For reference: (Compiled by Amber G, on August 20, 2023
For those who are not allergic to doing simple math and want to do their calculation to know accurate velocity, position of CY3 and CY2 (till next burn). This is in simple terms (each term explained for those who have basic understanding of orbits):
I have gotten the data from JPL/ISRO figures latest available information. (Will edit any correction)
(Some calculation is my own - I believe mathematically correct but will edit if there is any error/typo)
This is one place to look up the data for CY1, CY2, CY3 to calculate their position at any time. (If you have any orbit calculating software or are handy with slide rule (:) or doing calculation on pen and paper.
It has most uptodate reference data:
It contains:
CY3 - Reference data for both Vikram and PM. (PM data, as I post this message is not available from JP/Horizon system so I put it best I could get from ISRO and math)
CY2 - Ephemerides for both Vikram and Orbiter. (Vikram, of course, we know has crashed, but it's orbit just before crash is here)
CY1 - Is inactive there, but still orbiting. Calculating the position from last known position.
Moon/Sun - so one can understand what the lighting condition would be at the landing site .. where earth would be wrt to lander, and where the landing site would be, if you aim your telescope or try to aim your radio telescope..
Written for non-experts some basic astronomy and math is required.
]For CY3
General Info:
The lander will then touch down in the lunar south polar region, nominally
69.367621 deg. S, 32.348126 deg. E, with a velocity less than 2 m/s vertical
and 0.5 m/s horizontal, slope <= 120 degrees. The prime landing site target
zone is 4 x 2.4 km in dimension.
The propulsion module will remain in lunar orbit to act as a communications
relay between the lander and Earth. The lander and rover are designed to
operate for one lunar daylight period, about 14 Earth days. (CY2 will be the main relay per ISRO/see BRF post by Ashokk)
SPACECRAFT:
Launch mass : 3900 kg
Lunar lander mass: 1752 kg (solar arrays ~ 738 W)
Lander Propulsion : bi-propellant propulsion (MMH + MON3),
4 nos. of 800 N throttleable engines
8 nos. of 58 N
Rover mass 26 kg (solar arrays ~ 50 W)
6 wheels
SCIENCE PAYLOADS
Lander:
Radio Anatomy of Moon Bound Hypersensitive Ionosphere & Atmosphere (RAMBHA)
Chandra's Surface Thermo physical Experiment (ChaSTE)
Instrument for Lunar Seismic Activity (ILSA)
Laser Retroreflector Array (LRA, from NASA)
Propulsion module:
Spectro-polarimetry of HAbitable Planet Earth (SHAPE)
Rover:
Alpha Particle X-Ray Spectrometer (APXS)
Laser Induced Breakdown Spectroscope (LIBS) Propulsion Module:
Chandrayaan 3 Vikram JPL/Horizon id: CH3 - 158 EPOCH: JDN(Julian Day Number)=2460176.5 = August 20, 2023 at 00:00:00 UTC
Brief explanation of Reference system Below and values.
Reference center (origin) : Moon Center
Center radii 1737.4 km (To calculate altitude, subtract this from distance)
Keplerian GM : 4.902.8 km^3/s^2 (µ I used in previous BRF posts .. unit here is converted in km^3/sec^2 for ease of calculation)
Output units : KM-S, deg, Julian Day Number for Tp
Reference frame : Ecliptic of J2000.0 (Which NASA/JPL uses - it is essentially same as ecliptic - plane of earth's orbit around the sun)
So X-Y plane is ecliptic , Z axis pointing to ecliptic north. (This is within 1.5 degrees of Moon's equatorial plane)
X - axis is ICRF - points towards vernal equinox (first point of Aries वसंत विषुव )
e = (eccentricity) = .0294 (roughly circular), Inclination = 89.9 degrees (Nearly polar)
perigee = 1763.66 Km (Altitude 29.3 Km), Apogee = 1870.6 Km, a = (Semimajor axis) = 1817.1 Km
Period = 6950.7 Sec.
