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A Study on Phases of Moon,Chandrayaan-Ii ,Sidereal Month and Synodic Month

A Study on Phases of Moon,Chandrayaan-Ii ,Sidereal Month and Synodic Month

The International journal of analytical and experimental modal analysis ISSN NO: 0886-9367

A STUDY ON PHASES OF ,CHANDRAYAAN-II ,SIDEREAL AND SYNODIC MONTH

Dr.K.Kalaiarasi ¹ and D.Haritha²

1.Pg and Research Department of Mathematics,Cauvery college for women,Trichy-18,Tamilnadu,.

[email protected]

2.Pg and Research Department of Mathematics,Cauvery college for women ,Trichy-18,Tamilnadu,India

[email protected]

ABSTRACT:

In this resaearchpaper,a study on phase of moon,introduction of chandrayaan,siderealmonthsynodic month and their relationship are discussed.

KEYWORDS :

Phases of moon,siderealmonth,synodicmonth,history of chandrayaan ,composite of chandrayaan-II.

INTRODUCTION:

Chandrayaan-2 (candra-yāna, transl. "mooncraft";[15][16] pronunciation (help·info)) is the second lunar exploration mission developed by the Indian Space Research Organisation (ISRO),[17][18] after Chandrayaan-1.[19][20] It consisted of a lunar orbiter, the Vikram , and the , all of which were developed in India.[21] The main scientific objective is to map and study the variations in lunar surface composition, as well as the location and abundance of .[22][23] The mission was launched on its course to the Moon from the second launch pad at SatishDhawan Space Centre on 22 July 2019 at 2.43 PM IST (09:13 UTC) by a Geosynchronous Mark III (GSLV Mk III).[9][10][24] The craft reached the Moon's orbit on 20 August 2019 and began orbital positioning manoeuvres for the landing of the Vikram lander.[25]Vikram and the rover were scheduled to land on the , in the south polar region[26] at a latitude of about 70° south at approximately 20:23 UTC on 6 September 2019 and conduct scientific experiments for one lunar day, which approximates two Earth . However, the lander deviated from its intended trajectory starting at 2.1 kilometres (1.3 mi) altitude,[27] and had lost communication when touchdown confirmation was expected.[28][29] Initial reports suggesting a crash[30][31] have been confirmed by ISRO chairman K. Sivan, stating that the lander location had been found, and "it must have been a hard landing".[32]

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Both ISRO and NASA tried unsuccessfully to communicate with the lander for two weeks before the lunar night set in. The orbiter, part of the mission with eight scientific instruments, remains operational and is expected to continue its seven-year mission to study the Moon.

Chandrayaan-2

Chandrayaan-2 composite

Mission type Lunar orbiter, lander, rover

Operator Indian Space Research Organisation (ISRO)

SATCAT no. 2019-042A

Website www.isro.gov.in/chandrayaan2-home-0

Mission duration Orbiter: ~ 7 years Elapsed: 23 days Vikram lander ≤ 14 days[1][2]

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Pragyan rover: ≤ 14 days[2]

Spacecraft properties

Manufacturer Indian Space Research Organisation (ISRO)

Launch mass Combined (wet): 3,850 kg (8,490 lb)[3][4][5] Combined (dry): 1,308 kg (2,884 lb)[6] Orbiter (wet): 2,379 kg (5,245 lb)[4][5]

Orbiter (dry): 682 kg (1,504 lb)[6]

Vikram lander (wet): 1,471 kg (3,243 lb)[4][5]

Vikram lander (dry): 626 kg (1,380 lb)[6] Pragyan rover: 27 kg (60 lb)[4][5]

Power Orbiter: 1 kW[7]

Vikram lander: 650 W

Pragyan rover: 50 W

Start of mission

Launch date 22 July 2019, 14:43:12 IST (09:13:12 UTC)[8]

Rocket GSLV Mk III[9][10]

Launch site SatishDhawan Space Centre Second Launch Pad

Contractor Indian Space Research Organisation (ISRO)

Moon orbiter

Orbital insertion 20 August 2019, 09:02 IST (03:32 UTC) [11][12]

Orbital parameters

Periapsis altitude 100 km (62 mi)[13]

Apoapsis altitude 100 km (62 mi)[13]

Inclination 90° (polar orbit)

Moon lander

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Spacecraft component Rover

Landing date 7 September 2019, 01:53 IST (6 September 2019, 20:23 UTC)[14][12]

Chandrayaanprogramme ← Chandrayaan-1 Chandrayaan-3 →

History : On 12 November 2007, representatives of the Russian Federal Space Agency () and ISRO signed an agreement for the two agencies to work together on the Chandrayaan-2 project.[33] ISRO would have the prime responsibility for the orbiter and rover, while Roscosmos was to provide the lander. The Indian government approved the mission in a meeting of the Union Cabinet, held on 18 September 2008 and chaired by Prime Minister Manmohan Singh.[34] The design of the spacecraft was completed in August 2009, with scientists of both countries conducting a joint review.[35][36] Although ISRO finalised the payload for Chandrayaan-2 per schedule,[37] the mission was postponed in January 2013[38] and rescheduled to 2016 because Russia was unable to develop the lander on time.[39][40] Roscosmos later withdrew in wake of the failure of the Fobos-Grunt mission to , since the technical aspects connected with the Fobos-Grunt mission were also used in the lunar projects, which needed to be reviewed.[39] When Russia cited its inability to provide the lander even by 2015, India decided to develop the lunar mission independently.[38][41] The spacecraft's launch had been scheduled for March 2018, but was first delayed to April and then to October to conduct further tests on the vehicle.[42][43] On 19 June 2018, after the program's fourth Comprehensive Technical Review meeting, a number of changes in configuration and landing sequence were planned for implementation, pushing the launch to the first half of 2019.[44] Two of the lander's legs got minor damage during one of the tests in February 2019.[45] Chandrayaan-2 launch was initially scheduled for 14 July 2019, 21:21 UTC (15 July 2019 at 02:51 IST local time), with the landing expected on 6 September 2019.[20] However, the launch was aborted due to a technical glitch and was rescheduled.[46][8][47] The launch occurred on 22 July 2019 at 09:13 UTC (14:43 IST) on the first operational flight of a GSLV MK III M1.[48

THE MOON:

THE Moon is at a distance of about 2,40,000 miles (384403 km) from the earth and as such it is the nearest celestial neighbor to the earth. The linear diameter of the moon is about 2163 miles (3476km) and its mass is about 1 times that of the earth, the 81 angular diameter of the moon is about 30’ and its mean horizontal parallax is about 57’

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The moon is not a self-luminous body. It shines in the light it receives from the sun.

