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Amsat-UK's Oscar News, 1996 Jun No.119 p36-41
The Amsat Journal (USA) Vol 19 No.4, Jul/Aug 1996
Amsat-VK Newsletter No. 135/136, 1996 Jul/Aug
Amsat-DL Journal (D), Jg. 23, No. 3, Sep 1996
Jamsat Newsletter (JA) No. 176, 1996 Aug 30

From Hardware to Vapourware

AO-13 Re-Entry Plans


James Miller G3RUH


Without an atmosphere, Oscar-13 would collide with the Earth's crust on 1997 Feb 03. This is due to the pull of the Sun and Moon; the orbit eccentricity is increasing and that reduces perigee height.

But the presence of Earth's atmosphere at perigee robs AO-13 of energy, which is dissipated in the form of heat. This will cause burn-up around mid-December 1996.

End-of-life effects are discernible as a) orbital period decrease and b) changes of attitude, c) heating. The first two are already observable.

Aspects of AO-13's re-entry are explored in these notes. In particular a re-orientation to the unfamiliar attitude Alon/Alat = 90/0 is proposed from mid-August 1996.

This article is in two sections. The second provides a detailed numerical basis for understanding this re-entry scenario.

Section I - An Overview

Orbital Period

This article was written in late May 1996, seven months prior to AO-13's demise. The orbital eccentricity, presently 0.74 continues to increase slowly towards its zenith value of 0.745 in the first week of September 1996. Thereafter drag augments the luni-solar forces, circularising the orbit, with burn-up some three months later.

But even now, if you study the AO-13 keplerian elements and compare mean motion for 1996 January with the mean motion for 1996 April, it's increased from a value of 2.09725 rev/day to 2.09750 rev/day in just three months. This is equivalent to a reduction in period of 80 ms/orbit, and it's already noticeable how badly actual AOS and LOS times compare with predictions if you're using stale keplerian elements. This change in period is caused by atmospheric drag at each perigee encounter.

 Mean motion plot

Figure 1. The predicted values of Mean Motion and other elements are based a model that includes a best estimate of the aerodynamic profile of the satellite. Forces modelled are Earth's gravity up to degree 8, zonal, tesseral and sectoral terms from the GEM10B model, Sun, Moon, drag using US Standard Atmosphere 1976 and solar radiation pressure.

Fine details of orbital period and other keplerian elements for AO-13 have already been published [2,3].

Heating Effects

Heating is not yet observable as of 1996 May. At 300 km altitude it's tiny, just +0.2C extra on the solar panels. The temperature sensor resolution is 0.6C, and radiation from the Earth at perigee warms the panels by about 9C. Both these factors presently swamp any nuances due to friction.

Around 1996 September the solar panels could heat up by an additional +5C at perigee, which will be easy to detect.

Later, in November, heating will become extreme, resulting in spacecraft failure due to damage and/or melting of antennas and solar panels.

Attitude Changes

A more subtle effect is apparent in the spacecraft's attitude. AO-13 is spin stabilised, and should unswervingly point towards the same point in space.

We can measure AO-13's orientation by several different methods. One is based on measuring the off-pointing angle of the S-band antenna using its beacon frequency modulation [4]. By doing this a few times each orbit and for a few orbits, the satellite's orientation can be determined to about 5 degrees precision.

Now, given the satellite's orientation, one can predict the future Sun angle (the angle between Sun and solar panels). We find that predictions and measurements do not agree. They diverge by 0.1°/perigee. (Perigee altitude = 320 km, 1996 May).

The reason for this discrepancy is that the spacecraft's orientation is actually changing. The satellite passes through the upper atmosphere every perigee. AO-13 is not symetric as seen sideways on. The motor sticks out, and picks up an eccentric force Fx which applies a torque (twist) to the satellite, and slews the spin axis up out of the orbit plane 0.1° every pass.  Aero torque

Figure 2. Windage on the motor extension causes AO-13's orientation to change. See text.

