# Issue with SMA evolution derived from TLEs

I am experimenting with SGP4 propagator and TLEs of different satellites looking mainly at long term semi-major axis evolution. I have encountered an issue with with the some of the satellites, e.g. 40010. The problem is that the Semi major axis (SMA) seems to fluctuate long term by +/-2 km around a normal negative trend (for satellites without orbit maintenance). So the the TLE derived SMA is sometimes increasing over several months without any apparent reason.

Is this normal for the sort of accuracy the TLE/SGP4 can provide?

Seeing a negative trend in your SMA is not unexpected. Consider the specific mechanical energy, $\epsilon$, of an orbit, given by \begin{equation} \epsilon = -\frac{\mu}{2a} \end{equation} where $\mu$ is the gravitational parameter and $a$ is your SMA. Considering the case of a bird in low Earth orbit (LEO) where you would expect air drag and other perturbations to decrease your orbital energy, we can look at the sign of $d\epsilon/dt$ \begin{equation} \frac{d\epsilon}{dt} = \frac{\mu}{2a^2}\frac{da}{dt} \end{equation} Since $\mu > 0$ and $a > 0$, this relation tells us that a decreasing $da/dt$ indicates a decrease in orbital energy.