Differences between revisions 1 and 2

Near Circular Orbits

MORE LATER add pointers to orbit discussions

$ r = (1-e^2) a

Periods of M orbits

M orbits describe the number of minutes an orbit takes travel once around the earth and return to the same position overhead. For server sky, these are integer fractions of a 1440 minute synodic day; this makes it easier to calculate the sky position given the orbital parameters and the time of day. the M288 orbit returns to the same position 5 times per day, for example, and makes six synodic orbits in one synodic day. But not exactly. Because the earth orbits around the sun, the position of the sun makes a complete turn around the earth in one year, 365.256363004 days of 86,400 seconds, or 31558149.7635456 seconds

symbol		LEO 300Km	M288	M360	GEO	Moon	Earth	units
\mu	gravitational parameter	3.98600448E+14	3.98600448E+14	3.98600448E+14	3.98600448E+14	3.98600448E+14	1.32712440E+20	m³/s²
	relative to	earth	earth	earth	earth	earth	Sun
a_g	gravity	8.938095E+00	2.437062E+00	1.911369E+00	2.242078E-01	2.697573E-03	5.930053E-03	seconds
T	sidereal period	5431.009959	14393.432015	17270.542964	86164.090540	2360584.685000	31558149.763546	seconds
T_s	synodic period	5445.879572	14400.000000	17820.000000	86400.000000	2551442.900000	31558149.763546	seconds
T/2\pi	Sidereal / 2pi	864.372081	2290.785853	2748.692283	13713.440926	375698.721205	5022635.529703	seconds
\omega	Angular velocity	1.15690919E-03	4.36531419E-04	3.63809367E-04	7.29211585E-05	2.66170722E-06	1.99098659E-07	rad/sec
	orbits/year	5810.73318	2192.53822	1827.28185	366.25640	13.36879	1.00000
R	semimajor axis	6678000.00	12788970.60	14440980.32	42164169.86	384399000.00	149598261000.00	meters
R_a	apogee radius	6678000.00	varies	varies	42164169.86	405696000.00	152098232000.00	meters
R_p	perigee radius	6678000.00	varies	varies	42164169.86	363104000.00	147098290000.00	meters
e	eccentricity	0.000000	varies	varies	0.000000	0.055401	0.016711
V_0	mean velocity	7725.84	5582.79	5253.76	3074.66	1023.16	29784.81	m/s
V_a	apogee velocity	7725.84	varies	varies	3074.66	966.47	29287.07	m/s
V_p	perigee velocity	7725.84	varies	varies	3074.66	1079.84	30282.55	m/s
C_3	orbit specific energy	-59688596.59	-31167516.16	-27602035.26	-9453534.82	-1036944.55	-887125553.00	J/kg

-  ⇤ ← Revision 1 as of 2011-03-31 19:44:52 → 
  Size: 1343
  Editor: KeithLofstrom
  Comment:
+   ← Revision 2 as of 2011-04-01 01:30:32 → ⇥
  Size: 3625
  Editor: KeithLofstrom
  Comment:
-Deletions are marked like this.
+Additions are marked like this.
 Line 6:
-||  symbol   ||                  ||   m288     ||   m360   ||  GEO       || Moon || Earth     || unit     ||
||  $ a $    || semimajor axis   || 1,2788,866 ||          || 42,164,170 ||      ||           || meters   ||        
||  $ r $    || radius           ||  varies    ||  varies  || 42,164,170 || varies || varies || meters   ||
||  $ r_a $  || apogee radius    ||  varies    ||  varies  || 42,164,170 ||  || meters ||
||  $ r_p $  || perigee radius   ||  varies    ||  varies  || 42,164,170 || meters ||
||  $ T $    || sidereal period  ||
-Line 18:
+Line 15:
-M orbits describe the number of minutes an orbit takes travel once around the earth and return to the same position overhead.  For server sky, these are integer fractions of a 1440 minute day; this makes it easier to calculate the sky position given the orbital parameters and the time of day.  the M288 orbit returns to the same position 5 times per day, for example, and makes approximately six orbits in the time the earth turns once.  But not exactly.  Because the earth orbits around the sun, the position of the sun makes a complete turn around the earth in one year, 365.256363004 days of 86,400 seconds, or 31558149.7635456 seconds
+M orbits describe the number of minutes an orbit takes travel once around the earth and return to the same position overhead.  For server sky, these are integer fractions of a 1440 minute synodic day; this makes it easier to calculate the sky position given the orbital parameters and the time of day.  the M288 orbit returns to the same position 5 times per day, for example, and makes six synodic orbits in one synodic day.  But not exactly.  Because the earth orbits around the sun, the position of the sun makes a complete turn around the earth in one year, 365.256363004 days of 86,400 seconds, or 31558149.7635456 seconds