Clearly this can only get worse. At some point the attitude will change several degrees each perigee, and eventually precess whole revolutions at a time, effectively leaving a random re-orientation in attitude latitude after each encounter. The will render transponding useless and command very difficult. The best solution is a final re-orientation to ALON/ALAT 90/0, plus a spin- up for additional stability some time from mid August '96 onwards. Sun angle constraints require this be done anyway by 1996 Nov 02.

Section II - The Numbers Game

Environment in Detail

I cannot pretend yet to be an expert in the ballistics of irregular structures travelling at Mach 13 through a near vacuum. My understanding of the kinetic theory of gases, available in any physics text, provides the basis for what follows.

The numbers that characterise the drag problem are so enormous or so microscopic that they're hard to imagine. But with a little normalisation we can render them in familiar terms.

Atmospheric Density

At sea level air weighs 1.2 kg/m3, which is comprehensible enough. The average spacing between molecules is 3.3 nm.

At an altitude of 100 km the mean spacing is 450 nm, about the same as the wavelength of red light or the width of a pit on a Compact Disc.

At 300 km, the atmospheric density is a mere 24 milligrams per cubic kilometre. Even at that low value, the molecules are packed at an average spacing of 13 µm, and you'd count 500x1012 molecules in a cubic metre. The mean free path, or average distance travelled before colliding with another molecule is however 6.6 km!

          Mean Air       Molecular    Mean Free     Kinetic
Altitude  Density         Spacing       Path      Temperature
   km      kg/m3           µm                        K
    0   1.225 x100         0.003     0.13 nm        288
   50   5.821 x10-4        0.04       0.3 mm        272
  100   5.297 x10-7        0.5        0.3  m        204
  150   2.070 x10-9        3           78  m        635
  200   2.789 x10-10       6          580  m        859
  300   2.418 x10-11      13          6.6 km        973
  400   3.725 x10-12      24           43 km        993
  500   6.967 x10-13      41          230 km        997
 1000   3.019 x10-15     250        53000 km       1000
Table 1. Typical properties of Earth's atmosphere. Density above 100 km varies a lot, typically 2:1 to 3:1 either way at 300 km, more at higher altitudes. The collision cross section of a molecule is taken as 3 x 10-19 m2. Data from Wertz [1] appendix L3.


What makes these small densities significant of course, is the colossal speed of the spacecraft. This is typically 8000 m/s, so it collides with a lot of molecules per second, and the resulting drag forces are not insignificant.

In one second, an object of area A moving at speed V ploughs through a volume of A V cubic metres, and if that's full of material at density rho, the object collides with rho A V kilograms of matter per second, at a speed of V. The exchange of momentum decelerates the satellite with a force of order (rho A V) * V. Specifically, F = 1/2 Cd rho A V2 (Newton) where Cd is a dimensionless number typically 1 ~ 2 called the drag factor. It depends on the aerodynamic profile of the object.

Now though density is small that value V2 is a large number, and at 100 km altitude, an object of area 1 m2 experiences a force of order 17 N, equivalent to a weight of 1.7 kg on Earth. Given that AO-13 has a mass of 84 kg, this is a big force, relatively speaking, especially as the perigee encounter lasts a minute or two.

To put these forces into perspective, imagine AO-13 is put into a wind tunnel on Earth. We ask, what air speed is needed to exert the same force as AO-13 experiences in space when travelling at 8000 m/s? See Table 2.

  Perigee    Drag     Air Speed for
  Altitude  Force/g    Equal force
    km        kg           m/s
    50       1900         170
    60       1050         126
    70        286          66
    80         62          31
    90         11          13
   100          1.7       5.1
   150          0.007     0.32
   200          0.001     0.12
Table 2. Shows the ground air speed which exerts the same force on a square metre as AO-13 experiences in space at 8000 m/s at various altitudes. g = 9.81 m/s2. For comparison, the speed of sound at sea level is 340 m/s. Blowing gently onto your hand is 0.3 m/s.


