46th International Conference on Environmental Systems
10-14 July 2016, Vienna, Austria
ICES-2016- 249
Mercury Retro-Reflection - Modelling and Effects on MPO
Solar Array
Anja Frey1, Giulio Tonellotto2 and Daniele Stramaccioni 3
ESA ESTEC, 2201 AZ Noordwijk, Netherlands
BepiColombo is Europe's first mission to Mercury and it is developed in between ESA and JAXA. It will set
off in 2018 on a seven years journey to the smallest and one of the least explored terrestrial planet in our
Solar System.
Mercury’s surface is covered with regolith, which reflects the incident sun light preferably in the direction of
the Sun, causing the so called retro-reflection effect. While this effect can be considered negligible for
BepiColombo main spacecraft body, covered by high efficiency MLI, it might have an influence on the
temperature of the Solar Array (SA) of the BepiColombo Mercury Planetary Orbiter (MPO). The MPO SA is
continuously steered during orbit, in order to optimize its Sun aspect angle (maximum Sun power) without
exceeding its design temperature limits. The MPO SA steering profiles will be uploaded regularly during the
mission.
The commonly used thermal analysis Software’s tools allow modeling the Bond Albedo (diffusive), but do not
permit the implementation of the very specific retro-reflection effect. Therefore it has been decided to use an
already existing Mathcad tool, able to estimate planet heat fluxes, and to adapt it for the retro-reflection
simulation. This in-house tool is called Merflux and was previously developed by ESTEC’s D. Stramaccioni.
This paper presents the different albedo modelling options implemented, ranging from fully diffusive albedo
to full retro-reflection albedo. An intermediate case, called “directional reflection”, has been considered the
most realistic approach, based on findings in literature: sunlight is reflected back in all directions but with a
higher concentration into the direction of the Sun.
The results of an extensive sensitivity study, based on a very simplified 2-nodes model of the SA panel wings,
are presented. Conclusions are drawn about the impact of the directional albedo reflection along the orbit
and, in particular, in the proximity of the subsolar point. Finally, the feedback from the albedo “directional
reflection” study into the BepiColombo SA steering models definition and in orbit calibration is discussed.
Nomenclature
A
=
a
=
C1, C2, C3=
S
=
SC
=
T
area
albedo coefficient
factors to account for angles
surface
solar constant
I. Introduction
HIS paper presents the results of a study about the effect of retro-reflection on the temperature of the
BepiColombo MPO (Mercury Planetary Orbiter) Solar Panels. The objective of this activity is to adapt the
Merflux worksheet to account for retro-reflection in the albedo calculation. The results are then used to determine
the impact on the predicted solar panel temperature.
A. Activity Background
BepiColombo mission to Mercury is the ESA's Fifth Cornerstone Mission, and a joint mission between ESA
1
German Trainee, Thermal Division, Keplerlaan 1, 2200 AG Noordwijk, The Netherlands.
Thermal Engineer, Thermal Division, Keplerlaan 1, 2200 AG Noordwijk, The Netherlands.
3
MPO Module Manager, Bepi Colombo Project, Keplerlaan 1, 2200 AG Noordwijk, The Netherlands.
2
and the Japan Aerospace Exploration Agency (JAXA), executed under ESA leadership. The mission includes two
science elements, that are the Mercury Planetary Orbiter (MPO) and the Mercury Magnetospheric Orbiter (MMO).
The whole Spacecraft stack, called Mercury Composite Spacecraft (MCS), is composed of the MMO and MPO and
in addition by the MOSIF Sun Shield (Magnetospheric Orbiter Sunshade and Interface), and the MTM (Mercury
Transfer Module), as shown in Figure 1.
Figure 1: BepiColombo Spacecraft stack (MCS) modules composition
The MOSIF provides a sun-shield for the MMO to be protected from the strong Sun illumination until MMO
separation. The MTM is the electrical propulsion module utilized during the interplanetary cruise. ESA provides
MOSIF, MPO, MTM and the launch with Ariane 5. JAXA (Japan Aerospace Exploration Agency) provides the
MMO.
The MPO (shown in Figure 2) will study the surface and internal composition of the planet, and the MMO will study
Mercury's magnetosphere, that is, the region of space around the planet that is influenced by its magnetic field.
