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Received wisdom has it, that Newtonian gravity does not give a correct description of the observed gravitational acceleration of the stars of our galaxy. It is widely held that, according to Newtonian physics, the acceleration should be: a ~ 1/r2. Instead, we observe: a ~ 1/r.
The last relation has an important and very observable consequence: the rotational (tangential) velocity of every star in the outer region of a galaxy becomes the same at all distances from the centre.
The difference between the (supposed) Newtonian gravity and the observed gravity therefore is often illustrated by a graph of this velocity, the so called rotation curve:

To explain this discrepancy between theory and observation, two theories are proposed:
1: There be a lot of 'dark matter' surrounding the galaxy, that provides for the extra gravity, or
2: Newtononian gravity had to be modified (MOND: MOdified Newtonian Gravity)

Both of them have their qualities and their problems, but that is not the issue here. I will argue that neither one is a correct description of observed reality. Instead I will show that Newtonian gravity has been misinterpreted. When applied correctly there is no discrepancy between theory and observation. For our galaxy Newton predicts exactly what has been observed: an acceleration of a ~ 1/a, and a rotational speed of 230 km/sec.