The work done per second by the drag force is given by P = F V , which from the previous section gives P = 1/2 Cd rho A V3 watts. This power is of course expended as heat.

A satellite's chief source of heat is the Sun, which arrives at a power flux of 1358 W/m2. So, to gain some insight as to the scale of additional warming we can compare the frictional heating of a 1 m2 object to the Solar radiation constant.

From another perspective, we can also ask what speed do we have to drag AO- 13 through the air at sea level to expend the same amount of power. See Table 3.

Perigee   Normalised    Speed for
Altitude  frictional   Equal Power
  km       heating         m/s
  70       16532           326
  80        3591           196
  90         640           110
 100         100            59
 110          18            33
 120           4.6          21
 130           1.6          14
 140           0.73         11
 150           0.39          9.4
 200           0.053         4.8
 300           0.005         2.1
Table 3. Shows the heat generated by drag on a 1 m2 object moving at 8000 m/s at various altitudes. This is normalised to 1358 W/m2, the Solar radiation constant. Also shown is the speed at which one expends the same amount of power overcoming drag at sea level. For example, at 100 km altitude a satellite receives 100x more heat than from the Sun alone, equivalent to the power expended towing it through the sea-level atmosphere at 59 m/s (132 mph).

Spacecraft Behaviour


AO-13's normal thermal environment is very benign. It operates at shirt- sleeve temperatures throughout. The solar panels maintain 12C except during eclipses, internal temperatures are typically 15-25C.

But what can we expect to happen when additional frictional heating as per table 3 is apparent?

Of course, things will warm up to a temperature such that they re-radiate the extra heat. This is governed by the Stefan-Boltzmann law which states that the radiated power from a hot body is proportional to the fourth power of the absolute temperature. The constant of proportionality is 5.67 x 10- 8 W/m2/K4

Two items most vulnerable to excess heating are the solar panels and the antenna rods. If either fails, we lose our satellite.

Solar Panels

An AO-13 solar panel has an area of 0.183 m2, and delivers typically 8 watts of electrical power. Since the satellite is spinning, half the time a panel is in darkness, and even when illuminated, sunlight falls at an angle ranging from skimming to perpendicular. In fact the average illumination is 0.31 x Cos (Sun Angle) of the maximum possible. So taking a typical Sun angle of 20°, a panel receives 1358 x 0.31 x Cos(20) = 394 W/m2 of power. A panel is designed to reflect very little incident energy, say 5% (a guess) or 20 W/m2. The panel radiates to space from its outside surface, but receives some radiation from the spacecraft interior. Table 4 shows the full balance sheet:

Contribution                                 W/m2
------------------------------------------  ------
Incident sunlight:  1358 x 0.31 x Cos(20):    394
Reflected sunlight: 5% x 394                  -20
Converted to electricity: 8/0.183             -44
Radiation from interior Ti=20C to panel:       44
Radiation to space, Tp = 12C:                -374
Table 4. Solar panel radiation balance, panel at 12C.

I promise that table 4 was not "fixed". I wrote down the power balance equation and solved it for an unknown panel temperature. It came out as 12C, the same as shows in the spacecraft telemetry. Changing the Sun angle to 0° produces 14.5C, also as telemetered.

Antenna Rods

The 2m hi-gain antenna elements stick out directly from the AO-13 body. So they cannot really "see" the warm spacecraft, only sunlight and space. They are made of thin concave tape, painted matt black. Since they are spinning, they receive only 64% (2/pi) of the maximum available sunlight, and they re-radiate heat from both sides. From this we deduce these elements' temperature is given by the balance of 0.64 x 1358 = 2 x 5.67 x 10-8 x T4 W/m2 and so T = 296K or 23C.

