Tag Archives: orbital dynamics

Slicing the network

In a previous post I described an idea on how to triangulate on the orientation of the Brown Space Engineering (BSE) satellite EQUiSat using simultaneous observations from multiple SatNOGS ground stations. We’re running simulation software to model how the antenna beam might be changing orientation as the spacecraft spins. The gyroscope is reporting about 7 degrees per second around one axis. This seems very fast and we’re not sure if the readings are accurate. This initial modeling assumes they are correct.

In the figures below the antenna beam is shown by a torus surrounding the satellite. The pattern is projected to the ground as rainbow colored lines. The red lines are the center of the beam. This does not show how signal strength varies on the surface. We’ll get to that later. It is merely projecting the geometry of a dipole antenna to illustrate where the center of the beam could be and how it might be rotating as the spacecraft spins.

Projection of antenna beam
A projection of the antenna beam to the ground stations at 06:19:20 UTC.

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Close approach

We noticed a signal in a recording of transmissions from EQUiSat that had a very odd Doppler shift. It turned out that there was a second satellite above the horizon at the same time and it was transmitting on a similar frequency. SiriusSat-1 uses 435.57 MHz and EQUiSat uses 435.55 MHz. If the first satellite is Doppler shifted by -10 kHz and the second is +10 kHz the signals will overlap. To understand the potential for interference I examined the orbits of the two.

radio recption
Recording of radio reception on Nov. 2, 2018 from a ground station in Europe. The receiver was tuned to the Doppler shifted signal of SiriusSat-1 but a packet from EQUiSat was also captured. Credit: Cees Bassa / SatNOGS

Both satellites were deployed from the International Space Station (ISS) during the summer. EQUiSat in mid July then SiriusSat-1 and SiriusSat-2 in mid August. Because of the similar deployment the two satellites are in nearly identical orbits. The inclination of the two orbital planes is within a few ten thousandths of a degree.

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Project Space Track

During the early years of the space age techniques were developed to track objects in orbit and predict their future position. The mathematical technique for calculating an orbit is called a Simplified General Perturbations (SGP) model. These models were first used in the 1960s and were refined during the 1970s. This work was done by NORAD – the North American Aerospace Defense Command.

NORAD satellite tracking
“Satellite watchers in the Space Computational Center, NORAD Headquarters, track all the satellites orbiting earth.” Credit: U.S. Information Agency / National Archives, 1982

The computations were performed on large mainframe computer systems that cost several million dollars each. One of these computers was used for ballistic missile warning. A second was dedicated to space surveillance and tracking satellites. A third was available on standby as a backup system in case one of the primary computers failed. The various objects being tracked in air and space were displayed on consoles such as the one shown above.

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Orbital uncertainty

The amount of sunlight that a satellite receives during an orbit is critical to planning operations. In a prior post I examined the changing orientation of the orbital plane with respect to the Sun which is described by the beta angle. In another post I detailed the large uncertainty in tracking CubeSats that are simultaneously deployed. This uncertainty causes difficulty in calculating the beta angle from the early orbital elements and introduces error in predicting the number of hours of sunlight per day. It takes about 40 days for a group of CubeSats to spread apart enough that they can be individually tracked to generate orbital elements that have decent long term accuracy for predicting the beta angle.

One way to generate an early estimate of the beta angle and the amount of sunlight is to use the orbital elements for the International Space Station (ISS) from which the satellites were deployed. All of the CubeSats should have similar orbits that are very close to the ISS. There are some errors in using this method but it can be useful for a short while if care is taken in interpreting the results. This method has the advantage that calculations can be done before deployment.

Percent sunlight for ISS and EQUiSat
Percent sunlight for ISS and EQUiSat.

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Satellite orbital “seasons”

A spacecraft in low Earth orbit will move into the shadow of the planet for some part of each orbit. The amount of time spent in sunlight or shadow depends on how the orbital plane is tilted with respect to the Sun. This tilt is described by a number called the beta angle (represented by the Greek letter β) which changes slowly over time. This is an important consideration for operating a satellite because it determines how much solar energy the spacecraft receives. The blue line in the diagram shows the orbital plane around the Earth edge on with a small tilt with respect to the Sun.

Diagram showing shadow
The tilt of the orbital plane to the Sun determines how much time the satellite spends in the shadow of Earth. Credit: Steven L. Rickman / NASA

Once the orbit of a satellite is well known it is then possible to predict how this angle will change over time. Below is the beta angle for the Brown Space Engineering (BSE) satellite EQUiSat during the first year of the mission.

Beta angle of EQUiSat
The beta angle of EQUiSat during the first year of the mission.

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