Getting first and second time derivative of mean motion of spacecraft - without TLE? The Celestrak website provides information on reading the TLE ( Two-Line Element Set ) format. In Line 1, Column 34-43 & 45-52  give information about First Time Derivative of the Mean Motion  and Second Time Derivative of Mean Motion.
Is there any way to calculate or estimate these two parameters for a spacecraft, if you don't have its TLE at disposal to simply read them from there ? And what do they actually mean ?
 A: The mean motion $n$ of a satellite is its angular velocity, averaged over one period. In other words, if the satellite rotates around the Earth with period $P$, its mean motion $n$ is
$$
n = \frac{2\pi}{P}
$$
If the Earth were a perfectly spherical symmetric object, and there were no other perturbing agents in the Universe (in other words, if Earth + satellite were a closed system), then $n$ would be an exact constant of motion. 
However, several effects are not included in a two-body, idealized problem, and they make $n$ time-variable. One such effect is the Earth's oblateness, which makes the gravitational potential differ from a simple $1/r$ law. Another effect is the presence of the Moon, which also perturbs the satellite motion. If, instead of a human-built satellite, we were discussing the motion of moons around their planets, other perturbing agents would the gravitational influences of nearby planets and of the Sun. 
The fact that $n$ is not constant in time is clearly seen in accurate positional data extending over many orbits. Fitting the ensemble of these data yields both a first and a second derivative, to allow more precise predictions of the satellite position in the nearby future. Since however the variation of $n$ is not subject to any simple law, it needs to be recomputed all the time. 
So, in short, the answer is no, you cannot derive those parameters from data in your possession. In order to be able to do that, you should own the whole set of position measurements over very many orbits which is surely in the hands of both civilian and military space agencies. 
If you wanted instead to compute from first principles what those parameters ought to be, you will have to study the importance of the Earth's oblateness, and of the Moon, in a restricted three-body problem.  
