The TLEs accuracy for PSLV-C39/IRNSS-1H seems low when compared to that of the other LEO satellites (ISS, HST, Tiangong, Sfera 2, ...). Look, for example, at the following graph that shows the radius vector at perigee:


the perigee for the Tiangong-1 is much smoother (the scale is 24 km for both the objects). Is there some particular reasons for the low accuracy of the PSLV-C39/IRNSS-1H TLEs?

EDIT: The following graph show the same thing, but without linked points: http://cristianopi.altervista.org/IRNSS-1H_TIA1_peri_dot.png

1 point is 1 TLE. Each TLE is propagated (via SGP4) for at most 1 orbit (until I find the smallest radius vector for that TLE).

If I do the same kind of graph for the semi-major axis or for the apogee, the shape is much smoother.

EDIT #2: the next graph shows the apogee (the shape for the sma is the same): http://cristianopi.altervista.org/IRNSS_Apo.png

The graph also shows the interpolating line for the decay rate (9.3 km/day).

The radius vector is calculated with a time step = 10 s.

  • 1
    $\begingroup$ I think the question looks quite good now. Thanks for taking the time to be so quick and responsive! $\endgroup$
    – uhoh
    Commented Dec 15, 2017 at 12:52

2 Answers 2


I'll elaborate on @pericynthion's answer a bit, with regard to what the "noise" may be, and speculate on the cause.

Despite the visual appearance in the question, a plot of apogee is not any smoother than one of perigee. Currently you show one plot with a range of 24 kilometers and the other with a range of 1,000 kilometers. Below, I've plotted the incremental changes from one TLE to the next of the perigee, apogee and average of the two as a proxy for semi-major axis (e.g. apo[1:] - apo[:-1] etc. in Python). It's a little bit like the derivative except I haven't normalized to the uneven time increment from one TLE to the next.

You can see that the semi-major axis more stable than either apo or peri, indicating that much of the "noise" is in the determination of the eccentricity. The third plot is the change in eccentricity.

It's difficult to imagine a physical process that can "tickle" the eccentricity in this particular way, making it sometimes less circular and then more circular immediately afterward. If it were space-plane shaped, perhaps there's a way, but these objects are not space-planes.

Instead, what I believe is happening is that the reentering spacecraft is being observed mostly from a single location on Earth. If you look at the argument of periapsis, it's extremely stable as it should be. So this one location on Earth, wherever it may be, might always be seeing a similar section of the elliptical orbit. Mean motion can be extracted with high precision and independence from the other parameters from timing, but without several samples around the ellipse, the other parameters can have a high degree of correlation. Correlated parameters in fitting limited data can create all kinds of errors and noise.

Incidentally you can see that the change eccentricity of PSLV-C39 has a negative offset, as well as the plot of its perigee but not apogee. This is characteristic of what happens to an eccentric re-entry. At first the drag impulse lowers apogee until the orbit almost circularizes. Then the constant drag lowers the orbit much more quickly, as described in this answer and illustrated in the final figure.

enter image description here

below: Simple simulation of a spacecraft in elliptical orbit with low perigee. The orbit first circularizes, then decays. See this answer for a more thorough discussion.

enter image description here


The perigee altitude for PSLV-C39/IRNSS-1H is very low (< 200 km) in the timespan you selected. This makes it much more sensitive to atmospheric drag than an object at higher altitude. Atmospheric drag is notoriously difficult to predict due to atmospheric density fluctuations and spacecraft attitude variation. Also, the lower altitude means fewer opportunities for radar and visual observations. These factors combine to give inherently noisier ephemerides.


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