The moon is a satellite of the earth. It moves around the earth following the laws of Kepler. 1 The is at an angle of about 5 ̊8’ to the ecliptic and is eccentricity is . The two points of 18 intersection of the lunar orbit and ecliptic are called the nodes of lunar orbit. The point where the moon crosses the ecliptic in going north is called the ascending node* and the other point where the moon crosses the ecliptic in going south is called the descending node*. The line joining the nodes of the lunar orbit is called the nodal line and it is the line of intersection of the planes of the and the ecliptic.

PHASES OF THE MOON :

The phases of the moon are different forms in which the moon is seen by terrestrial observer. The phase of the moon is mathematically defined as the ratio of visible of moon’s disc to the whole illuminated disc.

Let S be the sun E the earth and M the Centre of Moon.Moon receives light form the sun in the direction SM and its hemisphere ACB turned towards the sun is illuminated.The moon is observed from the earth in the direction EM so that the visible portion is the projection of the illuminated portion on the plane LN perpendicular to the line sight of sight EM. Let D be the foot of the Perpendincular from A on this plane sothat the visible portion is the area XLYDX.

=semicircle XLY-semi ellipse XDY

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휋푎² 휋푎푏 = - 2 2

Where a is the radius of moon and b=MD,

Since the distance between the earth and the moon is very small compared to the distance of moon or earth from the sun,the earth also receives light from the sun in the same direction as the moon does.

Let 휃 be the elongation of moon

Clearly we get ∠퐴푀퐷

From ∆ AMDMD=AMcos휃

i.e. b=a cos 휃

휋푎² 휋푎2 cos 휃 ∴ visible portion = - 2 2

Whole illuminated disc = πa²

Phase of the moon = 풗풊풔풊풃풍풆 풑풐풓풕풊풐풏 풘풉풐풍풆 풊풍풍풖풎풊풏풂풕풆풅 풅풊풔풄

흅풂² 흅풂ퟐ 퐜퐨퐬 휽 − = ퟐ ퟐ 흅풂²

i.e phase=ퟏ−퐜퐨퐬 휽 ퟐ

successive phases of moon :

As the moon moves along its orbit around the earth its hemisphere turned towards the sun is illuminated. For an observer on the earth only that part of the hemisphere turned towardsthe earth is visible. Therefore the whole illuminated portion of the moon is not visible and it is seen in different shapes. These are call successive phases of moon.

when the moon is at M1 ,in conjunction with the sun,only the non illuminated portion of the moon isturned towards the earth.Therefore the moon is not visible and it is said to be new.

M2 is a position of the moon within seven days of age. At this position only a small portion of the illuminated surface of moon is visible . It is then said to be and is visible in the west

after sun set.M3 is the position of the moon when it is at 90 ̊ from the sun. At this position it is seen as a bright semi circle . The moon is said to be dichotomized and it is at the first quarter or

quadrature east. M4 is a position of moon after the first quarter. At this position more than half

the illuminated surface of moon is visible. The moon is said to be gibbous. M5 is the position of

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moon when it is in opposition with the sun. At this position the moon is seen as a bright circular disc and the moon is said to be full.

Thus in a lunation the moon exhibits all phases from new to full. In the remaining half lunation the phases are repeated in the reverse order from full to new.

When the moon is in conjunction or opposition with the sun, that is when it is new or full it is said to be in ; From to the moon is said to be waxing and from full moon to new moon it is said to be waning.

DEFINITIONS:

Sidereal month

The siderealmonth is the period of one complete revolution of the moon around the earth relative to any fixed star. It is about 271 days (27 days, 7 hours, 43 minutes). 3

Synodic month

The period of one complete revolution of the moon around the earth relative to the sun is called a synodic month. It is also called a or a lunation. It is about 291days(29 days, 12 2 hours, 44 minutes).

RELATION BETWEEN SIDEREAL MONTH AND SYNODIC MONTH

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Let x ,y, z be the number of days in a sidereal month, synodic month(lunation) and a year respectively.

In x days the moon describes 360 ̊ around the earth with respect to any fixed star A. Therefore in one day the moon describes 360 ̊ with respect to A. 푠

Similarly in one day the sun describes 360 ̊ with respect to the star A and the moon describes 360 ̊ 푧 푦 with respect to the sun.

We get 360 ̊ = 360 ̊ + 360 ̊ 푥 푧 푦

(ie) 1 = 1 + 1 푥 푧 푌

Objectives: The primary objectives of the Chandrayaan-2 lander were to demonstrate the ability to soft-land on the lunar surface and operate a robotic rover on the surface. Scientific goals include orbital studies of lunar topography, mineralogy, elemental abundance, the lunar exosphere, and signatures of hydroxyl and water .[49] The orbiter will map the lunar surface and help to prepare 3D maps of it. The onboard will also map the surface while studying the water ice in the south polar regionand thickness of the lunar regolith on the surface.[50] Design: The mission was launched on a Geosynchronous Mark III (GSLV Mk III) with an approximate lift-off mass of 3,850 kg (8,490 lb) from SatishDhawan Space Centre on Sriharikota Island.[3][13][10][51] As of June 2019, the mission has an allocated cost of ₹978 crore (approximately US$141 million) which includes ₹603 crore for space segment and ₹375 crore as launch costs on GSLV Mk III.[52][53] Chandrayaan-2 stack was initially put in an Earth of 170 km perigee and 40,400 km apogee by the launch vehicle.[54] Orbiter

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Chandrayaan-2 orbiter at integration facility

As of September 2019, the Chandrayaan-2 orbiter was orbiting the Moon on a polar orbit at an altitude of 100 km (62 mi).[55] It carries eight scientific instruments; two of which are improved versions of those flown on Chandrayaan-1. The approximate launch mass was 2,379 kg (5,245 lb).[4][5][37][56] The Orbiter High Resolution Camera (OHRC) will conduct high-resolution observations of the landing site prior to separation of the lander from the orbiter.[55][2] The orbiter's structure was manufactured by Hindustan Aeronautics Limited and delivered to ISRO Satellite Centre on 22 June 2015.[57][58]

