Space Technology Special Report - Version B. July 2023 - 10

Satellite Modeling
satellite itself is much colder than the
Sun and emits thermal radiation at
much longer wavelengths, primarily
at wavelengths greater than 2 µm.
Because of this, it is very common
to use thermal coatings that are
strongly wavelength dependent. A
coating with low emissivity at shorter
wavelengths will reduce solar heating,
but if that same coating has higher
emissivity at longer wavelengths, it
will radiate heat more effectively.
The satellite orbit. Defined by the
Figure 2. Imported CAD geometry and the
resultant finite element mesh after some
defeaturing and simplification. (Image:
COMSOL, Inc.)
the thermal contact resistance. The total
resistance can also be a function of
contact pressure, as determined by
the mounting hardware (Figure 2).
The emissivities of all exposed
surfaces. Emissivity (or absorptivity)
is a measure of how well a surface
emits and absorbs thermal radiation.
It can be a function of wavelength,
temperature, and angle of incidence.
The combination of the view factors
and surface emissivities is used to
compute the radiative heat exchange.
There is radiation both on the exterior
Figure 3. A visualization of a satellite in orbit,
showing the position and orientation relative to
the Sun and Earth as well as the irradiation onto
the satellite's exposed faces. (Image: COMSOL,
Inc.; Earth image by Visible Earth and NASA)
surfaces of the satellite and within
the interior. The exterior surfaces also
experience environmental heat loads,
such as the thermal irradiations from
the Sun and Earth. It is particularly
worth understanding the topic of
wavelength-dependent emissivities. The
Sun is the primary source of heating
and the only source of electrical energy,
via solar cells. The light from the Sun
is classified as short-wavelength light,
with peak intensity at the 500-nm
wavelength and with most energy in
the sub-5-µm wavelength range. The
standard Keplerian orbital elements,
the satellite orbit determines how the
satellite travels around the Earth and
when it goes into and out of eclipse.
When the satellite goes into eclipse,
there is no longer any solar irradiation,
which usually leads to significant drops
in temperature on the exterior surfaces.
For thermal modeling purposes, the
orbit itself can typically be treated as
periodic, especially in the context of
small satellites in low Earth orbits.
The satellite orientation. This
information determines which faces see
the Sun, the Earth, or deep space. The
satellite may be pointing in a particular
direction, spinning about its axes, or
even have parts of the structure that
are rotating and moving relative to the
satellite frame. This information affects
the irradiation onto the exposed faces.
The orientation, unlike the orbit, might
not be periodic. For example, a satellite
antenna might be pointed toward a
ground station only every few orbits.
The radiative properties of the
Earth and Sun. The solar flux varies
throughout the year, and this solar flux
is both directly incident on the satellite
and also diffusely reflected from the
Earth. The magnitude of this reflection,
known as the albedo, can vary over
the planet surface. The Earth itself is
also a radiator of infrared light, and
this radiated flux can be a function of
latitude and longitude. Although solar
flux is well known, the albedo and Earth
infrared radiation also vary significantly
over the planet's surface and over time.
The electrical dissipations of the
Figure 4. A simulation application showing the computed temperature variation of a cube satellite.
(Image: COMSOL, Inc.)
10 JULY 2023
components. The solar cells convert
incident light into electrical energy,
SPACE TECHNOLOGY SPECIAL REPORT

Space Technology Special Report - Version B. July 2023

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