Mission highlights
The Apollo 13 mission began with a lesser-known malfunction: during the second-stage burn, the center engine shut down two minutes early. The four outer engines were run for longer than planned, to compensate for this.[3] Engineers later discovered that this was due to dangerous pogo oscillations which might have torn the second stage apart; the engine was experiencing 68g vibrations at 16 hertz, flexing the thrust frame by 3 inches. However, the oscillations caused a sensor to register excessively low average pressure, and the computer shut the engine down automatically.[4] Smaller pogo oscillations had been seen on previous Apollo missions (and had been recognized as a potential problem from the earliest unmanned Titan-Gemini flights), but on Apollo 13 they had been amplified by an unexpected interaction with the cavitation in the turbo-pumps.[5] Later missions included anti-pogo modifications, which had been under development since before Apollo 13, that solved the problem. The modifications were the addition of a helium gas reservoir in the center engine’s liquid oxygen line to dampen pressure oscillations in the line, plus an automatic cutoff for the center engine in case this failed, and simplified propellant valves on all five second-stage engines.

Explosion
As the spacecraft was on its way to the Moon, at a distance of 321,860 kilometers (199,990 mi) from Earth, the number two oxygen tank, one of two tanks contained in the Service Module (SM), exploded. Mission Control had requested that the crew stir the oxygen tanks, a task required to prevent the oxygen ‘slush’ from stratifying. Damaged Teflon-insulated electrical wires, powering the stirrer motor, caught fire when power was applied. The fire heated the surrounding oxygen, increasing the pressure inside the tank above its nominal 1,000 PSI (7 MPa) limit causing the tank to explode. The true cause of the explosion was unknown at the time; one conjecture was that a meteoroid had impacted the SM or even the LM.
This explosion damaged other parts of the Service Module, critically including the number one oxygen tank. The Command/Service Module (CSM) relied on the oxygen tanks to generate electricity, so as a result of the explosion, very little power was available for the spacecraft. The Command Module (CM) contained batteries for use during re-entry, after the SM was jettisoned, but these would only last about ten hours. Because this power needed to be saved for re-entry, the crew survived by using the Lunar Module (LM), still attached to the CSM, as a "lifeboat". The LM "lifeboat" procedure had actually been created during a training simulation (in the simulator) not long before the flight of Apollo 13.[6](Lovell and Kluger 83-87)


Apollo 13 damaged Service Module (NASA)
The damage to the CSM meant that the Moon-landing at the Fra Mauro Highlands had to be abandoned. To return the crew as quickly and safely as possible, only a single pass around the Moon was made in what is called a free return trajectory, which uses the Moon's gravity to effectively "slingshot" the spacecraft back to Earth. To enter this trajectory, a significant course-correction was required; this would normally have been a simple procedure, using the SM propulsion engine. However, the flight controllers did not know the extent of the damage that the service module had suffered, and did not want to risk firing the main engine. Instead, the course correction was performed by firing the LM's descent engine, an option selected after extensive discussion among the engineers on the ground. The initial maneuver to change to a free return trajectory was made within hours of the accident. After passage around the Moon, the descent engine was fired again for a PC+2 burn (PeriCynthion + 2 hours) in order to accelerate the spacecraft's return to Earth. Only one more descent engine burn was required later, for a minor course correction.
Considerable ingenuity under extreme pressure was required from both the crew and the flight controllers to work out how to jury rig the craft for the crew's safe return, with much of the world watching the developing drama on television (although due to the severe electric power limitations following the explosion, no live TV broadcasts were made from the craft for the duration of the mission -- network commentators had to use models and animated footage to illustrate their coverage).
One of the major stumbling blocks was that the LM "lifeboat" was only equipped to sustain two people for two days, but it was now required to sustain three people for four days. One of the most critical problems was that the lithium hydroxide canisters available for the LM's carbon dioxide scrubbers would not last for all four days. Although the CM had an adequate supply of replacement canisters, they were the wrong shape to fit the LM's receptacle; an adapter had to be fabricated from materials in the spacecraft.
As the re-entry to Earth's atmosphere approached, NASA took the unusual step of jettisoning the Service Module before the Lunar Module, so pictures of the SM could be taken for later analysis. When the crew saw the damaged service module, they reported that the access panel covering the oxygen tanks and fuel cells, which extended the entire length of the Service Module's body, had been blown off.
There was some fear that the extensive water condensation in the CM, due to reduced temperatures during the return leg, might have seriously damaged the electronics of the Command Module, which would only become apparent upon activation. But the equipment worked perfectly when activated, at least partly due to the extensive design modifications made to the CM after the fire aboard Apollo 1.