||   symbol   ||                         || LEO 300Km      || M288           || M360           || GEO            || Moon           || Earth           ||   units   ||
|| $ \mu $    || gravitational parameter || 3.98600448E+14 || 3.98600448E+14 || 3.98600448E+14 || 3.98600448E+14 || 3.98600448E+14 || 1.32712440E+20  || m^3^/s^2^ ||
||            ||           relative to   || earth          || earth          || earth          || earth          || earth          || Sun             ||           ||
|| $ a_g $    || gravity                 || 8.938095E+00   || 2.437062E+00   || 1.911369E+00   || 2.242078E-01   || 2.697573E-03   || 5.930053E-03    || seconds   ||
|| $ T $      || sidereal period         || 5431.009959    || 14393.432015   || 17270.542964   || 86164.090540   || 2360584.685000 || 31558149.763546 || seconds   ||
|| $ T_s $    || synodic period          || 5445.879572    || 14400.000000   || 17820.000000   || 86400.000000   || 2551442.900000 || 31558149.763546 || seconds   ||
|| $ T/2\pi $ || Sidereal / 2pi          || 864.372081     ||  2290.785853   ||  2748.692283   || 13713.440926   ||  375698.721205 ||  5022635.529703 || seconds   ||
|| $ \omega $ || Angular velocity        || 1.15690919E-03 || 4.36531419E-04 || 3.63809367E-04 || 7.29211585E-05 || 2.66170722E-06 ||  1.99098659E-07 || rad/sec   ||
||            || orbits/year             || 5810.73318     ||   2192.53822   ||     1827.28185 ||      366.25640 ||      13.36879  ||       1.00000   ||           ||
|| $ R $      || semimajor axis          || 6678000.00     ||  12788970.60   || 14440980.32    || 42164169.86    || 384399000.00   || 149598261000.00 ||  meters   ||
|| $ R_a $    || apogee radius           || 6678000.00     ||  varies        ||   varies       || 42164169.86    || 405696000.00   || 152098232000.00 ||  meters   ||
|| $ R_p $    || perigee radius          || 6678000.00     ||  varies        ||   varies       || 42164169.86    || 363104000.00   || 147098290000.00 ||  meters   ||
|| $ e $      || eccentricity            || 0.000000       ||  varies        ||   varies       || 0.000000       ||  0.055401      ||      0.016711   ||           ||
|| $ V_0 $    || mean velocity           ||  7725.84       ||  5582.79       ||   5253.76      ||  3074.66       ||   1023.16      ||      29784.81   ||  m/s      ||
|| $ V_a $    || apogee velocity         ||  7725.84       ||  varies        ||   varies       ||  3074.66       ||   966.47       ||      29287.07   ||  m/s      ||
|| $ V_p $    || perigee velocity        ||  7725.84       ||  varies        ||   varies       ||  3074.66       ||   1079.84      ||      30282.55   ||  m/s      ||
|| $ C_3 $    || orbit specific energy   || -59688596.59   || -31167516.16   || -27602035.26   || -9453534.82    ||   -1036944.55  || -887125553.00   ||  J/kg     ||

Diff for "NearCircularOrbits"

Near Circular Orbits

Periods of M orbits