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Especially taking in account that acceleration need a force which leads to some conversion of energy. This is not the case for orbital motion, such a acceleration does not convert energy. That seems to be a good point why we talk in General Relativity in first line about curvature of space and time and not more about gravitational force.

So the question is, is there a principal difference in acceleration from an impulse and the free fall of a body in the orbit around a gravitational mass? This question is related to this about Can gravity accelerate light?

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we talk in General Relativity [...] about curvature of space and time

At least (without implying strict separability) about curvature of spacetime; right.

In this context it is however possible to distinguish "free (inertial, falling) motion" from "any other motion", The latter is accordingly said to be "due to (external) influence(s)", and its ("first order") deviation from "free motion" is quantified as a non-zero value of (instantaneous) acceleration.

Is there a principal difference [...] ?

The difference is most plainly and strikingly that the acceleration value is either zero, or non-zero.
A general prescription how to evaluate acceleration (from given more basic geometric notions, namely given values of spacetime interval ratios) is sketched here (PSE/a/146397).

Note that this mentioned prescription is based on non-zero spacetime intervals; it is indeed intended to be evaluated for ratios of certain time-like intervals. It is not even defined for a set of events which are all (pairwise) separated by null intervals. However, it may be argued that it is therefore consistent to attribute to the propagation of a signal front strictly an acceleration value of zero; calling it strictly "free" with respect to the possibly curved spacetime geometry of the experimental region under consideration.

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  • $\begingroup$ This is the only answer, so I give the award to you. $\endgroup$ – HolgerFiedler Nov 16 '15 at 4:46

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