COMSOL 6.2 - Orbit Calculation

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Orbit Calculation

This model is a first introduction to defining and verifying a satellite orbit, and computing the solar, albedo, and Earth infrared thermal loads.

A 1U CubeSat is in a circular orbit at 400 km altitude, inclination of 50°, and longitude of ascending node of 0°. The satellite is rotating slowly about its nadir-pointing axis.

This type of analysis is usually performed prior to computing the temperature evolution within the structure of the satellite. The model Spacecraft Thermal Analysis shows the workflow for computing the satellite temperature on multiple orbit periods.

Model Definition

For the purposes of a quick preliminary computation of the orbital heat loads, it is sufficient to use a geometry that describes the outside envelope of a 1U CubeSat satellite with a protruding sensor. A cube of 10 cm side length is used with a 2 cm radius cylinder protruding 2 cm from the center of one side.

The two-band solar and ambient radiation model is used, with the separation point of 2.5 μm between the spectral bands. The sides of the satellite have solar cells mounted on them, which have high absorptivity in all bands. All other surfaces have the same emissivity of 0.2 in the solar band and 0.85 in the ambient band. For surfaces of a temperature less than 573.15 K (300°C), 99% of all emitted radiation will be in the ambient band, while 97% of the solar and albedo irradiation will be in the solar band.

The solar loads are evaluated at the point where Earth is at perihelion, the winter solstice. The Sun is treated as an infinitely faraway ideal blackbody emitter with fixed intensity of 1414 W/m2 over the entire orbit, as long as the satellite is not in eclipse. The proportion of solar radiation incident onto Earth reflected diffusely back toward the satellite, or albedo, is set to 0.3 everywhere on the planet. Earth is relatively warm compared to background deep space and is modeled as a distributed emitter having a uniform flux of 225 W/m2.

The orientation of the satellite is such that the +Z direction, in the geometry coordinate system, points toward Earth. The satellite is slowly rotating about this primary axis, so the secondary axis can be any vector that is not parallel to nadir, in this case the vector parallel to the velocity direction is used.

Results and Discussion

Figure 1 shows the satellite in orbit around Earth. The yellow arrow represents the Sun vector. The orbit line is colored black or yellow depending on whether the satellite is in eclipse or not. Use this plot to verify that the sensor is facing Earth at all times.

Figure 1: Satellite orbit around Earth after 4165 s¹.

Figure 2 shows the external irradiation and the Sun and nadir vector, respectively, in yellow and blue. Again, the path of the Sun vector around the satellite is colored black or yellow depending on whether the satellite is in eclipse or not. Observe the partial shading around the sensor.

Figure 2: External irradiation after 3165 s.

Figure 3 shows the external irradiation over time. When the satellite is in eclipse, the irradiation is only due to Earth’s infrared flux.

Figure 3: External irradiation over time.

The average of the total environmental irradiation over the entire orbit is 20.5 W. This satellite has very few exterior surfaces that shadow and face each other. That is, its exterior is very nearly convex, so the total environmental loads are reasonably well estimated from the irradiation.

Heat_Transfer_Module/Orbital_Thermal_Loads/orbit_calculation

Modeling Instructions

From the menu, choose .

In the window, click

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In the window, click

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In the tree, select .

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In the tree, select .

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In the toolbar, click

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In the window for , locate the section.

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In the text field, type 10[cm].

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In the text field, type 10[cm].

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In the text field, type 10[cm].

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Locate the section. From the list, choose .

Cylinder 1 (cyl1)

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In the toolbar, click

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In the window for , locate the section.

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In the text field, type 2[cm].

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In the text field, type 2[cm].

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Locate the section. In the text field, type 5[cm].

Cylinder 2 (cyl2)

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In the toolbar, click

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In the window for , locate the section.

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In the text field, type 1.8[cm].

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In the text field, type 3[cm].

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Locate the section. In the text field, type 4.5[cm].

Partition Domains 1 (pard1)

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In the toolbar, click

and choose .

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On the object , select Domain 1 only.

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In the window for , locate the section.

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From the list, choose .

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On the object , select Boundary 4 only.

Difference 1 (dif1)

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In the toolbar, click

and choose .

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Select the objects and only.

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In the window for , locate the section.

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Click to select the

toggle button for .

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Select the object only.

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Clear the check box.

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Orbital Thermal Loads (otl)

Sun Properties 1

By default, the Sun vector and solar flux are set to correspond to the winter solstice.

Planet Properties 1

The Earth properties are used to define the planet.

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In the window, click .

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In the window for , locate the section.

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From the list, choose .

The proportion of solar radiation incident onto Earth reflected diffusely back toward the satellite, or albedo, is set to 0.3 everywhere on the planet.

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In the α0,λ text field, type 0.3.

Earth is relatively warm compared to background deep space and is modeled as a distributed emitter having a uniform flux of 225 W/m^2.

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From the list, choose .

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In the table, enter the following settings:


Spectral band	Planet radiative flux (W/m^2)
Ambient: [2.5[um], +infinity[	225[W/m^2]

Orbital Parameters 1

A circular orbit is defined at 400 km altitude, inclination of 50°, and longitude of ascending node of 0°.

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In the window, click .

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In the window for , locate the section.

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From the list, choose .

