# [amsat-bb] Re: Life Expectancy ARISat-1

Nico Janssen hamsat at xs4all.nl
Sun Aug 7 03:40:08 PDT 2011

```On 2011-08-07 09:34, Phil Karn wrote:
> On 8/6/11 8:55 PM, James wrote:
>>
>> Thank you for your informative contribution..
>>
>> Anyone with a real answer?
>
> Well, an educated guess can be made by looking at a plot of ISS altitude
> vs time:
>
> http://www.heavens-above.com/IssHeight.aspx
>
> 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.
>
> --Phil
>

Actually the TLEs give you the values for the drag (First Time
Derivative of the Mean Motion) and for the ballistic coefficient
(BSTAR drag term). Note that in the TLEs the definition of the
ballistic coefficient is the inverse of Phil's definition, i.e.
the higher the BSTAR value, the higher the drag.

When comparing the latest TLE sets for the ISS and for ARISSat-1,
it appears that the drag for the satellite is roughly twice as
high as for the ISS. But since the values for the drag vary a lot
from one TLE set to the next, it helps to use average values over
a number of TLE sets.

73,
Nico PA0DLO

```