5,000 Aldebaran (a Tau)
    M Red giants 2,000-3,500 Ras Algethi (a Her)
    S Red giants (zirconium) 2,000-3,500 R Andromedae
    C Red giants (carbon stars) <2,000 X Cancri

    LUMINOSITY CLASSES

     

    Spectral type Notes
    0 Very luminous supergiants
    Ia Bright supergiants
    Ib Supergiants
    II Bright giants
    III Giants (normal giants)
    IV Subgiants
    V Main sequence (dwarfs)
    VI Subdwarfs
    VII White dwarfs

    MISCELLANEOUS

     

    • Speed of light, c º 299,792,458. m/s
    • p = 3.14 15 92 65 35 89 79
    • Number of square degrees on a sphere = 41,253
    • For 360° = 24 h, 15° = 1 h, 15¢ = 1 min, 15² = 1 s

     

    SOURCES

     

    1. Observer’s HandBook, of the Royal Astronomical Society of Canada (RASC), edited by Mr. Roy Bishop, after taking his kind permission.
    2. Sky Catalogue 2000.0, by Hirshfeld, Sinnott, and Ochsenbein. After taking permission from Mr. Sinnott of the Sky Publishing Corp.
    3. The Amateur Astronomer, by Patrick Moore.
    4. StarList 2000, by Richard Dibon-Smith.

    Note: Many of the numbers listed above are determined by measurement. Exceptions include defined quantities (indicated by three lines in the equal sign º), quantities calculated from defined quantities (e.g. m/ly, AU/pc), and numbers of mathematical origin such as p and conversion factors in angular measure. Of the measured quantities, some are known to only approximate precision. For these the equal sign is reduced to ».