 Dimensions: 3.2 × 5.8 × 2.2 m[23]  Gross lift-off mass: 2,379 kg (5,245 lb)[3]  Propellant mass: 1,697 kg (3,741 lb)[6]  Dry mass: 682 kg (1,504 lb)[6]  Power generation capacity: 1000 W[23]  Mission duration: approximately 7.5 years, extended from the planned 1 year owing to the precise launch and mission management, in lunar orbit.[1][59] Vikram lander

Rover Pragyan mounted on the ramp of Vikram lander

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Images of the Earth captured by Chandrayaan-2 Vikram lander camera LI4[60]

The mission's lander is called Vikram (Sanskrit: विक्रम, lit. 'Valour[61]') Pronunciation (help·info) named after Vikram Sarabhai (1919–1971), who is widely regarded as the founder of the Indian space programme.[62] The Vikram lander detached from the orbiter and descended to a low lunar orbit of 30 km

× 100 km (19 mi × 62 mi) using its 800 N (180 lbf) liquid main engines. It then performed a comprehensive check of all its on-board systems before attempting a soft landing that would have deployed the rover, and perform scientific activities for approximately 14 Earth days. Vikram spacecraft apparently crash-landed.[30][1] The lander's location was spotted on the surface via thermal imaging, but its condition is unknown.[32] The approximate combined mass of the lander and rover is 1,471 kg (3,243 lb).[4][5] The preliminary configuration study of the lander was completed in 2013 by the Space Applications Centre (SAC) in Ahmedabad.[38] The lander's propulsion system consists of eight 50 N

(11 lbf) thrusters for and five 800 N (180 lbf) liquid main engines derived from ISRO's [63][64] 440 N (99 lbf) Liquid Apogee Motor. Initially, the lander design employed four main liquid engines, but a centrally mounted engine was added to handle new requirements of having to orbit the Moon before landing. The additional engine was expected to mitigate upward draft of lunar dust during the soft landing.[51] Vikram was designed to safely land on slopes up to 12°.[65][66] Some associated technologies include a high resolution camera, Altimeter (LASA),[67] Lander Hazard Detection Avoidance Camera (LHDAC), Lander Position Detection Camera (LPDC),[68] Lander Horizontal Velocity Camera (LHVC), an 800 N throttleable liquid main engine,[57] attitude thrusters, Ka band radio altimeters (KaRA),[69][70] Laser Inertial Reference & Accelerometer Package (LIRAP),[71] and the software needed to run these components.[2][55] Engineering models of the lander began undergoing ground and aerial tests in late October 2016, in Challakere in the Chitradurga district of Karnataka. ISRO created roughly 10 craters on the surface to help assess the ability of the lander's sensors to select a landing site.[72]

 Dimensions: 2.54 × 2 × 1.2 m[23]  Gross lift-off mass: 1,471 kg (3,243 lb)[3]  Propellant mass: 845 kg (1,863 lb)[6]  Dry mass: 626 kg (1,380 lb)[6]  Power generation capability: 650 W  Mission duration: ≤14 days (one lunar day)[2] Pragyan rover Main article: Pragyan (rover)

Pragyan rover of the Chandrayaan-2 mission

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The mission's rover is called Pragyan (Sanskrit: प्रज्ञान, lit. 'Wisdom[73][74]') Pronunciation (help·info))[75][73] with a mass of 27 kg (60 lb), would have operated on solar power.[4][5] The rover was to move on 6 wheels traversing 500 meters on the lunar surface at the rate of 1 cm per second, perform on-site analyses and send the data to the lander, which would have relayed it to the Mission Control on the Earth.[76][77][37][56][52] For navigation, the rover uses:

 Stereoscopic camera-based 3D vision: two 1 megapixel, monochromatic NAVCAMs in front of the rover to provide the ground control team a 3D view of the surrounding terrain, and help in path-planning by generating a of the terrain.[78] IIT Kanpur contributed to the development of the subsystems for light-based map generation and motion planning for the rover.[79]  Control and motor dynamics: the rover has a rocker- bogie suspension system and six wheels, each driven by independent brushless DC electric motors. Steering is accomplished by differential speed of the wheels or skid steering.[80] The expected operating time of Pragyan rover was one lunar day, or around 14 Earth days, as its electronics were not designed to endure the frigid lunar night. However, its power system has a solar-powered sleep/wake-up cycle implemented, which could have resulted in longer service time than planned.[81][82] Two aft wheels of the rover have the ISRO logo and the State Emblem of India embossed on them to leave behind patterned tracks on the lunar surface,[83][84] which is used to measure the exact distance travelled, also called visual odometry.[citation needed]

 Dimensions: 0.9 × 0.75 × 0.85 m[23]  Power: 50 W[23]  Travel speed: 1 cm/sec.[23]  Mission duration: ≤14 days (one lunar day) Payload:

Mission overview

ISRO selected eight scientific instruments for the orbiter, four for the lander,[85][3][86] and two for the rover.[37] While it was initially reported that NASA and ESA would participate in the mission by providing some scientific instruments for the orbiter,[87] ISRO in 2010 had clarified that due to weight restrictions it will not be carrying foreign payloads on this mission.[88] However, in an update just a month before launch,[89] an agreement between NASA and ISRO was signed to include a small laser from NASA to the lander's payload to measure the distance between the above and the microreflector on the lunar surface.[90][91]

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Orbiter Payloads on the orbiter are:[3][86][1]

 Chandrayaan-2 Large Area Soft X-ray Spectrometer (CLASS) from ISRO Satellite Centre (ISAC), makes use of X-ray fluorescencespectra to determine the elemental composition of the lunar surface.  Solar X-ray monitor (XSM) from Physical Research Laboratory (PRL), Ahmedabad for mapping major elements present on the lunar surface.[37]  Dual Frequency L and S band Synthetic Aperture Radar (DFSAR) from Space Applications Centre (SAC) for probing the first few meters of the lunar surface for the presence of different constituents, including water ice. DFSAR is expected to provide further evidence confirming the presence of water ice, and its distribution below the shadowed regions of the Moon.[37] It has lunar surface penetration depth of 5 meters (L-band).[59][86]  Imaging IR Spectrometer (IIRS) from Space Applications Centre (SAC) for mapping of lunar surface over a wide wavelength range for the study of minerals, water molecules and hydroxyl present.[37] It works up to 5 microns, an improvement over previous lunar missions whose payloads worked up to 3 microns.[59]  Chandrayaan-2 Atmospheric Compositional Explorer 2 (ChACE- 2) Quadrupole Mass Analyzer from Space Physics Laboratory (SPL) to carry out a detailed study of the lunar exosphere.[37]  Terrain Mapping Camera-2 (TMC-2) from Space Applications Centre (SAC) for preparing a three-dimensional map essential for studying the lunar mineralogy and geology.[37]  Radio Anatomy of Moon Bound Hypersensitive Ionosphere and – Dual Frequency Radio Science experiment (RAMBHA-DFRS) by SPL for the studying electron density in the Lunar ionosphere.  Orbiter High Resolution Camera (OHRC) by SAC for scouting a hazard-free spot prior to landing. It will later help prepare high- resolution topographic maps and digital elevation models of the lunar surface. OHRC has spatial resolution of 0.3 m from 100 km polar orbit.[86] Vikram lander The payloads on the Vikram lander are:[3][86]

