9:09 AM Yeah. I don't know how to put this but please let me try. I realized most people don't know what is a "burn" in space travel terms and this seems unacceptable to me so i make it a high priority right now to explain it.
Doing some searches was trying to figure the time of the burn of the initial launch. Actually, there are several. During the initial lift off we have two solid fuel boosters that burn i don't know, a minute of two.
Those deserve a few considerations as well. Solid rocket boosters are nothing but metal cylinders filled with (slower burning) explosive attached to the tanks with liquid fuel. Lit at one end, they will burn towards the other until they are spent. One must understand there is no control over those after lighting them up. All we have to do is hold our breath and wait until they are done and jettisoned.
It is very important that they finish both in the same time. Otherwise, the ship will take a turn in one direction or the other. Or simply expel them with explosive charges seconds before they are done.
During all this time the main liquid fuel engine(s) at the bottom of the ship move(s) around two axis many times a second (thrust vectoring), doing corrections, trying to keep up with irregularities and turbulences coming from solid fuel boosters.
The solid fuel boosters are a cheap way to bring more lift to the launch, lowering the size of tanks for liquid fuel which is most of the mass of the ship at launch anyway. I don't know what the ratio is but i i think is in the order of 1-5% of mass of fuel needed for useful payload lifted in orbit (which again most mass is fuel for subsequent burns) when the ship becomes briefly a satellite.
So yes, we have solid fuel booster burn, continued main engine(s) burn, and then silence. Once the ship is in the desired Earth orbit the fuel is mostly spent, there are no more burns except for corrections and compensating for very thin but existing atmosphere that slows down (and thus lowers orbit for any satellite, reducing its life time.
I could not find that as all the keywords used lead me only to the emotional news about the firs trip to the Moon in 50 years that flood searches no matter how much i try but i would think is in the order of minutes.
The main idea was that during the whole flight to the Moon and back that takes what, days, the only powered phases of the flight are in the order of minutes and those powered phases are called burns.
Here is a diagram showing Artemis main component including the 2 solid fuel boosters and the 4 liquid fuel engines at the bottom. All engines are designed and work for minutes during the whole mission (also because the burn fuel at a very high rate). 
In the case of Artemis II most of the power phases of flight occurred within the first minutes and first day of flight, rest of it been done by inertia alone, conserving the initial kinetic energy acquired from chemical energy of fuel during burns.
The equations needed to describe the flight path are extremely complicated, and the precision of the burns and feedback such as position and speed, before, during and after those burns have to be extreme so it can ensure the precise and safe return to Earth using inertia and gravity of Moon and Earth in a very smart way.
The final burn or the so called "lunar injection" is particularly critical (but not more critical than lift off, using solid fuel rockets, other burns), cause that burn uses the last of the fuel and there is no possibility of return except through gravity of Moon during flyby and there is a narrow window of angle, position and speed in which that can be done.
Besides equations, an input is being necessary as current position and speed. There are a number of ways to calculate those, starting from comparing observed stars positions to charts, inertial data (accumulation of accelerations/decelerations/direction changes since last calibration or reset), (ground based) radar, lasers and other EM means. Lately they begin to think about extending the GPS coverage to at least areas near Earth.
Any measurements done on Earth cannot be used in real time for that input to calculate the engine's parameters since there is a lag in EM transmission of tenths of a second due to speed of light and distances.
I know from videos i have seen that rocket engines are being steered during lift off, because i saw their movements, probably using inertial feedback, to keep pushing the rocket upward and especially to avoid tipping it over, especially during very first phase where no aerodynamic forces are there to help stabilize direction of the vehicle.
There are also no aerodynamic forces at work in space like after leaving the atmosphere or during the final burn and i assume the engine is being steered using inertial input as well, but don't know if they use other data to refine the direction during the 6 minute final burn.





















