One of the main reasons it's hard to restart a rocket in space is simply because there's no gravity to feed the propellant to the outlet of the tank. While the

One of the main reasons it's hard to restart a rocket in space is simply because there's no gravity to feed the propellant to the outlet of the tank. While the rocket is running, the acceleration caused by the motor causes the propellant to pool at the bottom of the tank where the outlet is. As soon as you stop the motor, the acceleration stops and the liquid starts floating around inside the tank. If you tried to restart it now, you would get an unstable mix of propellant and pressurizing gas which might not allow the rocket to startup properly. To restart reliably, you need to apply a force to the tank to force the liquid back down to the outlet. During Apollo, this was done with many small solid rocket motors called Ullage Rockets. These would fire for just a few seconds just immediately before the rocket was restarted. The force was just enough to get the propellant down to the outlet in time to be sucked into the turbo pumps before ignition.