The 70 cm hi-gain antenna elements are are black cylindrical rods mounted on the top face of the satellite, and can see 30% warm structure and 70% space. They too receive 64% of the available sunlight, but re-radiate from pi x more area than is exposed to the Sun. Proceeding in a similar way to the forgoing shows the 70 cm antenna rods to be at 17C.

Frictional Heat

We can now repeat the forgoing exercises with extra heat due to drag. The results are shown in Table 5:

 Perigee     Solar     2m  Hi   70cm Hi  Approx
 Altitude    Panel      Gain     Gain     Date
   km          C         C         C      1996
  300           12        23        17   May 25
  200           14        26        19   Aug 09
  180           16        30        22   Aug 30
  160           21        38        28   Oct 11
  150           27        48        35   Oct 27
  140           37        65        48   Nov 01
  130           62       102        76   Nov 13
  120          119       181       141   Nov 18
  110          249       345       283   Nov 26
  100          511       663       564   Dec 07
   90          969      1214      1055   Dec 11
   80         1638      2014      1770    --
   70         2526      3078      2720    --
   60         3597      4360      3865    --
   50         4219      5105      4531    --
Table 5. Equilibrium temperatures of components on AO-13 due to perigee frictional drag. Solder melts at 200-240C. Aluminium melts at 660C, and boils at 2500C. Spacecraft moving through atmosphere "sideways" on.

So for example, when perigee altitude is 180 km (1996 Aug 30), the solar panels will warm up from 12C to 16C, a rise of +4C which should be detectable in the telemetry. Whether or not the equilibrium temperatures are actually attained depends on the duration of heating power input.

Heating Profile

Perigee heating is short lived. It builds up to a peak, and then falls away in a matter of minutes. So we need to determine this profile to see whether components will reach the equilibrium temperatures predicted in table 5.

To do this one can seed a regular tracking program with the relevant keplerian elements and examine the satellite's speed at (say) 10 second intervals through a perigee encounter. This can be repeated for a selection of perigee heights.

Recalling table 3, we can say that perigee heating begins to be significant, in the sense of potentially damaging, when it exceeds 1 solar constant. That happens when perigee altitude is 135 km (1996 Nov 12) and below, and we can confine our interest to that regime. A typical heating profile is shown in figure 3.


Figure 3. Heating profile for Oscar-13. Vertical axis is logarithmic. Equivalent heating time (Area/Peak) is 100 sec, for perigee altitude less than 130 km. See text.

The total energy expended is given by the area under the power curve, and dividing this by the peak value of the curve gives an equivalent heating time as though the peak were considered rectangular in profile.

This time turns out to be between 90 and 110 seconds, and is essentially independent of perigee altitude. This is a very useful index.

100 seconds is long enough for "flimsy" parts of the spacecraft, such as the 2m hi-gain tape antenna, to reach the equilibrium temperatures detailed in table 5.

Heating Dynamics


I wrote a simulation for the differential equations of temperature for the 2m hi-gain tape antenna. It shows that when exposed to 10 solar constants additional heat flux (1996 Nov 24), the antenna elements reach a steady state of 260C within 25 seconds. If heated by 100 solar constants (perigee altitude ~100 km, 1996 Dec 07) it reaches melting point after only 5 seconds exposure!

The 70cm hi-gain rods are relatively more massive. Simulation shows that exposed to an additional 10 solar constants of heat they reach 170C after 100 seconds. However, exposed to 100 solar constants they melt after 1 minute.

Solar Panels

I do not know the failure mode of solar panels when suddenly exposed to additional heat. Presumably thermal shock will cause cells to crack.

There are six independent panels, connected via diodes to the battery charge regulator. Each panel comprises three arrays, and each array is configured as 3 x 23 cells. A cell is 14.05mm high x 21.65mm wide. The panel voltage is typically 30 - 35 volts.

There is redundancy in this construction, so that single cell failure is not catastrophic. But one suspects that once cells begin to break, a critical number of others will also break within a very short time.

