May 27, 2016

Learn Orbital Mechanics – motion of earth, sun, moon & satellites

Filed under: 08. Orbit & Space Tech., NIL - All Posts — myreaders @ 7:19 am

Title  :  Learn  Orbital  Mechanics – motion of earth, sun, moon & satellites

Ref URL  :

Access  :  Free,  no  registration  required.

Description  : Topics organized into 8 sections include tutorials & software  driven computations – Introduction to Orbital mechanics, Astronomical time standards & conversions, Positional astronomy – earth orbit around sun, Position of sun on celestial sphere, Position of earth on celestial sphere, Satellites orbit elements – ephemeris, keplerian elements, state vectors, Satellites motion around earth – orbital & positional parameters, Satellite pass for earth Station – prediction of ground trace. (Total 400 pages in 8 pdf files include text, graphics, examples, problems & OM-MSS software  driven test results).

Objectives  :  Free online self explanatory learning resources & teaching materials.

Who Should read  :  Beginners,  senior students,  professionals  and  researchers.

Author : RC Chakraborty, , Former Visiting Professor at JUET.

Conditions of Use :  Creative Commons Attribution-Noncommercial-No Derivative Works

4.0 International [Ref. ]

Update  on  Dec. 20, 2015

Tags : OM-MSS software, Orbital mechanics, Astronomical time, Positional astronomy, Sun position on celestial sphere, Earth position on celestial sphere, Earth motion around sun, Satellites orbit elements, Satellites motion around earth, Satellite pass ground trace for earth Station.

July 17, 2015

Satellite Pass for Earth Station – Prediction of Ground Trace Coordinates & more

   Satellite  Pass  for  Earth  Stn  –  Prediction  of  Ground  Trace  Coordinates   &  more.

by  R C  Chakraborty,   July 17,  2015,   Pages   268 – 390.

(This   is   Sec. 7,    pp  268 – 390,   of   Orbital   Mechanics  –  Model   &   Simulation   Software  (OM-MSS),   Sec.  1  to 10,   pp  1  –  402.)

Satellites,  look  like  slow-moving  Stars,  are  most  visible  when  they  are  in  Sunlight  while  the  viewer  is  in  darkness.

A  typical  Satellite  in  low  Earth  orbit  (LEO)   circles  the  Earth  about  16  times  each  day.

The  Orbital  Velocity  of  a  LEO  satellite  is  about  7500  meters/sec.

The  Orbital  Velocity  of  a  Geo-stationary  satellite  is  about  3007  meters/sec.

The  Moon,  the  only  natural  satellite  of  earth  has  orbital  velocity  about  1003  meters/sec.

Satellite  Pass  for  Earth  Stn,   is  Computed   for  following  six  satellites  :   LANDSAT 8,   SPOT 6,   CARTOSAT-2B,   ISS (ZARYA),   GSAT-14,   and   MOON.

The  ‘Satellites  Pass’   goes  through  a  Time_Step  of  2 minutes  (120 sec).   For  Moon  the  Time_Step  is  of  1 hr  (3600 sec).

The  input  is  respective  Satellite’s  NASA/NORAD  ‘Two-Line Elements’  (TLE).

The  Output  is   Predictions   of   instantaneous   Ground  trace  Coordinates,   look  angles  &  more  at  each  Time_Step   on   computer   screen   in   a   Table   form    where

respective   columns   indicate  :

Col 1 – Orbit no,                        Col 2 – Node  Ascending  or  Descending,          Col 3 to 6 – Input  time  GMT  D H M S,

Col 7 – True  Anomaly,            Col 8 – Sat  Height  from  earth  surface,             Col 9 – Sat  at  Perigee,  Equator,  or  Apogee,

Col 10 – Sat  Velocity,              Col 11 , 12 – Latitude & Longitude at sub-satellite point on earth surface,

Col 13 – Sat  Slant  Range  from  earth  stn,             Col 14 – Distance  of  sub-satellite  point  from  earth  stn,

Col 15 , 16 – Sat  Pitch  &  Roll  angles,                      Col 17 , 18 – Sat  Elevation  &  Azimuth  angles  at  earth  stn,

Col 19 – Access  to  Sat  through  On  Board  Computer  or  Direct  Line  Of  Sight  based  on  elevation  angle  at  ES,

Col 20 , 21 – Sun  Elevation  &  Azimuth  angles  at  sub-Satellite  point  on  earth  surface,

Col 22 – Data  Acquisition  using  Visible  Band  Camera  or  Night  Vision  Devices  as  per  illumination  over   observed  surface,

Col 23 to 26 – Local  Mean  Time  at  earth  stn,       Col 27, 28 – Sun  Elevation  &  Azimuth  angles  at  earth  stn,

Col 29 – Distance  of  Sub-Sun  point  on  earth  surface  from  earth  stn,

 Col 30 – Line  number .

For   complete   post  (Page  268 – 390)    Move   on   to   Website   URL  :

July 15, 2015

Satellites Motion around Earth : Orbital & Positional Parameters at Epoch

   Satellites   Motion   around    Earth   :   Orbital   &   Positional   Parameters   at   Epoch

by   R C  Chakraborty,   July 15,  2015,   Pages  193  –  267.

(This   is   Sec. 6,    pp  193 – 267,   of   Orbital   Mechanics  –  Model   &   Simulation   Software  (OM-MSS),   Sec.  1  to 10,   pp  1  –  402.)

The   Satellites   Orbit   around   Earth   Counterclockwise   in   the   same   way   as   Earth   orbits   around   Sun.

In  the  previous  section,   the  preliminaries  about  ‘Satellite  Orbit’   followed  by  NASA / NORAD  ‘Two-Line  Elements’ (TLE)   were  presented.   (Ref.

Here  presented  Satellites  Motion  around  Earth  :  Computing  Orbital  &  Positional  parameters,  the  OM-MSS software  utility.   This  utility  is  applied  one-by-one  to  six  satellites,   LANDSAT 8,   SPOT 6,   CARTOSAT-2B,  ISS (ZARYA),   GSAT-14,  &   Moon.   The  Input  is  NASA / NORAD  ‘Two-Line Elements’ (TLE)  Bulletin   of   the respective  satellite.   The  Output  is  corresponding  satellite’s  motion  around  earth,  the  orbital  &  positional parameters.