Longitude of Ascending Node = 268 deg Argument of Perifocus, = 228 degree
Tp= 2460176.471497831400 (Time in JDN when the spacecraft was at perigee.. so that at any given time you can find its position)
Mean Motion = .0518 degree/sec MA= 127.5 degree TA= 130.2 Degree
(MA is Mean anomaly - angle, if the orbit was circular, TA = True Anomaly - Actual angle at focus, from the major axis of the ellipse)
---
Chandrayaan 2 Orbiter JPL/Horizon id: CH2 - 152 EPOCH: JDN(Julian Day Number)=2460176.5 = August 20, 2023 at 00:00:00 UTC
SPACECRAFT:
Launch mass : 3850 kg
Lunar orbital mass: 2379 kg (solar arrays ~1000 W
Lunar lander mass: 1471 kg (solar arrays ~ 650 W)
Rover mass : 27 kg (solar arrays ~ 50 W)
e = (eccentricity) = .0117 (roughly circular), Inclination =90.5 degrees (Nearly polar)
perigee = 1823.13 Km , Apogee = 1866.17 Km, a = (Semimajor axis) = 1846.6
Period = 7109.4 Sec.
Longitude of Ascending Node = 270.2 deg Argument of Perifocus, = 22.57 degree
Tp= 2460176.462988432497 (Time in JDN when the spacecraft was at perigee.. so that at any given time you can find its position)
Mean Motion = .050635.064 \ degree/sec MA= 161.93 degree TA= 162.34 Degree
(MA is Mean anomaly - angle, if the orbit was circular, TA = True Anomaly - Actual angle at focus, from the major axis of the ellipse)
---
Chandrayaan 2 Lander (Vikram) JPL/Horizon id: CH2 - 153 EPOCH: JDN= 2458733.343750000 = 2019-Sep-06 20:15:00.0000 UTC
(Last Measured position
(The orbiter was eventually placed in a 119 x 127 km nearly circular polar
orbit after a series of engine burns.
The lander subsequently separated on 2019-Sep-02 07:45 UTC and was planned to touch
down at predetermined site close to the lunar south pole.
Touchdown is to occur 2019-Sep-07 on a high plain between two craters,
Manzinus C and Simpelius N, about 70 degrees south of the equator.
The orbiter mission covers 1 year, in a 100-km circular polar orbit but is *still* active - Its relay station for CY3)
The six-wheeled Pragyan is resting on the surface.
This is a merge trajectory solutions fit to tracking data
through 2019-Sep-06 ~15:37 UTC, with a planning prediction thereafter
(i.e., does NOT include the descent anomaly & final actual trajectory).
2458733.333333333 = A.D. 2019-Sep-06 20:00:00.0000 TDB
EC= .022 QR= 17679.4 IN= 91.52
OM= 277.3 W = 231.00 Tp= 2458733.339561445639
N = .052 MA= 331.9 TA= 3.30.7
A = 1807.1 AD= 1846.2 PR= 6.893.3 secs
(Yes, with this trajectory, in next 15 minutes it will crash on the moon - easy to see - unless braking is applied..We all know the braking was not sufficient and it hit the surface with greater velocity than expected.
---
Chandrayaan 1 Orbiter JPL/Horizon id: CH1 - 86 EPOCH: JDN= 2459852.500000000 = A.D. 2022-Sep-30 00:00:00.0000 UTC
Chandrayaan-1 was India's first mission to the Moon. It launched October 22,
2008 on a PSLV (Polar Satellite Launch Vehicle, PSLV-C11) from the Satish
Dhawan Space Center (SDSC) in Sriharikota, India.
Launch mass : 1050 kg
Lunar orbital mass: 550 kg
Dimensions : 1.5 meter cube, plus extended solar panel
RESULTS:
The mission studied the Moon's environment and surface processes for a period
of about nine months during 2008-2009, establishing ...
1) A tenuous but active hydrosphere,
2) a volcanically active and geologically dynamic Moon, and
3) global melting of Moon's surface regions and formation of magma
ocean early in the history of Moon.
On Aug. 29, 2009, ISRO abruptly lost contact with the Chandrayaan-1
spacecraft. All attempts to recover the mission failed.
The spacecraft operationally completed 312 days in orbit, making more than
3400 functional orbits of the moon, but the planned mission of two years was
cut in half. About 95% of the mission objectives were completed, including
collection of over 70,000 images.
TRAJECTORY: The inactive spacecraft, still in orbit around the Moon, was
detected by radar echoes seven times over Jul-Sep 2016 using the Goldstone
Solar System Radar. Delay and Doppler measurements were used to estimate
the current trajectory available here.