 Instrument for Lunar Seismic Activity (ILSA) MEMS based Seismometer by LEOS for studying Moon- quakes near the landing site[85][13][92]  Chandra's Surface Thermo-physical Experiment (ChaSTE) Thermal probe by SPL, VSSC for estimating the thermal properties of the lunar surface[13]  RAMBHA-LP Langmuir probe by SPL, VSSC for measuring the density and variation of lunar surface plasma.[85][13]

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 A laser retroreflector array (LRA) by NASA Goddard Space Flight Center for taking precise measurements of distance between the reflector on the lunar surface and satellites in lunar orbit.[93][89][90] The micro-reflector weighs about 22 grams and can not be used for taking observations from Earth-based lunar laser stations.[90] Pragyan rover Pragyan rover carries two instruments to determine the abundance of elements near the landing site:[3][86]

 Laser induced Breakdown Spectroscope (LIBS) from Laboratory for Electro Optic Systems (LEOS), Bangalore.[37]  Alpha Particle Induced X-ray Spectroscope (APXS) from PRL, Ahmedabad.

CHACE2

XSM

CLASS

ILSA MEMS sensor package

Laser retroreflector array (LRA)

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LIBS

APXS

MISSION PROFILE:

Animation of Chandrayaan-2

Geocentric phase

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Selenocentric phase

Lunar landing phase

Overall motion of Chandrayaan-2

Earth · Moon · Chandrayaan-2

Timeline of operations [94][95]

Result

Referenc Phase Date Event Detail Apogee / Perigee / es Aposelen Perisele e ne

22 July 45,475 k 169.7 k 2019 Burn time: 16 min m m Launch [48] 09:13:12 14 sec (28,257 (105.4 Geocentricphas UTC mi) mi) e

24 July 1st orbit-raising 45,163 k 230 km Burn time: 48 sec [96] 2019 maneuver m (140 mi) 09:22 (28,063

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UTC mi)

25 July 54,829 k 2019 2nd orbit-raising Burn time: 883 m 251 km [97] 19:38 maneuver sec (34,069 (156 mi) UTC mi)

29 July 71,792 k 276 km 2019 3rd orbit-raising Burn time: 989 m (171.5 [98] 09:42 maneuver sec (44,609 mi) UTC mi)

2 August 89,472 k 2019 4th orbit-raising Burn time: 646 m 277 km [99] 09:57 maneuver sec (55,595 (172 mi) UTC mi)

6 August 142,975 k 2019 5th orbit-raising Burn time: 1041 m 276 km [100] 09:34 maneuver sec (88,841 (171 mi) UTC mi)

13 August Burn time: 1203 2019 Trans-lunar injection — — [101] sec 20:51 UTC

20 18,072 k August Lunar orbit insertion Burn time: 1738 m 114 km 2019 1st lunar bound [102] sec (11,229 (71 mi) 03:32 maneuver mi) UTC Selenocentricph ase 21 August 4,412 km 2nd lunar bound Burn time: 1228 118 km 2019 (2,741 mi [103] maneuver sec (73 mi) 07:20 ) UTC

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28 August 3rd lunar bound Burn time: 1190 1,412 km 179 km 2019 [104] maneuver sec (877 mi) (111 mi) 03:34 UTC

30 August 4th lunar bound Burn time: 1155 164 km 124 km 2019 [105] maneuver sec (102 mi) (77 mi) 12:48 UTC

1 Septemb 5th lunar bound 127 km 119 km er 2019 Burn time: 52 sec [106] maneuver (79 mi) (74 mi) 12:51 UTC

2 Septemb 127 km 119 km er 2019 Vikram separation — [107] (79 mi) (74 mi) 7:45 UTC

3 Septemb 128 km 104 km er 2019 1st deorbit burn Burn time: 4 sec [108] (80 mi) (65 mi) 3:20 UTC Vikram lunar landing 3 Septemb 101 km 35 km er 2019 2nd deorbit burn Burn time: 9 sec [109] (63 mi) (22 mi) 22:12 UTC

6 Septemb Landing Landing er 2019 Powered descent Burn time: 15 min (planned (planned) 20:08 )

UTC

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Trajectory 6 deviation started Septemb at 2.1 km er 2019 Vikram landing altitude,telemetry 20:23 was lost seconds

UTC before touchdown.[28][110]

7 Septemb er 2019 00:00 Lander failure, Pragyan rover deploy UTC- rover was not — — [111][112] ment 01:00 deployed. UTC (planned )

Chandrayaan-2 lifting off on 22 July 2019 Launch Chandrayaan-2 launch was initially scheduled for 14 July 2019, 21:21 UTC (15 July 2019 at 02:51 IST local time).[20] However, the launch was aborted 56 minutes and 24 seconds before launch due to a technical glitch, so it was rescheduled to 22 July 2019.[46][8] Unconfirmed reports later cited a leak in the nipple joint of a helium gas bottle as the cause of cancellation.[47][113][114] Finally Chandrayaan-2 was launched on-board the GSLV MK III M1 launch vehicle on 22 July 2019 at 09:13 UTC (14:43 IST) with better-than-expected apogee as a result of the cryogenic upper stage being burned to depletion, which later eliminated the need for one of the apogee-raising burns during the geocentric phase of mission.[48][115][116] This also resulted in the saving of around 40 kg fuel onboard the spacecraft.[117] Immediately after launch, multiple observations of a slow-moving bright object over Australia were made, which could be related to upper stage venting of residual LOX/LH2 propellant after the main burn.[118][119] Geocentric phase