Satellite  motion  around  Earth  is  represented  by  computing  about  120  orbital  parameters,   put  into   28 groups.   The  number  is  large,   because  some  parameters  are  computed  using  more  than  one  model  equation, that  require  different  inputs.   This  confirms  accuracy  &  validation  of  results  and  understanding  the  different input   considerations.

Satellite  Orbital  &  Positional  parameters  for  computation  purpose  are  put  into  following  groups  :

1.    UT  Year  and  Days  decimal  of  year  :   Convert  into  UT  YY  MM  DD  hh  min  sec  &  Julian day.

2.    Satellite  Orbit  Semi-major  axis  in  km,   Ignoring   and   also  Considering  earth  oblatenes.

3.    Satellite  Mean  motion  in  rev  per  day,   Ignoring   and   also  Considering  earth  oblatenes.

4.    Satellite  Orbit  Time  Period  in minute  at  time_t  Considering  earth  oblatenes.

5.    Satellite  Rate  of  change  of  Right  Ascension  and  Argument  of  Perigee  in  deg  per  day  at  time_t.

6.    Satellite  Mean  anomaly,   Eccentric  anomaly,   True  anomaly  in  deg  at  time_t  considering   earth oblateness.

7.    Satellite  Position  vector [rp, rq]  from  Earth  Center (EC)  to  Satellite  in  PQW  frame,   perifocal  coordinate  system.

8.    Satellite  Position  Range  Vector  from  Earth  Center (EC)  to  Satellite (SAT)  –  finding  Range  Vector [rI,  rJ,  rK,  r]  Components  in  km  in  frame  IJK.

9.    GST  Greenwich  sidereal  time  and  GHA  Greenwich  hour  angle  in  0  to  360  deg,   at  input  at  time_t.

10.  Satellite (SAT)  Orbit  point  direction  :   Finding  Right  Ascension (Alpha)  deg  and  Declination (Delta)  deg  using  angles.

11.  Satellite  Longitude  &  Latitude  in  deg at  time_t ;   (ie  Sub-Sat  point  log  &  lat  on  earth  surface).

12.  Satellite  height  in  km  from  EC  to  Sat  and  from  Earth  surface  to  Sat  at  time_t.

13.  Distance  of  Sub-Sat  point  To  Earth  Stn (ES)  in  km  over  Earth  surface  at  time_t.

14.  Local  sidereal  time (LST)  and  Local  mean  time (LMT)  over  Sub-Sat  point  Longitude  on  earth.

15.  Local  sidereal  time (LST)  and  Local  mean  time (LMT)  over  Earth  stn (ES)  or  Earth  point (EP)  Longitude.

16.  Earth  Stn  Position  Vector  from  Earth  Center (EC)  to  Earth  Stn (ES)  :   Finding  Range  Vector [RI,  RJ,  RK,  R]  Components  in  IJK  frame.

17.  Satellite  Position  Range  Vector  from  Earth  Stn (ES)  to  SAT  :   finding  Range  Vector [rvI,  rvJ,  rvK,  rv]  components  in  km  in  IJK  frame.

18.  Satellite  Position  Range  Vector  from  Earth  Stn (ES)  to  SAT  :   finding  Range  Vector [rvS,  rvE,  rvZ,  rv]  components  in  km  in  SEZ  frame.

19.  Elevation (EL)  and  Azimuth (AZ)  angle  of  Satellite  at  Earth  Observation  point  ES  or  EP.

20.  Satellite  Velocity  meter  per  sec  in  orbit.

21.  Satellite  Velocity  Vector [vX,  vY,  vZ]  in  meter  per  sec  in  orbit  in  frame XYZ.

22.  Satellite  Pitch  and  Roll  angles.

23.  Satellite  State  Vectors  –  Position [ X,  Y,  Z ]  in  km  and  Velocity [ Vx,  Vy,  Vz ]  in  meter  per  sec  at  time_t.

24.  Satellite  Direction  ie  Right Ascension  Alpha  deg  and  declination  Delta  deg  using  sat  position  vector.

25.  Satellite  Angular  momentum  km  sqr  per  sec  :   finding  [Hx,  Hy,  Hz,  H]   using  state  vector  position   and velocity.

26.  Satellite  Orbit  normal  Vector  :   finding  [Wx,  Wy,  Wz,  W] ,  Delta,  Alpha,  using  r_sat_pos  frame  IJK,  i,  RA.

27.  Satellite  Position  Keplerian  elements  computed  using  State  Vector,   at  time  input  UT.

28.  Satellite  Position  State  Vectors,   computed  using  Keplerian  elements  at  time  input  UT.

All  these  Orbital  &  Positional  parameters  are  computed  respectively  for  six  satellites  LANDSAT 8,   SPOT 6,   CARTOSAT 2B,   ISS (ZARYA),   GSAT-14,   &   Moon.

For  complete  post  (Page  193  –  267)   Move  on  to   Website   URL  :

July 14, 2015

Satellites Orbit Elements – Ephemeris, Keplerian elements, State vectors

   Satellites  Orbit  Elements  –  Ephemeris,  Keplerian  elements,  State vectors

by   R C   Chakraborty,   July 14,  2015,   Pages  164 – 192.

(This   is   Sec. 5,    pp  164 – 192,   of   Orbital   Mechanics  –  Model   &   Simulation   Software  (OM-MSS),   Sec.  1  to 10,   pp  1  –  402.)

Satellite  is  an  artificial object,  intentionally  placed  into  orbit.  Thousands  of  Satellites  have  been  launched  into orbit  around  Earth.  A  few  Satellites  called  Space  Probes  have  been  placed  into  orbit  around  Moon,  Mercury,  Venus,  Mars,  Jupiter,  Saturn, etc.  The  Moon  is  the  Earth’s  only  natural  Satellite,  moves  around  Earth  in  the same  kind  of  orbit.