Figure 2: BepiColombo MPO with Solar Array (SA)
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BepiColombo Spacecraft is facing a very harsh thermal environment in orbit around Mercury. The proximity to
the Sun results in a solar irradiance ranging from 14,448 W⋅m-2 (at Mercury perihelion) to 6,272 W⋅m-2 (at Mercury
aphelion). Additionally, Mercury rotates around its axis only three times in two Mercury years. In combination with
the non-existent atmosphere these factors are responsible for temperatures swinging between 90 K and 725 K on its
surface.
Figure 3: BepiColombo MPO and MMO in their operational orbit (not in scale)
BepiColombo will experience very high heat fluxes during the Sun illuminated part of the orbit, in particular
when passing over Mercury’s sub-solar point. Therefore the solar panel has to be steered constantly in order to
maintain the temperature under a certain limit while providing as much power to the spacecraft as possible. The
solar panel attitude is controlled with the use of a simplified algorithm which predicts the solar panel temperature.
This algorithm currently takes into account a bond albedo of 0.12.
However, observations of the lunar surface indicate that the regolith reflects the sunlight directionally. This
means there is a peak in the reflected sunlight in the direction of the source (the Sun). With Mercury’s surface
expected to be similar to the lunar surface, this effect may also occur at Mercury. While the change in albedo flux is
considered negligible for the MPO body, covered by high efficiency MLI, it may have a significant impact on the
solar panel temperature and therefore on the steering algorithm.
While this work focuses mainly on Mercury, as it was conducted for BepiColombo, the findings are also relevant
for other bodies in the solar system which are covered with regolith and do not have a significant atmosphere [1]
such as the Moon. Many of the icy satellites of the outer Solar System show an opposition surge (a brightening of
the body’s surface when observed from directly behind the Sun) [2]. Opposition effects were found on asteroids and
meteorites and atmosphereless bodies [3]. A narrow brightness opposition spike can also be found on Saturn’s rings
[4].
B. Environmental Specification
The Mercury Environmental Specification [5] provides data about the planet Mercury and its environment for
use in the development of the BepiColombo mission. The document specifies the Mercury orbital parameters,
physical properties, and thermal environment. It provides two values for the Mercury albedo coefficient: 0.119 for
the bond albedo (the fraction of incident solar energy that is reflected back to space by a spherical body over all
wavelengths) and 0.138 for the visual geometric albedo (fraction of incident solar energy that is reflected back by a
planet into the direction of the Sun).
The higher geometric albedo means that considerably more incident solar energy is reflected back into the
direction of the Sun than the other directions.
In the quoted book [6], the albedo values are derived from a comparison to the Moon albedo. Both celestial
bodies are covered with regolith and therefore their reflectivity is assumed to be similar. The authors find that while
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both albedos preferably reflect the sunlight back in the direction of the Sun, this effect is more distinct in Mercury
than the Moon.
C. Merflux Programme
In order to get a simple and quick assessment of the heat fluxes experienced by a spacecraft in orbit around
Mercury, the Mathcad sheet Mercury Orbital Heat Fluxes Assessment (Merflux) was developed by D. Stramaccioni
and verified against standard thermal software [7].
As described above, the Mercury surface temperature varies significantly from the dark side to the sub-solar point.
This is taken into account in the Merflux programme by subdividing the planet into a grid and replacing the
spherical portions of the planet by flat facets. Then, each grid element is assigned a temperature Tgrid. The albedo
flux is calculated using the same meshing of the planet surface.
II. Albedo Modelling
Three different albedo modelling approaches were studied:
1) Diffusive Model:
- Incident flux is reflected diffusively in all directions
- The spatial distribution is even in all directions
2) Retro-reflection Model:
- The solar flux is reflected back into the direction of the Sun only
- The reflection resembles that of a flat mirror
3) Directional Reflection Model:
- Compromise between diffusive and retro-reflection
- Light is primarily reflected into one direction while some of it is still reflected diffusively
The different albedo modelling approaches are explained in more detail in the following sections. They were
combined with three sets of SA thermo-optical properties (front and back), and were studied both for fixed solar
aspect angles (90deg, 78deg and 65deg, where 0deg is Sun prepndicular to SA) and for two realistic steering profiles
(one for perihelion and one for aphelion) provided by ESOC (European Space Operations Centre). The results
reported within this paper only cover the steering profiles cases and are less conservative and more realistic.