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In the R text field, type otl.R_planet+400[km].

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In the i text field, type 50[deg].

Spacecraft Axes 1

By default, the axes of the satellite are defined such that the +Z direction, in the geometry coordinate system, is the primary axis and the +X direction is the secondary axis.

Spacecraft Orientation 1

The orientation of the satellite is such that the primary direction points toward Earth. The satellite is slowly rotating about its primary axis, so the secondary axis can be any vector that is not parallel to nadir. In this case the default setting, of the +X direction corresponding to the direction of travel, is used.

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In the window, click .

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In the window for , locate the section.

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Find the subsection. From the list, choose .

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In the ω text field, type 2*360[deg]/otl.T_orbit.

Diffuse Surface 1

Now, define the radiative properties of the different boundaries.

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In the window, click .

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In the window for , locate the section.

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From the ε list, choose .

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In the table, enter the following settings:


Spectral band	Emissivity (1)
Solar: [0, 2.5[um][	0.2
Ambient: [2.5[um], +infinity[	0.85

Diffuse Surface 2

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In the toolbar, click

and choose .

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In the window for , locate the section.

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In the dialog box, type 1 2 5 20 in the text field.

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In the window for , locate the section.

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From the ε list, choose .

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In the table, enter the following settings:


Spectral band	Emissivity (1)
Solar: [0, 2.5[um][	0.99
Ambient: [2.5[um], +infinity[	0.95

In the toolbar, click

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Orbit Visualization (otl)

This default plot is used to check that the orbit parameters, orientation, and events are correctly defined. Since neither the study nor the plot is computationally expensive, it is possible to adjust the model parameters and rerun the study to see the results very quickly.

Add an evaluation group to verify that the configuration is correct by extracting some orbit data.

Orbit Variables

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In the toolbar, click

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In the window for , type Orbit Variables in the text field.

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Locate the section. From the list, choose .

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Locate the section. Select the check box.

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Click to expand the section. From the list, choose .

Global Evaluation 1

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Right-click and choose .

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In the window for , locate the section.

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In the table, enter the following settings:


Expression	Unit	Description
otl.t_inEclipse	s	Beginning of eclipse
otl.t_outEclipse	s	End of eclipse
otl.T_orbit	s	Orbit period

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In the toolbar, click

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Once the orbit configuration is correct, an Orbit Thermal Loads study can be added to estimate the external irradiation on the satellite boundaries.

An integration operator is added to integrate the external irradiation over the spacecraft boundaries.

Integration 1 (intop1)

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In the toolbar, click

and choose .

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In the window for , locate the section.

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From the list, choose .

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From the list, choose .

Since this model is only used to evaluate irradiation, a quite coarse mesh is sufficient.

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In the window, under click .

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In the window for , locate the section.

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From the list, choose .

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In the toolbar, click

to open the window.

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Go to the window.

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Find the subsection. In the tree, select .

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Right-click and choose .

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In the toolbar, click

to close the window.

Step 1: Orbit Thermal Loads

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In the window for , locate the section.

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In the text field, type range(0,0.005,1).

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In the toolbar, click

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External Irradiation (otl)

This plot is used to show the external irradiation over time. The blue arrow shows the nadir direction and the yellow arrow shows the Sun direction.

Set the Line type to Tube to show the path of the Sun around the spacecraft.

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In the window, expand the node, then click .

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In the window for , locate the section.

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Find the subsection. From the list, choose .

Add velocity following plot to visualize the position of the satellite above Earth and the Sun vector.

Add Predefined Plot

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In the toolbar, click

and choose .

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Go to the window.

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In the tree, select .

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Click in the window toolbar.

Trajectory Following Visualization (otl)

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In the window for , locate the section.

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From the list, choose .

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In the toolbar, click

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Plot the evolution of the external irradiation on the satellite boundaries over time (Figure 3).

External Irradiation Over Time

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In the toolbar, click

and choose .

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In the window for , locate the section.

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From the list, choose .

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In the text field, type External Irradiation Over Time.

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Right-click and choose .

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In the window for , locate the section.

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In the table, enter the following settings:


Expression	Unit	Description
intop1(otl.Gext1+otl.Gext2)	W	External irradiation

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Click to expand the section. Clear the check box.

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In the toolbar, click

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Finally, add an evaluation to get the average of the total environmental irradiation over the entire orbit.

Surface Average 1

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In the window, right-click and choose .

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In the window for , locate the section.

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From the list, choose .

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From the list, choose .

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Locate the section. From the list, choose .

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Locate the section. In the table, enter the following settings:


Expression	Unit	Description
timeavg(0,otl.T_orbit,intop1(otl.Gext1+otl.Gext2),'nointerp')	W	Orbit-averaged irradiation

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In the toolbar, click

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NASA Goddard Space Flight Center Image by Reto Stöckli (land surface, shallow water, clouds). Enhancements by Robert Simmon (ocean color, compositing, 3D globes, animation). Data and technical support: MODIS Land Group; MODIS Science Data Support Team; MODIS Atmosphere Group; MODIS Ocean Group Additional data: USGS EROS Data Center (topography); USGS Terrestrial Remote Sensing Flagstaff Field Center (Antarctica); Defense Meteorological Satellite Program (city lights).