The  Motion  of  a  Satellite  is  a  direct  consequence  of  the  Gravity  of  a  body  (earth),   around  which  the  satellite  travels  without  any  propulsion.    A  satellite  move  around  Earth  is  pulled  in  by  the  gravitational  force (centripetal)  of  the  Earth.    Contrary  to  this  pull,  the  rotating  motion  of  satellite  around  Earth  has  an  associated  force  (centrifugal)  which  pushes  it  away  from  the  Earth.    The  centrifugal  force  equals  the  gravitational  force  and  perfectly  balance  to  maintain  the  satellite  in  its  orbit.

The  Velocity  of  a  Satellite  in  circular  or  elliptical  orbit  depends  on  its  altitude  ‘h’  at  that  point.   Secondly,  the  mass  of  satellite  does  not  appear  in  its  velocity  equations.    Thus  satellite  velocity  in  its  orbit  is  independent  of  its  mass.   Further,  a  satellite  in  elliptical  orbit  moves  faster  when  closer  to  earth  (near  perigee)  and  moves  slower  when  farther  from  earth  (near  apogee).

Preliminaries   about   Satellite   Orbit   :

Earth  Gravity  and  Satellite  Motion,   Velocity  equations,   Attitude  control,   Time  period,  Orbits,  Low  earth  orbit  (LEO),  Medium  earth  orbit  (MEO),   High   earth  orbit  (HEO),   Geosynchronous  orbit  (GSO),   Geostationary  (GEO),   Equatorial  Orbit,   Polar  Orbit,   Sun-synchronous  orbit.    Satellite  Ephemeris  data,   Satellite  Orbit  Keplerian  Element  Set,   Satellite  Orbit  State  Vectors   Set,   Ground  Trace.

Satellite   Ephemeris   data   and   conversion   utilities  of   the   OM-MSS   software   :

Satellite  Ephemeris  is  expressed  either  by  ‘Keplerian  elements’   or   by  ‘State  Vectors’,   that  uniquely  identify  a  specific  orbit.

1.   NASA / NORAD  ‘Two-Line  Elements’  (TLE)  Ephemeris  Data  Set   :    The  Keplerian  elements  are  encoded  as  text  in  different  formats.    The  most  common  format  is  NASA / NORAD      ‘Two-Line  Elements’  (TLE).

2.   Conversion  of  Keplerian  Element  Set  to  State  Vector  Set  and  Vice  versa   :    Applied  to  six  satellites,  LANDSAT 8,   SPOT 6,   CARTOSAT-2B,   ISS (ZARYA),   GSAT-14,   and   Moon .

3.   Computing  Satellite  Orbit  Keplerian  Element  set  at  Perigee   prior   to Epoch   :    Applied  to  six  satellites,  LANDSAT 8,   SPOT 6,   CARTOSAT-2B,   ISS (ZARYA),   GSAT-14,   and   Moon .

For  complete  post  (Page  164  –  192)   Move   on  to   Website   URL   :


July 12, 2015

Position of Earth on Celestial Sphere at Input Universal Time

   Position   of   Earth  on   Celestial   Sphere  at   Input   Universal   Time

by  R C  Chakraborty,  July 12,  2015,  Pages  68 – 163.

(This  is  Sec. 4,   pp  68 – 163,  of  Orbital  Mechanics  –  Model  &  Simulation  Software  (OM-MSS),  Sec 1  to 10,  pp 1 – 402.)

Earth  is  a  sphere,  the  third  planet  from  the  Sun  and  the  fifth  largest  of  the  eight  planets  in  the  Solar  System.

Planets  order  from  the  Sun  :   Mercury,  Venus,  Earth,  Mars,  Jupiter,  Saturn,  Uranus,  Neptune.

Earth  Rotates  on  its  axis  passing  through  the  North  and  South  Poles.   The  rotation  is  counterclockwise looking  down  at  North  Pole.  This  rotation  results  daytime  in  area  facing  Sun  and  night  time  in  area  facing  away  from  Sun.   Since  we  are  on  Earth,   we  do  not  sense  its  rotation,  but  experience  by  observing  the  relative  motion  of  the  Sun  (like  from  a  moving  vehicle  we  see  the  surroundings  move).

The  time  for  Earth  to  make  a  complete  rotation  is  approximately  24  hours  (exactly  23.9344699  hours  or  23  hours,  56  minutes,  4.0916  seconds).   The  earth’s  orbit  around  the  sun  is  not  a  circle,  it  is  slightly  elliptical.   Therefore,  distance  between  earth  and  sun  varies  throughout  the  year.

To  Compute  the  Position  of  Earth  on  Celestial  Sphere  at  any  instant,   we  first  need  to  Compute  Position of  Sun  on  celestial  sphere  and  then  at  same  instant  Compute  Position  of  Earth  on  celestial  sphere.   For  the  Position  of  Sun  on  celestial  sphere,  much  has  been  computed / illustrated  in  previous  section  (Ref.

The  Position  of  Earth  on  celestial  sphere  is  characterized  by  computing  around  120  orbital  parameters.   The number  is  large,  because  some  parameters  are  computed  using  more  than  one  model  equation,   that  require  different  inputs.   This  helps  in  validation  of  results  and  understanding  the  different  input  considerations.

The  Orbital  Parameters  that  Characterize  the  Position  of  Earth  on  Celestial  Sphere,   are  put  into  following  groups   :

1.    GST   Greenwich   sidereal   time   and  GHA  Greenwich  hour  angle  in  0 to 360 deg,    at  input  UT  time   YY MM DD HH.

2.    Earth   Log   in  0 to 360 deg   and   Lat  in  +ve or -ve  in  0 to 90 deg   pointing  to  Sun  Ecliptic  Log (Lsun)   at  time  input  UT.

3.    LST  Local  sidereal  time  using  GST  over  three  longitudes,   Greenwich  log,  Sun  mean  log (Lmean),   &  Sun epliptic  log (Lsun) .

4.    ST0  sidereal  time  over  Greenwich  longitude  =  0.0,   at  time  input  Year  JAN  day 1  hr 00.

5.    ST  sidereal  time,   at  time  input  UT,   over  three  log,  Greenwich  log,   Sun  mean  log (Lmean),   and  Sun  epliptic  log (Lsun).