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Chandrayaan-2 trajectory

After being placed into a 45,475 × 169 km parking orbit by the launch vehicle,[48] the Chandrayaan-2 spacecraft stack gradually raised its orbit using on-board propulsion over 22 days. In this phase, one perigee-raising and five apogee-raising burns were performed to reach a highly eccentric orbit of 142,975 × 276 km[100] followed by trans-lunar injection on 13 August 2019.[101] Such long Earth-bound phase with multiple orbit-raising manoeuvres exploiting the Oberth effect was required because of the limited lifting capacity of the launch vehicle and thrust of the spacecraft's on- board propulsion system. A similar strategy was used for Chandrayaan-1 and the during their Earth-bound phase trajectory.[120] On 3 August 2019, the first set of Earth images were captured by the LI4 camera on the Vikramlander, showing North American landmass.[60] Selenocentric phase After 29 days from its launch, the Chandrayaan-2 spacecraft stack entered lunar orbit on 20 August 2019 after performing a lunar orbit insertion burn for 28 minutes 57 seconds. The three- spacecraft stack was placed into an elliptical orbit that passes over the polar regions of the Moon, with 18,072 km (11,229 mi) aposelene and 114 km (71 mi) periselene.[102] By 1 September 2019 this elliptical orbit was made nearly circular with 127 km (79 mi) aposelene and 119 km (74 mi) periselene after four orbit-lowering maneuvers[103][104][105][106] followed by separation of Vikram lander from the orbiter on 7:45 UTC, 2 September 2019.[107] Planned landing site Main article: Pragyan (rover)

Landing site [121] Coordinates

Prime landing site 70.90267°S 22.78110°E

Alternate landing site 67.87406°S 18.46947°W

Two landing sites were selected, each with a landing ellipse of 32 × 11 km.[121] The prime landing site (PLS54) is at 70.90267 S 22.78110 E (~350 km north of the South Pole-Aitken Basin rim[26][121]), and the alternate landing site (ALS01) is at 67.874064 S 18.46947 W. The prime site is on a high plain between the craters Manzinus C and Simpelius N,[122][26] on the near side of the Moon. Hard landing

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Vikram began its descent at 20:08:03 UTC, 6 September 2019 and was scheduled to land on the Moon at around 20:23 UTC. The descent and soft-landing were to be done by the on-board computers on Vikram, with mission control unable to make corrections.[123] The initial descent was considered within mission parameters, passing critical braking procedures as expected, but the lander's trajectory began to deviate at about 2.1 kilometres (1.3 mi; 6,900 ft) above the surface.[124][125] The final telemetry readings during ISRO's live-stream show that Vikram's final vertical velocity was 58 m/s (210 km/h) at 330 meters above the surface which, according to some experts, is quite fast for a lunar landing.[28][110][126] Initial reports suggesting a crash[30][31] were confirmed by ISRO chairman K. Sivan, stating that the lander location was found and that "it must have been a hard landing".[32][127][128] Radio transmissions from the lander were tracked during descent by analysts using a 25- meter radio telescope owned by the Netherlands Institute for Radio Astronomy. Analysis of the doppler data suggests that the loss of signal coincided with the lander impacting the lunar surface at a velocity of nearly 50 metres (160 ft) per second (as opposed to an ideal 2 metres (6.6 ft) per second touchdown velocity).[3][129] The powered descent was also observed by the Lunar Reconnaissance Orbiter using its Lyman-Alpha Mapping Project (LAMP) instrument to study changes in the lunar exosphere due to exhaust gases from the lander's engines.[130] Status The mission's orbiter used thermal imaging to locate the lander.[131] Unconfirmed reports, citing an ISRO official, stated that the lander was intact,[132] but there has been no official announcement by ISRO on the lander's physical condition.[32][133] ISRO's Chairman, K. Sivan, tasked senior scientist P. S. Goel to head the Failure Analysis Committee to look into the causes of the failure.[134] Both ISRO and NASA attempted to communicate with the lander for about two weeks before the lunar night set in.[135][136] while NASA'sLunar Reconnaissance Orbiter (LRO) flew over on 17 September 2019 and acquired some images of the intended landing zone.[137] However, the location was near dusk, causing poor lighting for optical imaging.[138][139] The LRO will fly over again on 14 October under favorable lighting conditions.[140] The lander and rover were primarily engineering tests,[141] and the lander's success criteria was defined for every phase, scoring 90% to 95%.[141] The orbiter part of the mission, with eight scientific instruments, remains operational, and will continue its seven-year mission to study the Moon.[125]

We have to use the formula F=G⋅M⋅md2F=G⋅M⋅md2 to calculate the force of attraction between Earth and Moon. I will be using the scientific notation in a way that 12E34 means 12 × 10^34. These are the values we have to use: Mass of Earth (mₑ) = 6.0×1024 kg 22 Mass of Moon (mm) = 7.35×10 kg Distance between Earth and Moon (d) = 384,400 km = 3.8×108 m

F=GMeMm

d2

G=6.67*10-11(Gravitational constant)

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F=(6.674×10-11)(6.0×1024kg)(7.35×1022kg)

F=6.674×10−11⋅5.972×1024⋅7.34767309×1022(3.84×108)2 F=6.674⋅5.972⋅7.3476730914.7456×10351016 F=6.674⋅5.972⋅7.3476730914.7456×10351016 F=19.86064×1019 F=19.86064×1019 F=1.986064×1020 F=1.986064×1020 N

Team:

A view of Mission Operations Complex (MOX-1), ISTRAC[142] prior to the fourth Earth-bound burn.[99]

Key scientists and engineers involved in the development of Chandrayaan-2 include:[143][144][145]

 RituKaridhal – Mission Director  MuthayyaVanitha – Project Director  K. Kalpana – Associate Project Director[146]  G. Narayanan – Associate Project Director[147]  G. Nagesh – Project Director (former)[148]  Chandrakanta Kumar – Deputy Project Director (Radio frequency systems)  Amitabh Singh – Deputy Project Director (Optical Payload Data Processing, SAC)[149]

CONCLUSION:

A study of phases of the moon chandrayaan-II is capable of achieveingBETTER RESULTS AND FURTHER DETAILS will be discussed in my next paper. References:

1. ^ Jump up to:a b c d Chandrayaan-2 Latest Update. ISRO Press Release on 7 September 2019. 2. ^ Jump up to:a b c d e Nair, Avinash (31 May 2015). "ISRO to deliver "eyes and ears" of Chandrayaan-2 by 2015-end". The Indian Express. Retrieved 7 August 2016.

