This is an interesting question to ask but unfortunately is one with:
a) a complex answer requiring much study to explore the variables and
b) many different regimes according to altitude and the various perturbations that apply
A million years is a long time, perhaps a lot comes down to how much of an orbit disturbance is significant to you over that time. I don't wish to put you off but this could be several weeks study with a good orbit propagator. My first reaction would have been to ask for more information on the candidate orbit you have in mind but, realistically this is not going to help in the millions of years time frame because, I believe, this problem is intractable through integration errors. Consider that each of the disposal zones for satellites (LEO - de-orbit, MEO and GEO to local graveyard) has been the subject of stability assessments, i.e. funded studies, that are specific to the satellites in question even over the much shorter periods of a few tens of decades.
Your three tonne suggestion may have nothing like the very specialised characteristics of the 60cm, highly reflective, low area to mass LAGEOS satellites which are at almost 6000km. Even for these most favourable conditions I'd be surprised if the 8 million year estimate is anything better than an order of magnitude.
Over long periods all sorts of inter-relationships between lunar/solar/Earth precession topics come in to play at different timescales. My hazy recollection is that what might be considered to be a stable orbit over decades might not stay that way over hundreds of years.
Short of that effort, from memory and in the immediate timescale:
- solar radiation pressure begins to dominate over atmospheric drag beyond 1000km - 2000km.
- a tumbling object will behave differently to an inertially stable or Earth pointing mission.
- objects in a high Earth orbit with a large Area to Mass ratio, e.g. extended solar arrays, will adopt an increased eccentricity from solar radiation pressure.
These are plausibly hand-calculation territory for a few years. After that you are going to have to bite the bullet and do some serious simulations yourself and at some point in that process you will have to recognise where the uncertainties dominate over the result.
For the slightly longer term:
- the Sun's effect on the atmosphere can't be relied upon as a constant, consider the Maunder sunspot minimum.
As far as the effects of the environment on the satellite itself it is not unreasonable to expect an increase in thermal absorption from outgassing, atomic oxygen at LEO, UV and micrometeoroids in that order. Whether that is sufficient to cause any structural damage would be down to the details of design.
Still, its an interesting topic, I'd be happy to hear comments and corrections.