6.    H  hour  angle  in  0 to 360 deg  using  ST  over  five  longitudes,   Greenwich,   Lmean,   Lsun,   Earth  Sub  Sun  point  SS,   Earth  Observation  point  EP,   at  time  input  UT.

7.    Delta  E  is  Equation  of  Time  in  seconds,   using  p_julian_day,   n_sun,   w_sun  at  time  input  UT.

8.    GST  Greenwich  sidereal  time,   and  GHA  Greenwich  hour  angle  0 to 360 deg  at  time  when  earth  is  at  perihelion.

9.    ST  sidereal  time  &  MST  mean  sidereal  time  at  different  instances,  using  Earth  mean  motion  rev  per  day  and  Julian  century  days  from  YY  2000_JAN_1_hr_1200.

10.   Earth  orbit  radius,   sub  sun  point  on  Earth  surface  &  related  parameters,   using  SMA,   e_sun,   T_sun,   w_sun etc.

11.   Earth center(EC) to Sun center(SC) Range Vector [rp, rq, r]   in PQW  frame (perifocal  coordinate  system).

12.   Transform_1  Earth  position  EC  to  SC  Range  Vector [rp, rq]  in  PQW  frame  To  Range  Vector [rI, rJ, rK]  in  IJK  frame  (inertial system cord).

13.   Transform_2  Earth  point  EP (lat, log, hgt)  To  EC  to  SC  Range  Vector [RI, RJ, RK, R]  in IJK frame.

14.   Transform_3  Earth  position  EC  to  SC  Range  Vectors [rI, rJ, rK]   &   [RI, RJ, RK]  To  EP  to  SC  Range   Vector [rvI, rvJ, rvK]  in  IJK  frame.

15.   Transform_4  Earth  point  EP  to  SC  Range  Vector [rvI, rvJ, rvK]  in  IJK  frame  To  EP  to  SC  Range Vector [rvS, rvE, rvZ]  in  SEZ  frame.

16.   Elevation (EL)   and   Azimuth (AZ)  angle  of  Sun  at  Earth  Observation  point  EP.

17.   Distance  in  km  from  Earth  observation  point (EP)  to  Sub  Sun point (SS)  and  Earth  Velocity  meter  per  sec  in  orbit  at  time  input  UT.

18.   Earth  State  Position  Vector [X, Y, Z]  in  km  at  time  input  UT.

19.   Earth  State  Velocity  Vector [Vx, Vy, Vz]  in  meter  per  sec  at  time  input  UT.

20.   Earth  Orbit  Normal  Vector [Wx, Wy, Wz]  in  km  and  angles  Delta,   i,   RA   at  time  input  UT;   Normal  is  line  perpendicular  to  orbit  plane.

21.   Transform  Earth  State Vectors  To  Earth  position  Keplerian  elements.

22.   Transform  Earth  position  Keplerian  elements  To  Earth  State  Vectors .

The  values  of  all  these  parameters  are  Computed  are  at  Standard  Epoch  JD2000  and  when  Earth  is  at  Perihelion,  Aphelion,  Equinoxes,  and  Solstices.   The  time  at  perihelion,  aphelion,   equinoxes,  and  solstices,  were  computed  earlier  for  the  input  year  in  section 2.  (Ref.

For   complete   post   (Page 68 – 163)   Move   on   to   Website   URL  :


July 11, 2015

Position Of Sun on Celestial Sphere at Input Universal Time

   Position   Of   Sun   on   Celestial   Sphere   at   Input   Universal   Time

by  R C  Chakraborty,  July 11,  2015,  Pages  57 – 67.

(This   is   Sec. 3,   pp 57 – 67,   of   Orbital   Mechanics  –   Model   &   Simulation   Software  (OM-MSS),   Sec 1  to 10,  pp 1 – 402.)

Sun  is  a  star  at  the  center  of  our  Solar  System.   Although  stars  are  fixed  relative  to  each  other,  but  Sun moves   relative   to   stars.

Sun   follows   a   circular  path  on  the  celestial  sphere,  once  a  year.   This  path  is  known  as  the  ‘Ecliptic’, representing  the  plane  of  the  Earth’s  orbit.

The  Inclination   of   the  Earth’s  equator  to  the  Ecliptic  (or  earth’s  rotation  axis  to  a  perpendicular  on  ecliptic) is  called  Obliquity  of  the  ecliptic.

The  Obliquity  of  the  ecliptic  is  currently  23.4392794383  deg   with  respect  to  the  celestial  equator,  at standard  epoch  J2000 .

The   position   of   any   point   on   the  Celestial  Sphere   is   given  with  reference   to   the   equator  or  the  ecliptic.

The  Earth  moves  in  an  elliptical  orbit  around  the  Sun.   Therefore  the  distance  from  Earth  to  Sun  is  not same   at   all   points   on   the   orbit.

(a)   Find   Julian   day   of   interest   corresponding   to   the   input   Universal   Time;

(b)  Find  Corresponding  Ecliptic  coordinates  :   Mean  anomaly  of  the  Sun,  Mean  longitude  of  the  Sun, Ecliptic   longitude   of   the   Sun,

      Ecliptic  latitude  of  the  Sun  is  always  nearly  zero,   Distance  of  the  Sun  from  the  Earth  in  astronomical   units,   Obliquity   of   the   ecliptic

(c)   Find   Corresponding   Equatorial   coordinates   :    Right ascension,    Declination.

In  addition  to  these  Ecliptic  and  Equatorial  coordinates,   computed  many  other  parameters  related  to  Sun’s Position  on  Celestial  Sphere.

The   Position   of   Sun   on   Celestial   Sphere   is   represented   by   computing   following  parameters   :

 1.     Semi-major axis (SMA),                  2.    Mean movement per day (n sun),      3.     Mean distance (As),

 4.     Mean anomaly (m sun),                  5.     True anomaly (T sun),                         6.     Eccentric anomaly (E sun),

 7.     Right ascension (Alpha),                 8.     Declination (Delta),                               9.     Mean longitude (Lmean),

 10.   Ecliptic longitude (Lsun),                11.   Nodal elongation (U sun),                   12.   Argument of perigee (W sun),

 14.   Obliquity of ecliptic (Epcylone),     14.   Mean dist (d_sun),                               15.   Radial distance (Rs).

