More on fireballs/re-entries

Robert H. McNaught, Anglo-Australian Observatory (RMN@aaocbn2.aao.gov.au)
Sun, 14 Jul 1996 14:23:36 +1000 (EST)

>> Whilst solar-system debris can collide with the atmosphere tangentially, this
>> is a relatively rare event and few meteoric fireballs would last more than
>> about 30 seconds.  The vast majority lasting under 10 seconds.

>Don't forget the grazer over North America on August 10, 1972.  It was
>captured on film by a US military satellite and numerous cameras on the
>ground.

Yes, I was aware of that which was why I said "a relatively rare event".  There
was another such event recorded by the European fireball network in the late
'80s and I seem to remember a third recent event but have no details.  "Chant's
procession" or whatever it was called, from Canada to Barbados (or wherever)
may be the first recording of such an event.

Fireballs tangential to the Earth's surface would probably have a perigee
between 50 and 100 km above the Earth's surface (radii 6428 and 6478km).
Below that I would suspect drag would capture the slower fireballs, but if not
they would be objects of large mass and have apparent magnitudes probably well
above -15.

If one imagines an annulus around the Earth of radii r1=6428 to r2=6478 km,
this would represent the target area for such events.  For higher angles of
entry the target area is the circle of radius r1=6428 km.  The ratio of these
areas would give a ball park figure for the occurance of tangential fireballs.

  (pi * r2^2) - (pi * r1^2)       r2^2 - r1^2         r2^2
  -------------------------    =  -----------    =    ----  - 1   = 0.016
         (pi * r1^2)                 r1^2             r1^2

This would suggest that around 1% to 2 % of fireballs would be tangential to
the Earth's surface.  I suspect this simplistic analysis will fail badly due to
not considering the compression of the incoming flux by the Earth's gravity, and
that the tangent point (perigee) occurs on the far side of the Earth from the
incoming direction.  I'll calculate these effects later but I believe the
OBSERVED proportion is somewhat less than this, possibly by over an order of
magnitude.  

I would not be surprised if the frequency of tangential fireballs is of a
similar order of magnitude to re-entries, but there is one important difference.
Satellite re-entries will be in almost circular orbits (e~0.0) whereas meteoric
fireballs are in hyberbolic orbits round the Earth (e>1.0).  For a meteoric
fireball with e=1.0 (limiting case) and a perigee of Hp km, one can calculate
the time the fireball is below a height of say 90km.  Low velocity meteoric
fireballs are not likely to start ablating above this height, whereas with the
continual heating over a long period for a re-entering satellite, it presumably
would.  The outward leg of a tangential fireball would last longer than
the inbound, for three reasons (the first two are really the same);

a) drag slows it
b) drag lowers the trajectory
c) the heated surface will ablate at greater heights than at entry

The table below gives the drag-free duration of the INBOUND leg from a height
of 90km to the perigee heights listed, for a geocentric eccentricity = 1.0.

                     Perigee       Inbound
                    height (km)  duration (secs)
                       40            102
                       50             91
                       60             79
                       70             65
                       80             46
                       85             32

Bearing in mind that meteoric objects reaching as low as 40 km in a tangential
trajactory will be of exceptional brilliance, it would seem that to
discriminate between meteoric fireballs and re-entries one would have to
adopt a duration of around 150 to 200 seconds, so my earlier hand-waving
suggestion of 30 secs is quite inadequate as an absolute criterion, but may be
of practical use.  For faster objects (e>1.0) the times in the above table are
reduced (trajectory less curved and moves along it faster).

This is where I reach my limit, as I don't have any data to hand on re-entry
durations, brightnesses or heights.  Data for Shuttle re-entries will be of
interest, but with deliberate de-orbiting steepening the descent, it is not
directly comparable with a natural decay.

It is interesting to note that the Aug 10, 1972 object is predicted to be
in the vicinity of the Earth again in 1977 with Ceplecha predicting it to
pass within 4 days (+/- 8) of the Earth (around Aug 10).  This time it might
not miss!  It is also interesting to note that such "escaped fireballs" have
their orbits modified to become more similar to the Earth's in terms of
orbital period.  There may thus be a class of asteroid with orbits similar
to each planet but having ablated surfaces.  Perhaps this is a source of
Trojan asteroids and the mysterious asteroid 1991 VG, suspected by some to be
a lost returning satellite.  (Impact debris on the Earth, Moon, Mars, etc
would also tend to follow orbits similar to the impacted object.)

Cheers, Rob McNaught
rmn@aaocbn2.aao.gov.au