A. Retro-Reflection Model
The first approach was to model the albedo with only retro-reflection. This means that all the incident radiation
coming from the Sun is fully reflected back in the same direction. The model is implemented similar to the eclipse
calculation in the Merflux programme. This approach is very conservative, and as such is applied only for an
extreme worst case analysis.
B. Directional Reflection Model
A compromise between the diffusive and the retro-reflection is the directional reflection. Here, the light is
primarily reflected into one direction while some of it is still reflected diffusively. The model used for the analysis is
derived from the model for directional emissivity in the IR flux section of the Merflux sheet.
Instead of diffusive reflectivity (comparable to the blackbody emissivity), the reflected radiation is concentrated
into one direction. The distribution of the radiation in space is in the same form as the directional IR emission:
(1)
with the geometric albedo aretro, and the exponent αn.
calculated:
The corresponding hemispherical albedo can be
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(2)
Figure 4: Sketch of directional reflection.
From the environmental specification it is known that the hemispherical albedo should be 0.12, while the
geometric albedo is 0.138. This yields an exponent αn of 0.3.
In this case, the peak of reflected radiation is not directed normal to the surface but in the direction of the Sun.
Therefore, the distribution is rotated to point towards the Sun. Every grid facet on the sun-illuminated side of the
planet is assumed to reflect the incident radiation with the above described distribution, as it is schemately indicated
in Figure 4.
The reflected radiation is then summed over the sunlit half of the planet:
(3)
Here, the solar constant SC at 1AU (Astronomical Unit) is multiplied by factor n to obtain the total Sun
irradiance at the actual distance from the Sun; this is further multiplied by the geometric albedo aretro and by the
factor C1αn, which accounts for the drop-shaped distribution shown in Figure 4. Note that 1SC is equal to 1366
W/m2 in average, however within BepiColombo project we use 1370 W/m2, that should include all the variations of
the Sun irradiance at 1 AU.
The angle between the reflection direction and spacecraft position is taken into consideration with the factor C14:
4
Bold characters are used in the formulae to denote vector entities and dots denote inner product between vectors.
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where
(4)
with the unit vector from the centre of the planet pointing to the Sun sun, position vector OS, planet mean radius
Rgrid, and angular extension of the grid latitude bands ∆η.
The angle between the normal of the spacecraft surface nk and the location of the facet with the angle C2:
(5)
C3 represents the angle between the sun incident flux and the vector normal to the grid facets NP:
(6)
III. Heat Flux
The above models were implemented into Merflux which was used to determine the incident environmental
fluxes. A reference orbit with a periapsis altitude of 400 km and apoapsis of 1508 km with an inclination of 90° was
chosen. The spacecraft is nadir-pointing. For the following calculations we have assumed a cube of unity area and
black surfaces, therefore all the numerical results are equivalent to W/m2, i.e. fluxes. The surfaces A1 to A6 are
oriented as per Figure 5 (1=Anti-Velocity; 2=Normal to Orbit; 3=Nadir; 4=Velocity; 5=Normal to Orbit; 6=Zenith).
Figure 5: Cube surfaces orientation
First analyses gave the results presented in the left plot of Figure 6 for the diffusive reflection case. The nadir
pointing surface A3 receives the highest flux of 610 W; the other surfaces experience fluxes around 100 W. The
peak for the orbit-normal surfaces A2 and A5 occurs right over the sub-solar point. The anti-velocity pointing
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surface A1 sees this peak later, and the velocity pointing surface A5 accordingly a little earlier. The directional
reflection model was assessed for the reference case, as shown in the right plot of Figure 6. The peak heat flux of
1300 W is higher than in the diffusive case.
QAi=albedo heat flux on face “i” (i=1, …, 6)  1=Anti-Velocity; 2=Normal to Orbit; 3=Nadir; 4=Velocity; 5=Normal to Orbit; 6=Zenith;
Figure 6: Diffusive (left plot) and directional (right plot) albedo flux for nadir pointing case.