For   complete   post   (Page 57 – 67)     Move    on    to    Website    URL   :

Positional Astronomy – Earth Orbit around Sun

   Positional   Astronomy  –  Earth  Orbit  around   Sun

by   R C  Chakraborty,   July 11, 2015,   Pages 33 – 56.

(This  is  Sec. 2,  pp 33 – 56,   of   Orbital   Mechanics  –  Model   &   Simulation   Software  (OM-MSS),   Sec.  1  to 10,   pp  1  –  402.)

Positional  Astronomy  is  measurement  of  Position  and  Motion  of  objects  on  celestial  sphere  seen  at  a particular  time  and  location  on  Earth.   The  Positional  Astronomy,  also  called  Spherical  Astronomy,  is  a System  of  Coordinates.

The  Earth  is  our  base  from  which  we  look  into  space.   Earth  orbits  around  Sun,  counterclockwise,  in  an elliptical  orbit  once  in  every  365.26  days.  Earth  also  spins  in  a  counterclockwise  direction  on  its  axis  once every  day.   This  accounts  for  Sun,  rise  in  East  and  set  in  West.   Earth  Revolution  refers  to  orbital  motion  of the  Earth  around  the  Sun.   Earth  axis  is  tilted  about  23.45 deg,  with  respect  to  the  plane  of  its  orbit,  gives four  seasons  as  Spring,  Summer,  Autumn  and  Winter.

Moon  and  artificial  Satellites  also  orbits  around  Earth,  counterclockwise,  in  the  same  way  as  earth  orbits around  Sun.

In  the  early  1600s,  Johannes  Kepler  proposed  three  laws  of  planetary  motion.

First  Look  at  the  Preliminaries  about  ‘Positional  Astronomy’,  before  moving  to  the  computation  &  predictions of  astronomical  events.

Preliminaries  about  Positional  Astronomy  :  Explained  Celestial  Sphere,  Celestial   coordinates, Horizontal  Coordinate  system,   Equatorial  coordinate  system,   Ecliptic  coordinate  system,   Celestial  Orbit,   Orbit  Elements  or  Parameters,  State vectors  (Positions & Velocities)  at  Epoch,   Kepler  elements  (Inclination, Longitude of ascending node,   Argument  of  periapsis,   Eccentricity,   Semi-major  axis,   Mean  Anomaly)  at  Epoch, Heliocentric  Orbit  Characteristics   and   Orbit  Events (Equinox,  Solstice,  and  Seasons).

Prediction of Astronomical Events :   Computing  Anomalies,   Equinoxes,   Solstices,   Years   &   Seasons .

The  precise  time  of  occurrence  of  following  astronomical  events  at  input  UT,   Year   :

(a)   Earth  orbit  Mean  anomaly,   Eccentric  anomaly,   True  anomaly;

(b)   Earth  reaching  orbit  points,   Perihelion,  Aphelion,   Vernal Equinox,   Autumnal  Equinox,   Summer  Solstice,   Winter  Solstice;

(c)   Earth  reaching  orbit  points,   Semi-Major Axis,   Semi-Minor Axis;

(d)   Astronomical  years,   Anomalistic  Years,   Tropical  Years,   Sidereal  Years;

(e)   Earth  orbit  oblateness,   Semi-Major Axis,   Semi-Minor Axis;

(f)   Four  Seasons,   Start  time  of  Spring,   Summer,   Autumn,   Winter.

For   complete    post   (Page 33 – 56)    Move   on   to    Website   URL   :

July 10, 2015

Astronomical Time Standards and Time Conversions

   Astronomical  Time  Standards  and  Time  Conversions

by  R C  Chakraborty,   July 10, 2015,   Pages 6 – 32.

(This  is  Sec. 1,  pp 6 – 32,   of   Orbital   Mechanics  –  Model   &   Simulation   Software  (OM-MSS),   Sec.  1  to 10,   pp  1  –  402.)

First  Look  into  few  preliminaries  and  then  time  conversion  utilities.

Time  is  a  dimension  in  which  the  events  can  be  ordered  from  the  past  through  the  present  into  the  future.    Our  clocks  are  set  to  run  (approximately)  on  solar  time  (sun  time).    For  astronomical   observations,   we  need  to   use   sidereal   time  (star  time).

Time  Standards  and  designations   :   Solar Time,   Sidereal  Time,   Equation  of  time,   Precession,   Nutation,   Hour Angle HA,   GMT,   GMST,   LMT,   LMST,   Universal  Time  UT,   International  Atomic  Time  TAI,   Ephemeris  Time  ET,   Gregorian  calendar,   Julian  Day  JD.

The  Precise  time  conversion  utilities  :

*   Conversion  of  Universal  Time  To  Julian  Day;

*   Conversion  of  Julian  Day  To  Universal  Time;

*   Conversion  of  Fundamental  Epoch  To  Julian  day  and  Julian  century;

*   Add  or  Subtract  time  (days,  hour,  minute  seconds)  to  or  from  input  time;

*   Julian  day  for  start  of  any  Year;

*   Solar  Time  :   Local  Mean  Solar  Time  (LMT)  over  observer’s  Longitude;

*   Sidereal  Time  :   Greenwich  universal  time  at  hour  0.0  (ST0)   and   GMST;

*   Greenwich  Sidereal  Time  (GST),   Hour  Angle  (GHA)  &   Mean  Sidereal  Time  (MST);

*   Local  Mean  Sidereal  Time  (LMST)   over  observer’s  Longitude ;

*   Time  Conversions  :   LMT  to  LST,    LST  to  LMT,   LMT  to  LMST,   LMST  to  LMT .

For  complete  post  (Page 6 – 32)   move  on  to  Website  URL :

July 9, 2015

Introduction to OM-MSS Software

   Introduction  to  OM-MSS  Software

by   R C  Chakraborty,   July 09, 2015,   Pages 1 – 5.

Earth,   Sun,   Moon   &   Satellites   Motion   in   Orbit  –   Model   &   Simulation   Software.