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3. ^ Jump up to:a b c d e f g h i "Launch Kit of GSLV Mk III M1 Chandrayaan- 2" (PDF). ISRO. 19 July 2019. Archived (PDF) from the original on 19 July 2019. Retrieved 21 July 2019. 4. ^ Jump up to:a b c d e f g "Chandrayaan-2 to Be Launched in January 2019, Says ISRO Chief".Gadgets360. NDTV. Press Trust of India. 29 August 2018. Retrieved 29 August 2018. 5. ^ Jump up to:a b c d e f g "ISRO to send first Indian into Space by 2022 as announced by PM, says DrJitendra Singh" (Press release). . 28 August 2018. Retrieved29 August 2018. 6. ^ Jump up to:a b c d e f g "Chandrayaan-2: All you need to know about India's 2nd Moon mission". 22 July 2019. Archived from the original on 14 July 2019. Retrieved 22 July 2019. 7. ^ "Chandrayaan-2 – Home". Indian Space Research Organisation. Retrieved 20 June2019. 8. ^ Jump up to:a b c "Chandrayan-2 Launch Rescheduled on 22nd July, 2019, AT 14:43 HRS". Indian Space Research Organisation. 18 July 2019. Retrieved 18 July 2019. 9. ^ Jump up to:a b Singh, Surendra (5 August 2018). "Chandrayaan-2 launch put off: India, Israel in lunar race for 4th position". The Times of India. Times Network. Retrieved15 August 2018. 10. ^ Jump up to:a b c Shenoy, Jaideep (28 February 2016). "ISRO chief signals India's readiness for Chandrayaan II mission". The Times of India. Times News Network. Retrieved 7 August2016. 11. ^ Ratcliffe, Rebecca (22 July 2019). "India's Chandrayaan-2 moon mission lifts off a after aborted launch". Retrieved 23 July 2019. 12. ^ Jump up to:a b "GSLV-Mk III – M1 / Chandrayaan-2 Mission". ISRO.gov.in. Retrieved 21 July 2019. 13. ^ Jump up to:a b c d e f Kiran Kumar, AluruSeelin (August 2015). Chandrayaan-2 – India's Second Moon Mission. YouTube.com. Inter-University Centre for Astronomy and Astrophysics. Retrieved 7 August 2016. 14. ^ "ISRO aims for Chandrayaan-2 landing at 1.55 AM on September 07, says Dr K. Sivan". Retrieved 24 August 2019. 15. ^ MonierMonier-Williams, A Sanskrit-English Dictionary (1899): candra: "[...] m. the moon (also personified as a deity Mn. &c)" yāna: "[...] n. a vehicle of any kind , carriage , waggon , vessel , ship , [...]" 16. ^ "Chandrayaan-2 FAQ". Retrieved 24 August 2019. The name Chandrayaan means “Chandra- Moon, Yaan-vehicle”, –in Indian languages (Sanskrit and Hindi), – the lunar spacecraft. 17. ^ Kumar, Chethan (10 June 2019). "Chandrayaan-2 nearly ready for July launch". The Times of India. Retrieved 14 July 2019. 18. ^ d. s, Madhumathi (9 June 2019). "ISRO gears up for Chandrayaan-2 mission". The Hindu. 19. ^ "ISRO begins flight integration activity for Chandrayaan-2, as scientists tests lander and rover". The Indian Express. Press Trust of India. 25 October 2017. Retrieved21 December 2017. 20. ^ Jump up to:a b c "Press release on Chandrayaan-2, ISRO". www.isro.gov.in. Retrieved 1 May2019. 21. ^ Bagla, Pallava (4 August 2018). "India Slips in Lunar Race with Israel As Ambitious Mission Hits Delays". NDTV. Retrieved 15 August 2018. 22. ^ Rathinavel, T.; Singh, Jitendra (24 November 2016). "Question No. 1084: Deployment of Rover on Lunar Surface" (PDF). RajyaSabha. 23. ^ Jump up to:a b c d e f g "Launch kit at a glance".

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24. ^ "Chandrayaan-2 Launch Mission: Bahubali set to take-off at 2:43 pm today". 25. ^ Kottasová, Ivana; Gupta, Swati (20 August 2019). "India's Chandrayaan-2 moon mission enters lunar orbit". CNN. Retrieved 6 September 2019. 26. ^ Jump up to:a b c Geological Insights into Chandrayaan-2 Landing Site in the Southern High Latitudes of the Moon. Rishiosh K. Sinha, VijayanSivaprahasam, Megha Bhatt, Harish Nandal, NanditaKumari, NeerajSrivastava, IndhuVaratharajan, Dwijesh Ray, Christian Wöhler, and Anil Bhardwaj. 50th Lunar and Planetary Science Conference 2019 (LPI Contrib. No. 2132). 27. ^ "Extra brake thrust may have sent Vikram out of control in home stretch". 28. ^ Jump up to:a b c Neel V. Patel (6 September 2019). "India's Chandrayaan-2 lander likely crashed into the moon's surface". MIT Technology Review. Retrieved 7 September 2019. 29. ^ "Did India's Chandrayaan-2 Moon Lander Survive? The Chances Are Slim". 30. ^ Jump up to:a b c India's Moon Mission Continues Despite Apparent Lander Crash. Mike Wall,Space. 7 September 2019. Quote: "India's Moon Mission Continues Despite Apparent Lander Crash." 31. ^ Jump up to:a b "India's Vikram Spacecraft Apparently Crash-Lands on Moon". www.planetary.org. Retrieved 7 September 2019. 32. ^ Jump up to:a b c d Vikram lander located on lunar surface, wasn't a soft landing: Isro. Times of India. 8 September 2019. 33. ^ Chand, Manish (12 November 2007). "India, Russia to expand n- cooperation, defer Kudankulam deal". Nerve. Archived from the original on 13 January 2014. Retrieved12 January 2015. 34. ^ Sunderarajan, P. (19 September 2008). "Cabinet clears Chandrayaan-2". The Hindu. Retrieved 23 October 2008. 35. ^ "ISRO completes Chandrayaan-2 design". Domain-b.com. 17 August 2009. Retrieved20 August 2009. 36. ^ "India and Russia complete design of new lunar probe". Sputnik News. RIA Novosti. 17 August 2009. Retrieved 20 August 2009. 37. ^ Jump up to:a b c d e f g h i j "Payloads for Chandrayaan-2 Mission Finalised" (Press release). Indian Space Research Organisation. 30 August 2010. Retrieved 4 January 2010. 38. ^ Jump up to:a b c Ramachandran, R. (22 January 2013). "Chandrayaan-2: India to go it alone". The Hindu. 39. ^ Jump up to:a b Laxman, Srinivas (6 February 2012). "India's Chandrayaan-2 Moon Mission Likely Delayed After Russian Probe Failure". Asian Scientist. Retrieved 5 April 2012. 40. ^ "India's next moon mission depends on Russia: ISRO chief". NDTV. Indo-Asian News Service. 9 September 2012. 41. ^ "Chandrayaan-2" (Press release). Department of Space. 14 August 2013.Chandrayaan-2 would be a lone mission by India without Russian tie-up. 42. ^ Clark, Stephen (15 August 2018). "Launch Schedule". Spaceflight Now. Archived fromthe original on 16 August 2018. 43. ^ "Chandrayaan-2 launch postponed to October: ISRO chief". The Economic Times. Press Trust of India. 23 March 2018. Retrieved 16 August 2018. 44. ^ "ISRO to launch PSLVC-46 followed by PSLVC-47, Chandrayaan-2 in May: K. Sivan".Asian News International. 1 April 2019. Retrieved 1 April 2019. 45. ^ "India's Moon Lander Damaged During Test, Chandrayaan 2 Launch Put on Hold". The Wire. Retrieved 7 April 2019.