For comparison, the solar and Mercury IR flux are plotted in Figure 7. It shows that the albedo flux is the
smallest of the three, but it is not negligible.
QSi=solar heat flux on face “i” (i=1, …, 6)  1=Anti-Velocity; 2=Normal to Orbit; 3=Nadir; 4=Velocity; 5=Normal to Orbit; 6=Zenith;
QIRi=planet heat flux on face “i” (i=1, …, 4)  1=Anti-Velocity; 2=Normal to Orbit; 3=Nadir; 4=Velocity;
Figure 7: Solar and Planet IR flux for reference case
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In order to get a more realistic case, focused on MPO solar array, a steering profile SAA (Sun Aspect Angle) was
supplied by the European Space Operations Centre (ESOC). The solar panels will be constantly steered in order to
ensure maximum power while remaining under 175° C. The two examples for Mercury true anomaly 0° (Perihelion)
and 180° (Aphelion) are shown in Figure 8. The solar array is steered so that the solar aspect angle varies between
72° and 83° in the perihelion, and 52° and 71° in the aphelion case, where SAA=0° means Sun perpendicular to the
SA (Solar Array).
Figure 8: SA steering profile (SAA)
This steering profile is reflected in the fluxes of Figure 9 which shows the solar flux received by the solar panels at
perihelion. It can be clearly seen that the flux follows the steering profile. The larger the solar aspect angle, the
lower the solar flux received by the solar panel. The values for this case vary between 4321 W/m2 and 1784 W/m2.
Figure 9: Solar flux on solar panel SAA steering profile
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Concerning the Planet IR heat flux, in the described case, the back of the panel sees a higher IR flux with a
maximum of 3092 W/m2. The highest peak of IR flux on the front side is 2595 W/m2 (Figure 10).
QIRi= planet IR heat flux on face “i” (i=3 or 6)  3=SA front; 6=SA back;
Figure 10: Planet IR flux on solar panel SAA steering profile
Similar to the IR flux, the back of the solar array sees more albedo flux than the front, as shown in Figure 11. In the
diffusive case the maximum flux on the back is 421 W/m2, on the front it is 354 W/m2. In the directional case, this
difference is even bigger: the maximum flux on the panel’s back side is 597 W/m2, on the front 370 W/m2.
QAi=albedo heat flux on face “i” (i=3 or 6)  3=SA front; 6=SA back;
Figure 11: Diffusive (left plot) and directional (right) albedo flux on solar panel with SAA steering profile.
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IV. Solar Panel Thermal Analysis
The results from this analysis were further exploited to estimate their impact on the solar panel temperature. For
this purpose, a simple thermal model of the BepiColombo solar panel was created. It consists of two nodes; one for
the front side, one for the back. It represents one of the three panels of the whole SA.
The front of the solar panel is covered with a mix of optical solar reflector (OSR) and solar cells which reduces
the influence of the solar flux and hence increases the relative influence of the different albedo fluxes. The
percentage of OSR varies between the different SA panels. It is highest for the innermost panel.
The back is also covered with OSR in the case of the inner panel. The outermost panels have the back side bare,
so the CFC is exposed directly to the environment.
The actual BepiColombo solar panel will be steered continuously in order to keep its temperature as close as
possible to its design limit. It will therefore be in a quasi steady-state situation with a nearly constant temperature.
Additionally, thanks to their low mass per unit surface, the panel temperature generally reacts quickly to heat
changes. In order to approach this in a simplified manner the thermal inertia of the solar panel was set to zero in the
investigated cases. This supplies instant steady state results. Test cases, where a temperature dependent thermal
inertia is considered, showed small temperature differences with respect to the null inertia cases. Therefore, a worstcase approach was chosen and only results for null inertia will be presented in this paper.
A realistic case is presented in Figure 12, by considering the steering profile of the SA SAA reported in Figure 8.
The left plot of Figure 12 shows the temperature of the outer panel over one orbit by assuming the steering profile
provided by ESOC for Perihelion; the right plot shows the difference in temperature between the two albedo models.