We  look  into  space  from  Earth,  which  is  3rd  planet  from  Sun.    Earth  takes  around  365.25  days  to  moves around  Sun  in  an  Elliptical  orbit.   The  average  distance  from  the   Earth  to  the  Sun  is  called  one  Astronomical Unit (AU);  1 AU = 149,597,870.7 km.   Mars   is  4th   planet  from  Sun,  that  takes  686.971  Earth days  to  orbit  around  Sun.   The  orbital  path  of  Mars  is  highly  eccentric.   Mars  &  Earth  move  along  their orbits,  and  come  near  to  one  another  approximately  every  two  years.   This  approach  of  coming  near  facilitate  launching  of  spacecraft  every  two  years,  even  that  takes  about  eight  months  to  reach Mars. Example :  On Apr. 08, 2014,  the  near  or  close  distance  between  Mars  and  Earth  was  92.4  million  km.   Moon moves  around  Earth  in  the  same  kind  of  orbit.   The  Moon  is  the  Earth’s  only  natural  Satellite.   The  average distance  of  the  Moon  from  the  Earth  is 384,403 km.   A  Satellite  is  an  artificial  object,  intentionally  placed  into  orbit.   Thousands  of  Satellites  are  launched  into  orbit  around  Earth.   A  few  Satellites  called  Space  Probes have  been  placed  into  orbit  around  Moon,  Mercury,  Venus,  Mars,  Jupiter,  Saturn,  etc.   Understanding  the motion  of  Earth  around  Sun,  and  the  motion  of  Moon  and  Satellites  around  Earth  is  of  interest  to  many.

The  OM-MSS  is  a  software  that  simulates  motion  of  Earth,   Moon  &  Satellites   in   their   respective  Orbits  with  respect  to Sun.   The  Software  is  written  in  ‘C’  Language.  The  Compiler  used  is  Dev  C++  and  the Platform  is  a  Windows 7,  64 bit  Laptop.  The  Source  Code  around  30,000 Lines,  is  Compiled.  The ‘OM-MSS.EXE’  File  generated  is  of  Size 1.5 KB.  The  Executable  File, < OM-MSS.EXE >,  is  RUN  Step-by-Step for  a  Set  of  Inputs.   The  execution  of  ‘Orbital  Mechanics – Model & Simulation  Software  (OM-MSS)’,   illustrates  its  Scope,  Capability,  Accuracy,  and  Usage.   The  OM-MSS  Software  is  quite  exhaustive  for beginners,  experts,  researchers  &  professional  in  Spherical  Astronomy.   The  source  code  of  OM-MSS  Software  in  full  or  in  parts  has  a  cost  if  there  is  buyer.  The  cost  has  not  been  evaluated / decided.   The OM-MSS  Software  includes  the  following :

(a)   Astronomical  Time  Standards  and  Time  Conversions  Utilities :

GMT – Greenwich Mean Time,  LMT – Local Mean Time,   LST – Local Sidereal Time,   UT – Universal Time,

ET – Ephemeris Time,   JD – Julian Day,   Standard Epoch J2000,   Gregorian Calendar date   and  more.

 (b)   Positional  Astronomy  of  Earth,   Sun,   Moon,  and  Satellites  Motion  in  Orbit,  includes  computations  of  :

* Position  of  Sun  and  Position  of  Earth  on  Celestial  Sphere  at  Epoch ;

* Keplerian  elements :  Inclination,  RA  of  asc.  Node,   Eccentricity,   Arg. of Perigee,   Mean Anomaly,   Mean Motion;

* Motion  Irregularities :  Mean,  Eccentric  and  True  anomaly  in  deg;

* Precise  Time  at  Earth  Orbit  Points :  Perihelion,  Aphelion,  Equinoxes,  Solstices,  Semi-Major  & Minor-axis;

* Astronomical years :  Anomalistic,  Tropical,  and  Sidereal  Years;

* Four Seasons :  Spring,  Summer,  Autumn  and  Winter  start  time  and  duration;

* Position  of  Satellites  around  Earth  :  Keplerian  elements  and  State  Vectors  at  epoch,  and  computing, Sub-Sat point lat / log, EL & AZ angles,  Distances,  Velocity,  and  more;

* Satellite Pass,  Ground  Trace  for  Earth  Stn  using  NASA/NORAD  2-line  bulletins;

 (c)   Customized  Utilities  and  products  :  On  special  request  either  developed  or  configured  and  generated.

These  are  Presented  in  Section  –  1  to  8.    The  Section – 9  contains  References,  and  Section – 10  contains   few related  Diagrams.

For   complete   post  (Page 1 – 5)     Move    on    to    Website    URL :

Orbital Mechanics – Model & Simulation Software (OM-MSS)

   Orbital   Mechanics   –   Model   &   Simulation   Software  (OM-MSS)

by  R C  Chakraborty,   July 09,   2015,   Page 1 – 402.

A   Monograph  of   Earth,   Sun,   Moon   &   Satellites  Motion  in   Orbit.

Presented   the   Earth,  Sun,  Moon  &   Satellites  Motion  in  Orbit  –  Model  &  Simulation  Software   with Examples,    Problems    and    Software   Driven   Solutions.

The  Software  is  written  in  ‘C’ Language.   The  Compiler  used  is  Dev C++  and  the  Platform  is   a   Windows 7,   64 bit  Laptop.   The  Source  Code  around  30,000  Lines,   is   Compiled.    The ‘OM-MSS.EXE’   File  generated  is  of  Size  1.5 KB.  The  Executable  File,  < OM-MSS.EXE >,   is  RUN   Step-by-Step  for  a  Set  of   Inputs.

The   execution   of   OM- MSS    illustrates   its   Scope,   Capability,   Accuracy,   and   Usage.

The  Results   seen   on   Computer   Screen   are   put   in   a   File,   that   in   effect   becomes    :

A   Monograph   of   Orbital   Mechanics   with   Examples,   Problems   and   Software   Driven   Solutions‘,   Page 1 – 402,   which  includes   the  following  :

*   Introduction   to   OM-MSS   Software

*   Astronomical   Time   Standards   and   Time   Conversions.

*   Positional   Astronomy  –  Earth  Orbit  Around  Sun,    Anomalies  &  Astronomical   Events  (Equinoxes,   Solstices,   Years   &    Seasons).

*   Position   of   Sun   on   Celestial   Sphere   at   input   universal   time  (ut).