2459852.500000000 = A.D. 2022-Sep-30 00:00:00.0000 TDB
EC= .0283 QR= 1889.64 IN= 91.01
OM= 159.06 W = 272.8 Tp= 2459852.544464385603
N = .0468 MA= 180.3 TA= 180.3
A = 1944.7 AD= 1999.7 PR= 7695.33
(Work in progress - Will add for CH2, and PM later)
(Let me know if additional detail is desired)
-- To be added: Sun/Moon/Earth positions --
Planetary mean elements for Moon on 2000-01-01.5
a = 384400 Km, e=.0554 , argument of periapsis= 318.15 Mean Anomaly = 135.27
Inclination= 5.16 Degree Ascending Node=125.08 sidereal period =27.322 days
periapsis period =5.997 years node precession period= 18.600 Years.
This means: Using the same coordinate system as we are using for CY3, CY2, etc, to locate earth use:
2460176.500000000 = A.D. 2023-Aug-20 00:00:00.0000
EC= 5.578175491289343E-02 QR= 3.628316980985817E+05 IN= 5.084369946976682E+00
OM= 2.614997325954256E+01 W = 1.284636134449790E+02 Tp= 2460187.527413775679
N = 1.527906903728645E-04 MA= 2.144258354450509E+02 TA= 2.110110607437462E+02
A = 3.842667730542630E+05 AD= 4.057018480099443E+05 PR= 2.356164496157914E+06
So position of the Earth (On days August 20 to September 08 -- One day for CY3) as viewed from the moon ,, (Will explain details later)
******************************************************************************************************************************************************************************
Date__(UT)__HR:MN R.A.___(ICRF)__DEC APmag S-T-O
******************************************************************************************************************************************************************************
2023-Aug-20 00:00 00 23 45.84 +00 37 52.5 -16.540 30.064730
2023-Aug-21 00:00 01 06 38.89 +06 17 00.7 -16.364 30.450113
2023-Aug-22 00:00 01 51 07.05 +11 47 40.0 -16.138 30.976100
2023-Aug-23 00:00 02 38 15.25 +16 57 10.8 -15.857 31.657571
2023-Aug-24 00:00 03 29 05.37 +21 29 59.4 -15.515 32.498406
2023-Aug-25 00:00 04 24 22.93 +25 06 55.6 -15.105 33.483971 .
2023-Aug-26 00:00 05 24 14.64 +27 25 59.4 -14.616 34.573119
2023-Aug-27 00:00 06 27 44.82 +28 05 54.4 -14.040 35.691963
2023-Aug-28 00:00 07 32 53.81 +26 52 28.4 -13.367 36.733643
2023-Aug-29 00:00 08 37 16.25 +23 44 45.2 -12.593 37.569359
2023-Aug-30 00:00 09 38 59.78 +18 56 49.0 -11.721 38.073415
2023-Aug-31 00:00 10 37 19.52 +12 53 58.9 -10.904 38.157325
2023-Sep-01 00:00 11 32 32.69 +06 06 38.2 -11.558 37.798938
2023-Sep-02 00:00 12 25 33.36 -00 55 01.4 -12.423 37.050907
2023-Sep-03 00:00 13 17 28.68 -07 44 03.2 -13.192 36.023455
2023-Sep-04 00:00 14 09 22.64 -13 57 54.1 -13.861 34.851457
2023-Sep-05 00:00 15 02 05.15 -19 18 22.5 -14.436 33.662348
2023-Sep-06 00:00 15 56 02.78 -23 31 15.2 -14.928 32.555993
2023-Sep-07 00:00 16 51 11.51 -26 26 13.4 -15.346 31.598153
2023-Sep-08 00:00 17 46 55.31 -27 57 20.3 -15.701 30.823247
2023-Sep-09 00:00 18 42 15.16 -28 03 39.8 -16.000 30.241169
2023-Sep-10 00:00 19 36 07.72 -26 49 20.9 -16.248 29.844659
'R.A._____(ICRF)_____DEC' =
Astrometric right ascension and declination
Units: RA in hours-minutes-seconds of time, HH MM SS.ff{ffff}
DEC in degrees-minutes-seconds of arc, sDD MN SC.f{ffff}
'APmag ' = The targets' approximate apparent visual magnitude ( brightness) -16 is very bright)
'S-T-O' = The angle between sun and Earth in degrees.
And for sun (wrt to Moon):