The directional model predicts higher temperatures around the sub-solar point at 4185s (true anomaly of 180°),
while the temperatures are lower closer to the poles. The diffusive reflection produces up to 5.2°C higher
temperatures around true anomalies of 100° and 240°, while the directional reflection increases the solar panel
temperature by 7.6°C near the sub-solar point. These ∆T are local peaks with limited time duration and not
applicable to the whole orbit.
Figure 12: Temperature of outer panel with ESOC SAA profile at perihelion
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Similar results are found when applying the same analysis case to the inner panel. The temperature is overall
lower for this case, as to be expected considering that the front side of the inner panel is covered with more OSR
than the outer panels and its back side is also covered in OSR (Figure 13). In reality, the inner panel is the hottest,
due to the effect of the Spacecraft body (view factors and reflections from MLI) not modelled in this study. The
behavior remains similar to the one of the outermost panels, with higher temperature for diffusive albedo near the
poles, and for directional albedo near the sub-solar point; the ∆T between the diffusive and directional model is in
the range +3.4°/-3.4°C.
Figure 13: Temperature of inner panel with ESOC SAA profile at perihelion
Due to the simplicity of the thermal model used in this study, the absolute temperatures along the orbit are
varying much more than they do for the detailed model: this is explained by the fact that the steering profile is
optimized to keep the maximum local temperatures of the detailed model stable. It is not tuned to the temperature of
the simplified model which has one single node for the front face. A comparison of identical diffusive albedo cases
showed that the sensitivity of the detailed model used in Industry and the simple model used in this study are very
similar (less than 5% difference in the maximum delta-temperature along the orbit for the average front and back
temperature along the panels). This validates the simplified model for this kind of sensitity analyses, that is the
scope of the study.
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Results for SA steering profile (provided by ESOC) at aphelion were also obtained for the outer and the inner
panel. The outer panels experience ∆T between the albedo models of +7.3°/-2.8°C (Figure 14), while the inner panel
sees +5.6°/-2.3°C (Figure 15). Again, the directional reflection causes higher temperatures around the sub-solar
point and lower temperatures nearer to the poles.
Figure 14: Temperature of outer panel with ESOC SAA profile at aphelion
Figure 15: Temperature of inner panel with ESOC SAA profile at aphelion
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V. Conclusion
A simplified model of the Mercury albedo was proposed and was used to calculate the environmental heat fluxes
in orbit around Mercury. The impact on the MPO solar array temperatures has been studied for perihelion and
aphelion orbits. The albedo directional reflection modelling approach is considered the most realistic. It is modelled
as diffused reflection with a much higher energy concentration around the direction of retro-reflection (i.e. direction
of the Sun).
It can be noted that the Albedo modelling has a non-negligible influence on the solar array temperatures because
the solar arrays’ thermal time constant is low and they react rapidly to variations of the heat loads. The realistic
steering profile case showed that the solar array front side worst ∆T during orbit is less than +7.6°/-5.2°C for the
outermost panels and less than +5.6°/-3.4°C for the innermost panel. The driver for the MPO SAA profile definition
is the innermost panel, which is the hottest. The worst ∆T are local peaks of limited time duration and they are not
applicable to the whole orbit: the directional albedo provides the highest temperatures only around the sub-solar
point. There are parts of the orbit where the diffusive albedo approach is conservative and in those areas the industry
models are therefore safe for hot temperatures. On the other hand, the steering profile might not be optimized at
best, which causes reduced power generation. For a set of intermediate Mercury true anomalies, in between the
analysed perihelion and aphelion seasons, the complete Spacecraft orbit is expected to benefit of the retro-reflection
effect, by experiencing lower heat fluxes on the solar array (i.e. while moving away from the subsolar point the
MPO orbit will exit the “cylinder” with higher abedo). As this study was focused on worst cases, these intermediate
seasons have not been analysed. The results presented are preliminary estimations based on simplified models of
planet and solar array (e.g. 2 nodes for one solar array panel), and averaged optical properties. The directional
albedo modelling approach for Mercury has not been consolidated against measurements. The worst cases occur in
solar panels with bare CFC on the backside (outermost panels) and are usually more pronounced in cases with
bigger solar aspect angles (i.e. little Sun irradiance incident on SA).
Acknowledgements
The authors would like to thank the colleagues from ESA/ESOC and Airbus for the support in the definition of
representative analysis cases and in the verification of the results.
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