*   Position   of   Earth  on   Celestial   Sphere   at   input   universal  time (ut).

*   Satellites  Orbit  Elements  –  Ephemeris,    Keplerian   elements,    State  vectors.

*   Satellites   Motion   Around   Earth  –   Orbital   &   Positional   parameters   at   epoch.

*   Satellite   Pass   for   Earth  Station  –   Prediction   of   Ground   Trace   Coordinates,   Look  angles,   Universal / Local   time  &  more.

For   complete    post  (Page 1 – 402)     Move    on    to    Website   URL   :

December 31, 2007

Satellite Image, Source for Terrestrial Information, Threat to National Security

Satellite Image, Source for Terrestrial Information, Threat to National Security

An invited talk in MANIT Training Programme On Information Security, December 10 -14, 2007, at Maulana Azad National Institute of Technology, Bhopal by R C Chakraborty, Visiting Prof. JIET, Guna & Former Dir. DTRL & ISSA (DRDO). The Highlights of the talk / presentation are as follows.

(a) Remote sensing, Communication, and Global positioning systems – Remote sensing satellites, Communication satellites, and the Global Positioning System (GPS) together have immense strategic value. These systems are driving the commercial engine of the new information-based economy. Use of Remote sensing imageries, range from military (reconnaissance, mapping, damage assessment), commercial (farming, mining, real estate), humanitarian (human rights abuses) and environmental catastrophe. Similarly, Satellite communications, have connected businesses located on opposite sides of the globe, increased capacity and speed of command and control links on battlefield. Finally, the Global positioning systems have significantly enhanced precision targeting and troop coordination, improved airline safety, tracking of vehicles and many more. Satellite systems have dual use – both civil and military. The governments and businesses around the world recognize the immense value, the satellite applications can offer them. The satellite industry traditionally dominated by programs run with government funding are now controlled by commercial interests. Even military for their operational necessity have now been looking for ways to save money by absorbing private sector capabilities rather than preferring expensive classified systems. The proliferation of satellite technology is largely because of commercial interests. The industry associations estimated, that the global commercial satellite service revenues will be triple by 2009. One good reason is that satellite images are most preferred source for terrestrial information. (Ref. Commercial Space and United States National Security, ).

(b) Concept of Remote Sensing – Remote Sensing is a technology by which characteristics of the objects of interest can be identified, measured and analyzed without direct contact. Remote sensing systems include : Source which is electro-magnetic radiation, reflected or emitted from an object is the source of remote sensing data;  Sensor which is camera or scanner to detect the electro-magnetic radiation reflected or emitted from an object;  Platform which aircraft or satellite, carries remote sensor; and Output which is data usually an image. The data are processed by computer and interpreted by humans, and finally used in agriculture, land use, forestry, geology, hydrology, oceanography, meteorology, environment, and more.

(c) Satellite Image of desired Resolutions – Different spatial resolutions are required for detection, location, identification of objects on earth surface. Satellite images are of spatial resolutions as 1, 10, 30 and 80 meter. Using 1 m resolution, you can Identify and Map, manhole covers, automobiles, bus shelters, highway lanes, sidewalks, utility equipment, fence lines, and free-standing trees and bushes. Using 10 m  resolution, you can Locate and Map, buildings, yards, roads, property boundaries, athletic fields, farm fields, and side streets. Using 20/30 m resolution, you can Locate airports, city centers, suburbs, shopping malls, sports complexes, large factories, forest stands, and large farm fields. Using 80 m resolution, you can Map regional geological structure and assess health of vegetation in a large region. Using 1 km resolution, you can assess vegetative indices for states and entire countries and track events like insect infestation, drought and desertification.

(d) Covert Military Line up in 1950s – From mid 1940 to early 1990 was the period of tension, competition and conflict known as cold war between the United States and the Soviet Union. Few events occurred between 1950 and 1960. In early 1950, U.S thought of an Spy plane U-2 to photograph a particular location. In 1955, U.S. offered to Soviet Union an “Open Skies” policy, allowing mutual territorial surveillance which was not agreed by the later. In 1956, U.S. stated U-2 fly-over program, secretly gathered data on Soviet missile capabilities. In October 1957, Sputnik the first satellite was successfully launched by Soviet Union. On May 1, 1960 the spy plane U-2 shot down over the Soviet Union and U.S. denied it true purpose. In August 1960, U.S. secretly developed Discoverer XIV, a   spy satellite and recovered its first film capsule.

(e) Freedom of International Space – Soon after Sputnik was launched in 1957, the U.S. perceived, that the Soviet Union unintentionally established the concept of freedom of international space. U.S. talked about peaceful uses of space for the benefit of mankind, while pursuing military applications. U.S. launched of first scientific experiment satellite Vanguard-1, on March 17, 1958, into orbit around the earth as part International Geophysical Year (July 1, 1957 to Dec. 31, 1958). Secondly, U.S. campaigned for Reconnaissance satellites, necessary for gathering reliable information about military developments behind the iron curtain, to negotiate arms control and to retain defense sufficiency in the absence of agreements. This is likely only if usage of imaging satellites are legitimatized. Thus U.S. became the champion of openness, international cooperation, and the rule of law in space.

(f) The Roots Of Remote Sensing Satellites – Viewing earth from space has three main facets, image resolution, satellite’s revisit days, and sensor’s spectral coverage. The image resolution largely decides its military utility. The commercial potential of satellites imageries were envisaged long ago. NASA launched the civilian remote sensing satellite Landsat in 1972, that provided images of 80 m resolution of earth to the non-governmental sector. But U.S. soon lost its superpower monopoly, because of economic competitiveness. A more capable French Imaging competitor launched remote sensing satellite SPOT-1 in Feb. 1986, followed by SPOT-2 in Jan. 1990 that provided images of 10 m resolution. The competition became more while India launched IRS-1A in 1988 and IRS-1B in 1991 which provided images of 36 m resolutions, followed by IRS-1C and IRS-1D launched in 1995 and 1997, which provided images of 5.8 m resolution. The result was, in the year 1992, U.S. declared new initiative, known as Land Remote Sensing Act of 1992.

