from From: Phil Karn
Well, an educated guess can be made by looking at a plot of ISS altitude
The ISS is periodically reboosted, accounting for the sudden jumps in
this sawtooth-like graph. Obviously ARISSat-1 won’t be reboosted, so if
you extrapolate the downward-sloping parts of the graph you can get a
rough idea of what will happen.
The ISS orbital decay rate varies with changes in upper atmospheric
density with solar activity, but also because of changes in its attitude
and the operation of the solar panels.
The orbital decay rate also depends on qthe ballistic coefficient of the
object. This has units of mass divided by area — the mass of the object
divided by the cross-sectional area it presents in its direction of
flight. The larger the ballistic coefficient, the less its deceleration
from drag as it flies through the thin upper atmosphere.
The ISS probably has a larger ballistic coefficient than any other
satellite simply because it’s so huge. The volume of most objects
increases as the cube of the size while the cross-sectional area
increases with the square. Since mass is usually a function of volume, a
large object will generally have a higher ballistic coefficient and last
longer in a given orbit than a small object.
Obviously there are exceptions to the “large lives longer” rule such as
the “Echo” balloons. The actual ballistic coefficient for any given
satellite has to be computed from its actual mass and dimensions and its
orientation relative to its velocity vector. The ISS is a huge
satellite, but it also has lightweight solar wings that greatly increase
its cross-sectional area without increasing its mass very much, so they
decrease its ballistic coefficient somewhat.
ARISSat-1 is far smaller than the ISS, but it is fairly heavy for its
size and it lacks large solar wings that create a lot of drag. This will
reduce its decay rate, but it will still probably decay more quickly
than the ISS.
It was tossed out the back of the ISS against the velocity vector, and
that immediately put it in a lower energy orbit with a higher mean
motion. But any further increase in mean motion will be due to orbital
decay, and from that we should be able to estimate its ballistic
coefficient and how it will likely behave in the future. Determining an
exact lifetime would be difficult because of the difficulty of
predicting solar activity, but a good estimate can probably be made.