Apollo 13's successful splashdown (NASA)
The crew returned unharmed to Earth, although Haise had a urinary tract infection, resulting from the scarcity of potable water on the damaged ship and the difficulty of disposing of urine, and had to be treated in an infirmary.

The crew was instructed to store urine and other waste products onboard instead of dumping it into space to avoid disturbing the trajectory which might have required an additional course correction.[7]
Although the explosion forced the mission to be aborted, the crew was fortunate that it occurred on the first leg of the mission, when they had a maximum of supplies, equipment, and power to use in the emergency. If the explosion had occurred while in orbit around the Moon, or on the return leg after the LM had been jettisoned, the crew would have had significantly less chance of survival.

Paradoxically, the crew's lives may have been saved by another failure in the oxygen tanks. At around 46 hours and 40 minutes into the mission, the oxygen tank 2 quantity gauge went "off-scale high" (reading over 100%) and stayed there. As a result of this failure, and to assist in determining the cause, the crew was asked to perform cryo tank stirs more often than planned: in the original mission plan, the stir which blew out the tank would have occurred after the lunar landing. Lovell and Haise might have walked on the Moon, but would never have walked on Earth again.

After the completion of the mission, there was a full investigation of the event, and the craft was modified to prevent future occurrences of the fault.

Cause of the accident
The explosion on Apollo 13 led to a lengthy investigation of the underlying cause. Based on detailed manufacturing records and logs of mission problems, the oxygen tank failure was tracked to a combination of multiple faults; individually, they were not critical problems, but together they nearly led to disaster for Apollo 13.

Supercooled gases, such as liquid oxygen or liquid hydrogen, require great care in handling, and most storage containers holding them are unsealed so that pressure from expanding gas will not cause the container to fail (much like freezing water will shatter even the strongest sealed container). However, Apollo’s liquid oxygen tanks were capable of safely holding liquid oxygen at supercritical pressures for years before it evaporated, because of their design and insulation. Each tank was able to hold several hundred pounds of the highly pressurized liquid to supply the craft with oxygen, fuel for electricity, and water from the byproducts of the fuel cells. However, the very characteristics that made the tank useful made internal inspection impossible.

The tank was made of several basic components that were relevant to the accident:

&Mac183; a thermostat to control the heater within the tank, used to speed the evaporation of the liquid into gas;
&Mac183; a thermometer to determine the temperature of the heater;
&Mac183; valves and piping that were designed to allow the tank to be completely emptied of liquid, by forcing gas into the tank;
&Mac183; an interior coating of teflon that protected the wiring from the extremely cold gas; and
&Mac183; an internal fan to stir the liquid oxygen (which will turn into a "slush" at these pressures if it is allowed to sit for a long period of time).
These were the basic design, manufacturing, and operational problems that led to the accident:
&Mac183; The thermostat was originally designed to handle the 28-volt supply that would be used in the command module. However, the specification for the tank was changed, so that it had to handle 65 volts on the launch pad. Most of the wiring was changed to handle the higher voltage, but the thermostat was not. Engineers at Saturn V subcontractor Beechcraft later admitted they knew they had put 65 volts on a line designed for only 28 volts. The tank then made it into the Apollo 13 Service Module which crippled the mission.
&Mac183; The thermometer was designed to read out at the highest operational temperature of the heater, about 100 degrees Fahrenheit. As a result, higher temperatures registered at only 100 °F. At the time, this was not an issue, because the thermostat was supposed to cut out at 80 °F (27 °C), making higher temperatures impossible.
&Mac183; During assembly, the structure carrying the tank that failed was dropped about 2 inches (5 cm). The exterior was undamaged, but the pipes that directed flow within the tank became misaligned.
&Mac183; For ground-testing, the tank was filled. However, when it came time to empty it, the problem with the piping was discovered. As such, the tank could not be properly emptied except by running the heater to evaporate the liquid gas. Not using this tank would have delayed the mission, and there was no alternate tank available. Lovell was aware of the decision to use the heater to evaporate the oxygen, which was calculated to take a few days at the highest operational temperature of 80 °F (27 °C).
&Mac183; However, when the heater was turned on continuously, the higher 65-volt supply fused the thermostat, which was only wired to handle 28 volts. This malfunction eliminated the thermostat's ability to switch off the heater, which in turn allowed the heater to keep heating up past 80 °F (27 °C), and eventually past 100 °F. The current recorder in the power supply showed that the heater was not cycling on and off, as it should have if the thermostat was functioning correctly, but no-one noticed it at the time. Because the thermometer did not register temperatures higher than 100 degrees Fahrenheit (38 degrees Celsius), the monitoring equipment did not register the true temperature inside the tank -- an estimated 800 degrees Fahrenheit (430 °C). Instead of taking several days, the gas evaporated in hours. The high temperatures burned off the teflon coating, leaving the wires inside the tank exposed.
&Mac183; When the tank was refilled with oxygen, it became a bomb waiting to go off. During the "cryo stir" procedure, the electricity needed to run the fans passed through the exposed wires inside the tank, setting off sparks which led to the explosion.
&Mac183; The close proximity of the two oxygen tanks exacerbated the situation. Although the remaining tank survived the explosion, its valves were damaged, allowing the oxygen within to leak out. In subsequent Apollo missions, the two oxygen tanks were situated farther apart, while a third tank was installed in an isolated location.