(g) Land Remote Sensing Act of 1992 – This act enabled U.S. to maintain its leadership in land remote sensing by providing data continuity for the Landsat program. U.S. established a new national Land Remote Sensing Policy, implementing commercialization in favor of long-term, and protective development of remote sensing industry under the guidance of the DoD and NASA. (Ref Land Remote Sensing Policy

(h) Commercial Earth Surface Imaging satellites – To acquire images of earth from space, many satellites were launched starting from the year 1972, owned by countries, U.S., France, India, Israel.  These satellites are :  Landsat , SPOT and Pleiades, IRS & Cartosat, IKONOS, OrbView & GeoEye, EarlyBird, QuickBird, WorldView, EROS.

  • Landsat 1 , 2 , 3, 4 , 5 , 6, 7 :   These seven satellites were launched in last 27 years, starting from the year 1972. Landsat-7 offers 15 m resolution. The orbit and Imaging characteristics, mostly same for all satellites, but image resolutions constantly improved from 80 to 15 m. These satellites archived millions of scenes of U.S. and world over, a unique resource for global change research and applications in agriculture, cartography, geology, forestry, regional planning, surveillance, education and national security.
  • SPOT 1, 2, 3, 4, 5, Pleiades-1, 2 :   These seven satellites were launched in last 16 years, starting from 1986. SPOT-5 offers 2.5 m resolution. The Pleiades is France’s high-resolution imaging satellite offer images of 0.7 m resolution. The program, is supervised by CNES, the France Space Agency. Pleiades is part of European Earth Remote Sensing program. The orbit and Imaging characteristics, mostly same for all satellites, but image resolutions constantly improved from 10 to 2.5 m. These satellites provided global coverage as well daily observation accessibility to any point on Earth. Thus, images are of dual use, civil and military, and applications in Land use, agriculture, forestry, geology, cartography, regional planning.
  • IRS 1A , 1B, P2, 1C, 1D, P6, P5, Cartosat-2 :   These eight satellites were launched in last 19 years, starting from the year 1988. Cartosat-2 offers < 1 m resolution. The orbit and Imaging characteristics, mostly same for all satellites, but image resolutions constantly improved to from 36 to < 1 m. These satellites provided global coverage as well daily observation accessibility to any point on Earth. Thus images are of dual use, civil and military, and applications in crop land yield estimation, survey of forest resources, urban mapping, flood mapping, wasteland mapping, drought monitoring and assessment.
  • Ikonos, OrbView , GeoEye :   Lockheed Martin in 1991 started a remote sensing Imaging satellite project CRSS. The objective is to offer commercial high-resolution (1 m PAN and 4 m MSS) images in near real-time and offline. The images are of military use and applications for national security, military mapping, air and marine transportation. GeoEye-1 offers 0.41 m resolution.
  • EarlyBird, QuickBird, WorldView :   In 1992 the WorldView Imaging Corporation was formed as a commercial business enterprise with the idea of converting space-based weapons system technology into a viable earth-observation system.  WorldView-1 offers 0.45 m resolution. The applications include highly detailed imagery for precise map creation, precise change detection and in-depth image analysis, mapping at unprecedented resolutions in multi-spectral imagery, and opens door to creation of numerous new products. By 2008, DigitalGlob’s constellation of satellites would enable commercial and government customers around the globe to access geospatial information products from a single source. WorldView-1 alone is capable of collecting up to 500,000 square kilometers per day of 0.5 m resolution imagery.
  • EROS-A, EROS-B, EROS-C :   These are Earth Resources Observation Satellites, a series of commercial earth observation satellites, designed and manufactured by Israel Aircraft Industries (IAI). The optical payload is supplied by, Elbit Systems Ltd, one of Israel’s largest defense electronics manufacturers and integrators. The space borne remote sensing technology for the EROS family was approved by the government of Israel in Oct. 1996. The satellites are owned and operated by ImageSat International (ImageSat), another Israeli company. EROS-2 offers 0.45 m resolution imagery.
  • Other Commercial Earth Surface Imaging satellites :  USA, France, India, and Israel have highly efficient commercial Earth remote sensing programs. They offer image resolution 1 meter and less. More importantly, they regularly supplement the space segment with new satellite and hold the positions as the primary suppliers of space data. Many other countries, Korea, Russia, Italy, U.K., JAPAN, Malaysia, Taiwan, and Thailand also have high resolution satellites. The launch, orbit and imaging characteristics of these satellites are typical of their own. These satellites have resolutions 2.5 to 1 m, comparatively less and thus the applications for which they are used.

(i) Applications of Very High Resolution Imaging Satellites –  The images acquired by many commercial civilian remote sensing satellites are capable in detection, identification and recognition objects of military interest like, bridges, radar, supply dumps, troop units, airfield facilities, rockets and artillery, aircraft, command & control HQ., missiles (ssm/sam), surface ships, nuclear weapons components, vehicles, minefields (land), ports and harbors, coasts and landing beaches, railroad yards and shops, roads, urban areas, terrain, submarines (surfaced). Targeting is closely related to the ability to detect and precisely identify the given object and/or their location.

(j) Commercial Satellite Imagery Companies –  Viewing Earth from space have become necessary for every country. Therefore, the world market of Geo-data and Space imagery have grown and would continue to grow towards Globalization of Terrestrial Information.  The U.S, Israel, India, and France, hold the world market for satellite based earth imagery. They run highly efficient operational earth remote sensing programs. They regularly supplement the space segment with new satellite and become primary suppliers of earth imagery.

(k) National Security and International Regulations –   Space-based remote sensing consists, collecting data regarding the surface of the earth via satellite. The information gathered from such data can be used in many applications. The commercial availability of high-resolution imagery presents great benefit to civilian sector and a deep concern for national security. Such paradox is true every where, it is true even for military users. The International Regulations related to National Security are illustrated in :

(l) Concern about National Security –   The views reported in the world wide web about security related challenges and threat because high resolution images are available commercially or even freely in public domain. Views expressed,   ( ),  ( ).

Conclusion.   Providing satellite imageries, we are bring a revolution in ‘Globalization of Terrestrial Information’ about the world we live in.

For complete lecture slides move on to Website URL :


Create a free website or blog at