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46. ^ Jump up to:a b "Chandrayaan 2 Moon Mission Launch Aborted After Technical Snag: 10 Points".NDTV.com. Retrieved 15 July 2019. 47. ^ Jump up to:a b "Isro pinpoints GSLV-MkIII leak to 'nipple joint' of cryo engine". The Times of India. 17 July 2019. Retrieved 23 July 2019. 48. ^ Jump up to:a b c d "GSLV MkIII-M1 Successfully Launches Chandrayaan-2 spacecraft".www.isro.gov.in. ISRO. Retrieved 23 July 2019. 49. ^ "Chandrayaan 2". NSSDCA Master Catalog. NASA. Retrieved 3 July 2019. 50. ^ Banerji, Abigail (13 July 2019). "Chandrayaan 2: Everything you need to know about the orbiter's mission and design". Tech2. Retrieved 14 July 2019. 51. ^ Jump up to:a b Kumar, Chethan (12 August 2018). "Isro wants Chandrayaan-2 lander to orbit moon first". The Times of India. Times News Network. Retrieved 15 August 2018. 52. ^ Jump up to:a b Ramesh, Sandhya (12 June 2019). "Why Chandrayaan-2 is ISRO's 'most complex mission' so far". ThePrint. Retrieved 12 June 2019. 53. ^ Singh, Surendra (20 February 2018). "Chandrayaan-2 mission cheaper than Hollywood film Interstellar". The Times of India. Times News Network. Retrieved 3 March 2018. 54. ^ "Department of Space presentation on 18 Jan 2019" (PDF). 18 January 2019. Retrieved 30 January 2019. 55. ^ Jump up to:a b c "Annual Report 2014–2015" (PDF). Indian Space Research Organisation. December 2014. p. 82. 56. ^ Jump up to:a b "Chandrayaan-2 to get closer to moon". The Economic Times. Times News Network. 2 September 2010. Archived from the original on 12 August 2011. 57. ^ Jump up to:a b "Annual Report 2015-2016" (PDF). Indian Space Research Organisation. December 2015. p. 89. Archived from the original (PDF) on 5 July 2016. 58. ^ "HAL Delivers the Orbiter Craft Module Structure of Chandrayaan-2 to ISRO". Hindustan Aeronautics Limited. 22 June 2015. Archived from the original on 2 September 2018. 59. ^ Jump up to:a b c Singh, Surendra (7 September 2019). "Orbiter will have a lifespan of 7.5 years, it's possible to find Vikram Lander from orbiter: Isro chief | India News - Times of India". The Times of India. Retrieved 7 September 2019. 60. ^ Jump up to:a b "First set of beautiful images of the Earth captured by Chandrayaan-2 Vikram Lander". Archived from the original on 6 August 2019. Retrieved 25 August 2019. 61. ^ Wilson, Horace Hayman (1832). A dictionary in Sanscrit and English. Calcutta: Education Press. p. 760. 62. ^ Kumar, Chethan (12 August 2018). "Chandrayaan-2 Lander to be named 'Vikram' after Sarabhai". The Times of India. Times News Network. Retrieved 15 August 2018. 63. ^ "ISRO developing vehicle to launch small satellites". Frontline. Retrieved 29 August2018. Making a throttleable engine of 3 kilonewtons or 4 kilonewtons is a totally new development for us. But we wanted to make use of available technologies. We have a LAM [liquid apogee motor] with a 400 newton thruster, and we have been using it on our satellites. We enhanced it to 800 newtons. It was not a major, new design change. 64. ^ Mondal, Chinmoy; Chakrabarti, Subrata; Venkittaraman, D.; Manimaran, A. (2015).Development of a Proportional Flow Control Valve for the 800N Engine Test. 9th National Symposium and

