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See the diagram which show the first two phases.  The other diagram shows MOM.

1st phase:

    MOM was launched from Surface of Earth on 5th November 2013, in the first phase called Geo-centric phase.  The launch was done from Satish Dhawan Space center at Sri Hari Kota in Andhra Pradesh.  It was in this phase for 25 days.  PSLV XL-C25 rocket carried MOM into space at the launch. In this duration MOM travelled 192,800 km from Earth’s centre.  There some technical problems in putting MOM in 2nd phase and making MOM escape from Earth’s gravitational field.  The escape velocity was not reached properly in expected manoeuvres.

   PSLV does not have capability to launch MOM directly into the trans-mars orbit.  So Apogee of MOM around Earth raised a lot and then induced in to trans-Mars orbit.  During this phase the control of the space craft control center at ISRO, Peenya, Bangalore.

2nd phase:

     MOM was introduced into a trans-Mars orbit on 30th November 2013, in the second phase called Helio-Centric Phase.  It took a 23-minute long engine firing to escape from Earth.  In this phase MOM travelled 780 million kilometres around Sun to reach the intended orbit around Mars.  During 10 month travel of MOM, some manoeuvres (test firing) are done to correct its orbit and path.  During this phase the communication was shifted from low gain antenna to a medium gain antenna, as the distance increased. 

3rd phase:

    MOM started orbiting in the specified orbit around Mars on 24th September 2014. That is the 3rd phase of MOM called Areo-Centric phase.   Now MOM is sending signals corresponding to images of Mars and its atmosphere.  In this orbit, MOM goes in an elliptical orbit around Mars with a periapsis of 421 km (nearest distance from Mars) and with an apoapsis of 77, 000 km (farthest distance from Mars).

    MOM has fuel to last for 1 year as against 6 months intended mission.  In the high gain antenna is used.  There is a reflector that receives signals and transmits signals towards Earth.  A transponder communicates with master control facility of ISRO, via a TWT amplifier and an antenna array. 

MOM description

     MOM weighs 1350 kg along with its fuel.  It has solar panels to generate 800 Watts of energy and is stored in a Lithium ion battery.
     MOM has 5 instruments (Payloads):  Lyman-Alpha Photometer (LAP) , Methane sensor (MSM), Exospheric Neutral composition Analyzer(MECNA), Thermal  Infrared Imaging Spectrometer (TIS), Mars Color Camera (MCC).  These are functioning now and sending data (which is captured by sensors) to us.

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Introduction Total Weight (kg) 1,350 Science Payload Weight (kg) 14.49 Fuel Load (kg)     850 Launch Date November 5, 2013 Trans Mars Injection December 1, 2013 Mars Orbit Insertion September 24, 2014 Planned Mars Orbit  Periapsis: 365-km, Apoapsis: 80,000 km, Orbital Period: Approx 77-hr
ISRO launched the 1,350 kg Mars Orbiter Mission - Manglayaan - from Sriharikota using PSLV-C25, an XL variant of the launcher, on November 5, 2013 at 14:38 hrs to avail of the November 2013 launch window for the planet. The launch was earlier scheduled for October 28, 2013, but was postponed to accommodate the delay in the arrival in South Pacific, due to bad weather, of one of the two SCI ships to be used for tracking the launch of the spacecraft.

ISRO was sent hurtling on a Mars intercept trajectory from earth orbit at 0.42 hours on December 1.

The Mars orbiter will be placed in an orbit of 372 x 80,000 km around Mars on September 24, 2014.

The spacecraft carries 14.49 kg of scientific payload on- board. 

ISRO initially planned to use the GSLV to launch a 500 kg Mars orbiter with 25 kg scientific payload, but scaled down its plans because of two back to back failures of the launcher in 2010.

The GOI sanctioned seed money of Rs 10 crore in August 2009 to carry out studies on suitable experiments for the mission.
The budget for FY 2012-13 allocated Rs. 125 crore for the mission during the financial year. The union cabinet cleared the project on Friday, August 3, 2012.
MOM Launch ComplexityThe MOM was launched nearly 25 days before the start of its journey to give mission planners sufficient time to raise its orbit before the opening of the Mars journey start window on November 27.
The lift off time slot varied each day starting November 5 with five minutes leeway.

Propelling the MOM accurately on a Mars intercept trajectory required a complex set of maneuvers during and after launch. Trajectory calculations were specific to the date of the launch; they had to be recomputed in case of any launch delay.

"The time of lift-off and required coasting duration is different for each day of launch; and one has to work out a series of different trajectory management strategies corresponding to each possible launch date," says V Adimurthy, professor at Satish Dhawan Space Center and senior adviser (interplanetary missions) of ISRO. [via The Economic Times] 
The spacecraft's orbital insertion involved long coasting of the rocket between third and fourth stage. 
"The management of the long coast between third and fourth stage is a complex issue," says Adimurthy. 
PSLV-C-25 was to inject the MOM into a 250 X 23000 km orbit with an inclination of 17.864 degree. The MOMS velocity was planned be progressively increased to the Earth escape velocity of 11 km per second using three to five burns of the MOM's Liquid Apogee Motor (LAM).

In order to minimize the energy requirement for the journey to Mars, the Argument of Perigee (AOP) of the MOM  needed to be between 276.4 deg to 288.6 deg, compared to 178 deg in earlier missions. (The AOP is the angle between the perigee of a earth satellite and its ascending node.)
The MOM launch flight regime was planned to last 2,657s, as against 1,200s for regular PSLV missions, with a  1,580-1,800s coasting before the ignition of the PS4 stage.
According to ISRO, the long coasting necessitated specific modification and validation of the coast phase guidance algorithm, on-board battery capacity augmentation, assessment on the performance of inertial systems for extended flight duration and deployment of two ship-borne terminals to capture the crucial telemetry data during flight in the non-visibility zone.
ISRO said that additional provisions were made for the thermal management of Vehicle Equipment Bay, PS4 stage and also the Spacecraft elements considering the longer exposure to extreme cold space.

The MOM's 55 million miles journey to Mars is expected take 300-days. Its trajectory would need to be accurate enough to bring it within 60 km of the Red Planet on September 24, 2014 to ensure successful Mars capture. 
MOM will be travelling at a velocity of 34-km/sec at the time of Mars capture. [via DNA]
Liquid Engine The Liquid Engine (LM) on the MOM, also called the 440-Newton Liquid Engine, is a modified version of the Liquid Apogee Motor (LAM) used on earlier missions that required orbit raising, such as Chandrayaan.
The Liquid Motor is meant to raise the orbit of the MOM, propel it on a Trans-Mars trajectory, and slow it down for Mars orbit insertion.
The LM is capable of generating 440 Newton thrust. One of the mission challenges would be the restart of LM after a 300 day journey to Mars.
The MOM is also fitted with 8 22-Newton thrusters for controlling the orientation of the spacecraft and also for correcting the trajectory during the heliocentric phase of the mission.
The Liquid Engine and the thrusters us monomethyl hydrazine as fuel and nitrogen tetroxide as oxidizer. Pressurized helium gas is used to force the propellants into the combustion chamber.