Mission notes

Plaque that was to be attached to Aquarius
&Mac183; There was no time to properly replace the original lunar plaque on Aquarius (which bore Mattingly’s name), so Jim Lovell was given a replacement (with Swigert’s name) to put over the original plaque once they landed on the moon. However, because the lunar landing was never made, Lovell kept the plaque, which is one of the few mementos from the mission that he has on display at his home.
&Mac183; As a result of following the free return trajectory, the altitude of Apollo 13 over the lunar far side was approximately 100 km greater than the corresponding orbital altitude on the remaining Apollo lunar missions. This could mean an all-time altitude record for human spaceflight, not even superseded as of 2006; however, the variation in distance between Earth and the Moon, owing to the eccentricity of the Moon's orbit about Earth, is much larger than 100 km, so it is not certain whether the actual distance from Earth was greater than that of all other Apollo missions. The Guinness Book of Records listed this flight as having the absolute altitude record for a manned spacecraft, and Lovell should have received a certificate from them attesting to this record. (Lovell stated in the book Lost Moon that apart from the plaque and a couple of other pieces of salvage, the only other item he has, regarding this mission, was a letter from Charles Lindbergh.)
&Mac183; The splashdown point was 21°38_S 165°22_W, SE of American Samoa and 6.5 km (4 mi) from the recovery ship, USS Iwo Jima.
&Mac183; Superstitious people have associated the belief that 13 is an unlucky number with the mission, due to the fact that the mission began at 13:13 CST, the problems began on April 13, and the mission is called Apollo 13. Other coincidental appearances of the number 13 connected to the mission included the explosion occurring at 19:13 CST, and a post-flight estimate that, had the explosion occurred on the ground, repairing the damage would have cost $13 million.
&Mac183; The A7L spacesuit worn by Lovell would have been the first to feature red bands on the arms and legs of the suit, as well as on the life-support backpack and lunar EVA helmet assembly, to easily distinguish him from Haise. This was done because there was confusion by Mission Control personnel on them distinguishing the Apollo 12 landing team (before they accidentally destroyed the electron tube in the camera when it was exposed to direct sunlight), which had no distinguishing marks for the commander, and both Charles Conrad and Alan Bean had their side sunshades extended down. The red bands were a feature for the remaining Apollo flights, and are used on the Extravehicular Mobility Units worn by Shuttle and ISS astronauts.
&Mac183; The Apollo 13 mission has been called "A Successful Failure," in that the astronauts were successfully brought home despite not landing on the moon.
&Mac183; The Apollo 13 Mission Operations Team was awarded the Presidential Medal of Freedom for their actions during the mission, as were the astronauts
&Mac183;
Credit to: http://en.wikipedia.org/wiki/Apollo_13#Quote.