Physics/Space question !?

[pajsouth]

They calculated that just using rockets there would not be enough fuel to make the shorter trip. By going around the moon they were able to slingshot back to earth because of the moons gravity pulling on them. They also didn't have to use more fuel this way which helped for the reentry burn to make sure they hit the earths atmosphere at exactly the right degree to steep they would burn up to shallow they would bounce off. The biggest hazard of taking the long route was running out of oxygen and electrical power. These were unknowns because They could not get out of the spacecraft to visualise the extent of the damage.

[Henry Chan]

When apollo 13 was halfway to the moon, it developed problems in the oxygen system. Rather than turning back to earth, mission control decided the craft should proceed to the moon before returning to earth.
Why did they do so? (physics based)
What was the the major risk in doing so?
Thanks !

[166moons]

There's a great movie that is solely about this topic, watch "Failure is Not an Option".

[johnbonnechappe]

When a spacecraft is set on a trajectory it would take a huge amount of force and therefore fuel to turn it around. Far more than what the service module of Apollo13 had. The solution is to use a "gravitational assist" to turn the spacecraft and send it back to Earth.

And that's exactly what they did!. The moon provided a gravitational assist, turned Apollo13 around and sent it on a trajectory back to Earth. The rest is, as they say, history!