When is it best to switch on the auxiliary engine, Physics

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A rocket is intended to leave the Earth's gravitational ?eld.

The fuel in its key engine is a little less than the amount that is essential, and an auxiliary engine, only capable of operating for a short time, has to be used as well.

When is it best to switch on the auxiliary engine: at take-off, or when the rocket has nearly stopped with respect to the Earth, or does it not matter?

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