# How far in the future can SGP4 make accurate predictions?

I want to find out how long before predictions for a satellites location made using the SGP4 algorithm break down.

For example if I use TLE data from a satellite which was gathered today, how far into the future can I make accurate predictions for that satellites location using that TLE.

The reason I am asking is that TLE data for satellite's are updated irregularly, so I want to have some idea of how long they can be used for predicting the location.

For example if I want to know if any earth observing satellites line of sight passes over my house at exactly 5pm in 7 days time, could I use the SGP4 algorithm to give me a correct result? Or would I need to use a more accurate propagator?

According to the wikipedia page, the error of the SGP4 model is ~1km at epoch and grows at ~1-3km a day. https://en.wikipedia.org/wiki/Simplified_perturbations_models

But I'm wondering what this means for making accurate predictions using this model, is an error of 5-10km much when talking about the area covered by the satellites point of view? (can't remember the name for the area of ground a satellite covers along its path during orbit)

If the satellite is at 150 miles altitude, it can see a spot of radius $\sqrt{4150^2-4000^2}\approx 1105$ miles-draw a right triangle from the center of the earth to the limb of the earth to the satellite. $5-10$ km is trivial compared to that. Even if the satellite insists on being at a $30^\circ$ elevation the radius is $285$ miles. The field of view of the sensor may be much smaller, however. That will depend on the particular satellite.

• Please read the question. Your answer fails to account for satellite movement at all. – Deer Hunter Sep 4 '15 at 7:59
• @DeerHunter: OP specified an accuracy of the prediction. That prediction accounts for the motion of the satellite. The question is how that accuracy compares to what the satellite can see-if being wrong by 5-10 km changes whether the satellite can see his house or not. That is what I answered. – Ross Millikan Sep 4 '15 at 14:41

There is a related question, one answer gives a rule of thumb.

This, present, answer addresses the first part of the question "how far into the future can I make accurate predictions for that satellites location using that TLE" specifically the satellite orbit parameters rather than the consequences for the ground track line of sight etc.

This is a crude assessment, think "system engineer without the budget to pay for an orbit analyst", that attempts to generalise to any orbit of interest.

1. Identify a non manoeuvering object with similar characteristics to the satellite of interest and obtain a short TLE history, or pick a stretch of time between known manoeuvres.

2. From the first TLE, propagate forwards and compare with each of the later TLEs. The difference at each comparison is a proxy for the progressively worsening uncertainty due to propagation.

3. Repeat for several different start points and different objects to obtain an average.

Note that this doesn't account for the inaccuracy of the first TLE, only the degree of worsening through propagation.

Note also that the options to "to use a more accurate propagator" are limited because a TLE gives you "mean" elements whereas other propagators may expect to be fed "osculating" elements. I don't know what would result from trying such a mix though I suspect it may be no improvement or worse than TLE/SGP4 which at least have the advantage of being designed together.