Let us suppose that a temperature rise to 300C breaks the panels. From table 5 this should occur at a perigee altitude of ~105 km, 1996 Nov 29, assuming a sideways presentation to the atmosphere. A "bottom" presentation would obviate this problem.

Attitude Changes

Earlier it was remarked that the attitude direction is no longer stable. This is attributed to aerodynamic forces acting on the motor extension. We see a 0.1°/perigee increase in ALAT, and this increase is cumulative. (Perigee altitude = 320 km, 1996 May). ALAT is the angle that the motor- antenna (spin) axis points up out of the orbit plane. Its nominal value is zero so that the satellite is Earth-centre pointing during the operational part of the orbit.

Whilst, 0.1°/perigee is minor, 1°/perigee would be an embarrassment. We can expect this to happen when perigee altitude is around 200 km, 1996 Aug 09, 3 months before any burn-up effects.

Final Re-orientation

The foregoing thoughts lead to some important conclusions. Towards end of life we should NOT keep AO-13 pointing the conventional way because from some time after mid 1996 August it will be useless as transponder and impossible to command. This is because:

  • ALAT constantly cycling, end-over-end and/or

  • Exposure of the panels and antennas to great heat.

    If we re-orient the satellite to ALON/ALAT=90/0 then the spacecraft presents bottom/motor to the atmosphere. This has the following benefits:

  • Satellite will not re-orient as there are no unbalanced forces.

  • The solar panels will be almost completely protected from direct heating.

  • The top-mounted antennas are sheltered by the spacecraft body. Only the 2m hi-gain is exposed. The 2m omni, 70cm omni, most of the 70cm hi-gain, 23cm helix, and 13cm helix are protected.

  • The 2m and 70cm omnis, which will survive longest, are correctly aligned at apogee and perigee for both transponder use and command/telemetry. The omni antennas can be ON full time.

  • Motor side of the satellite is the most robust. There is a temperature sensor attached to the bottom with which we can conveniently monitor heating, as was done during the original motor burns.  Bar chart

    Figure 4. This bar chart summarises the final months of Oscar-13.


    The predicted tumbling due to aero-pressure was not observed, so the re-orientation to 90/0 was not performed. Heating of the solar panels was clearly seen in the telemetry from 1996 October onwards. The panels failed rapidly, and on 1996 Nov 24 the batteries went flat and telemetry ceased. AO-13 re-entered 1996 Dec 05 as predicted.


    1. Wertz, J.R. (Ed), Spacecraft Attitude Determination and Control, D. Reidel Publishing Company, 1984, ISBN 90-277-1204-2.

    2. J.R.Miller, The Re-Entry of Oscar-13, Proceedings of the 12th annual Amsat Space Symposium, Orlando, Florida, USA, 1994. Also: Oscar News (UK) 1994 Oct No. 109 p 16-20. Also: Jamsat Newsletter (JA) No. 166, 1995 March 25. p1-4. Also: Amsat-DL Journal (D), Jg. 22, No. 1, Mar/May 1995. Also: Amsat OZ Journal (OZ) No. 37, 1995 May. Also: The Amsat Journal (USA) Vol 18 No.3, May/June 1995. WWW includes a listing of the numerical integration.

    3. J.R.Miller, AO-13 Re-Entry Keplerian Elements, Oscar News (UK) 1995 Oct No. 115 p36-37. Also: Satellite Operator (US), 1995 July, p11-12. Elements. General archive.

    4. J.R.Miller, Measure AO-13 Squint Directly!, The Amsat Journal (USA) Vol 16 No. 1, January 1993. Also: Oscar News (UK) 1993 Feb No. 99 p26-28. Also: Amsat-DL Journal (D), Jg. 20, No. 1, March 1993. Also: Amsat-VK Newsletter (VK), No. 94, February 1993.

    Feedback on these pages to Webmaster. Feedback on the article should be sent to James Miller

    Created: 1995 Feb 11 -- Last modified: 2023 Apr 13