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Exhibition on Aerospace and Related Mechanisms. January 2015. Bengaluru, India. 65. ^ "Chandrayaan-2: First step towards Indians setting foot on moon in near future". The New Indian Express. Retrieved 8 July 2019. As solar energy powers the system, a place with good visibility and area of communication was needed. Also, the place where the landing takes place should not have many boulders and craters. The slope for landing should be less than 12 degrees. The South pole has a near- flat surface, with good visibility and sunlight available from the convenience point of view, 66. ^ Subramanian, T. S. "Chandrayaan 2: Giant leap for ISRO". Frontline. Retrieved 9 July2019. 67. ^ "How ISRO Plans To Pull Off An Unprecedented Landing On Moon's South Pole".NDTV.com. Retrieved 5 September 2019. 68. ^ "Space Applications Centre, Annual Report 2016–17" (PDF). SAC. p. 35. Archived(PDF) from the original on 2 January 2018. Retrieved 20 July 2019. 69. ^ "Key payload for Chandrayaan-2 leaves for Bengaluru". The Times of India. Retrieved20 July 2019. 70. ^ "SAC Seminar 2016" (PDF). SAC.gov.in (in Hindi). 21 July 2017. p. 94. Archived(PDF) from the original on 5 September 2019. Retrieved 5 September 2019. 71. ^ "Department of Space Annual Report 2016– 17" (PDF). ISRO.gov.in. Archived(PDF) from the original on 18 March 2017. Retrieved 20 July 2019. 72. ^ D. S., Madhumathi (25 October 2016). "ISRO starts landing tests for Chandrayaan-2 mission". The Hindu. Retrieved 28 October 2016. 73. ^ Jump up to:a b "Chandrayaan-2 Spacecraft". Retrieved 24 August 2019. Chandrayaan 2's Rover is a 6-wheeled robotic vehicle named Pragyan, which translates to 'wisdom' in Sanskrit. 74. ^ Wilson, Horace Hayman (1832). A dictionary in Sanscrit and English. Calcutta: Education Press. p. 561. 75. ^ Elumalai, V.; Kharge, Mallikarjun (7 February 2019). "Chandrayaan – II" (PDF).PIB.nic.in. Archived from the original (PDF) on 7 February 2019. Retrieved 7 February2019. Lander (Vikram) is undergoing final integration tests. Rover (Pragyan) has completed all tests and waiting for the Vikram readiness to undergo further tests. 76. ^ "ISRO to Launch Chandrayaan 2 on July 15, by September 7". The Wire. Retrieved 12 June 2019. 77. ^ Singh, Surendra; 2019; Ist, 14:02. "Chandrayaan-2 will carry 14 payloads to moon, no foreign module this time". The Times of India. TNN. Retrieved 11 May 2019. 78. ^ Laha, Jayanta; Dinesh, B.; Selvaraj, P.; Krishnamoorthy, Subhalakshmi (2018)."Realization of Space Grade Miniature Digital Camera for Lunar Navigation" (PDF).International Journal of Pure and Applied Mathematics. 118 (16): 1105–1116. Archived(PDF) from the original on 26 September 2018. 79. ^ "With hands, IIT-K profs bring joy to paralytics". The Times of India. 2019. Retrieved 10 July 2019. 80. ^ Annadurai, Mylswami; Nagesh, G.; Vanitha, Muthayaa (28 June 2017). ""Chandrayaan-2: Lunar Orbiter & Lander Mission", 10th IAA Symposium on The Future of : Towards the Moon Village and Beyond, Torin, Italy". Archived from the original on 29 June 2017. Retrieved 14 June 2019. Mobility of the Rover in the unknown lunar terrain is accomplished by a Rocker bogie suspension system driven by six wheels. Brushless DC motors are used to drive the wheels to move along the desired path and steering is accomplished

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by differential speed of the wheels. The wheels are designed after extensive modelling of the wheel-soil interaction, considering the properties, sinkage and slippage results from a single wheel test bed. The Rover mobility has been tested in the Lunar test facility wherein the soil simulant, terrain and the gravity of moon are simulated. The limitations w.r.t slope, obstacles, pits in view of slippage/sinkage have been experimentally verified with the analysis results. 81. ^ "Dr M Annadurai, Project director, Chandrayaan 1: 'Chandrayaan 2 logical extension of what we did in first mission'". The Indian Express. 29 June 2019. Retrieved 30 June2019. 82. ^ Payyappilly, Baiju; Muthusamy, Sankaran (17 January 2018). "Design framework of a configurable electrical power system for lunar rover". ResearchGate: 1– 6.doi:10.1109/ICPCES.2017.8117660. ISBN 978-1-5090-4426-9. 83. ^ "Ashoka Chakra, ISRO Logo, Flag: Chandrayaan 2 Set to Engrave India's Name on Moon for Centuries". Retrieved 4 September 2019. 84. ^ Curtain Raiser video (Hindi) (in Hindi). Event occurs at 1 minute 55 seconds. 85. ^ Jump up to:a b c Bagla, Pallava (31 January 2018). "India plans tricky and unprecedented landing near moon's south pole". Science. Retrieved 8 March 2018. 86. ^ Jump up to:a b c d e f "Chandrayaan-2 Payloads". 12 June 2019. Archived from the original on 13 July 2019. Retrieved 13 July 2019. 87. ^ Beary, Habib (4 February 2010). "NASA and ESA to partner for Chandrayaan-2". Sakal Times. Retrieved 22 February 2010. 88. ^ Laxman, Srinivas (5 September 2010). "'We're launching Chandrayaan-2 for a total coverage of the moon'". The Times of India. 89. ^ Jump up to:a b Bartels, Meghan (24 March 2019). "How NASA Scrambled to Add Science Experiments to Israeli, Indian Moon Probes". Retrieved 25 March 2019. 90. ^ Jump up to:a b c Science, Chelsea Gohd 2019-07-26T16:42:31Z; Astronomy. "50 Years After , India Is Carrying a NASA Laser Reflector to the Moon (And It's Only the Start)".Space.com. Retrieved 26 July 2019. 91. ^ "Implementing arrangement between India and of America for cooperation on the Chandrayaan mission- 2" (PDF). Ministry of External Affairs. 11 February 2019.Archived (PDF) from the original on 30 July 2019. Retrieved 30 July 2019. 92. ^ Mallikarjun, Y. (29 May 2013). "India plans to send seismometer to study moonquakes".The Hindu. Retrieved 1 June 2013. 93. ^ India Heads to the Moon WithChandrayaan 2. David Dickinson, Sky & Telescope. 22 July 2019. Quote: "Vikram carries a seismometer, thermal probe, and an instrument to measure variation and density of lunar surface plasma, along with a laser retro-reflector supplied by NASA's Goddard Spaceflight Center." 94. ^ "Chandrayaan-2 update:Mission Plan of Chandrayaan-2 spacecraft - ISRO".www.isro.gov.in. Retrieved 24 July 2019. 95. ^ "Live media coverage of the landing of Chandrayaan-2 on lunar surface - ISRO".www.isro.gov.in. Retrieved 2 September 2019. 96. ^ "Chandrayaan2 update: First earth bound maneuver - ISRO". www.isro.gov.in. Retrieved 24 July 2019. 97. ^ "Chandrayaan2 update: Second earth bound maneuver". ISRO.gov.in. 26 July 2019.Archived from the original on 25 July 2019. Retrieved 26 July 2019.

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98. ^ "Chandrayaan2 update: Third earth bound maneuver - ISRO". www.isro.gov.in. Retrieved 29 July 2019. 99. ^ Jump up to:a b "Chandrayaan2 update: Fourth earth bound maneuver". www.isro.gov.in. Retrieved2 August 2019. 100. ^ Jump up to:a b "Chandrayaan2 update: Fifth earth bound maneuver". www.isro.gov.in. Retrieved6 August 2019. 101. ^ Jump up to:a b "Chandrayaan-2 Successfully enters Lunar Transfer Trajectory". www.isro.gov.in. Retrieved 14 August 2019. ^ Jump up to:a b "Chandrayaan-2 update: Lunar Orbit Insertion"

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