The activity of the Sun increases and decreases in a cycle that lasts approximately 11 years. When the cycle reaches a maximum there are a larger number of sunspots and an increase in solar radiation and charged particles reaching our planet. This can cause the atmosphere of the Earth to expand slightly. A satellite in low Earth orbit experiences a small amount of atmospheric drag despite the low density of air. The exact amount depends on how active the Sun is. Each cycle varies somewhat in duration. A cycle can be as short as 9 years or as long as 14. The average is about 10.7 years. These variations complicate the process of making predictions of future activity which are important for estimating the orbital decay of a satellite.
The magnitude and shape of the peaks in activity is also variable. The maximums in the early 1800s were very small, a time period known as the Dalton minimum. The next figure is a closer look at the Sun’s activity during the space age. The maximum in the late 1950s when Sputnik launched was the largest ever observed. During the Apollo missions the maximum was lower than other recent peaks but greater than the most recent maximum.
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.
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.
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.
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.
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.
In a previous post I described the difficulty in distinguishing multiple CubeSats that are simultaneously deployed from the ISS. In this post I’ll describe how the satellites move away from the International Space Station (ISS) and drift apart from one another.
Below are maps showing the ground track of the small satellites as they orbit 400 km (250 miles) above the Earth. Also shown are the paths they take across the sky as they pass above the K1AD ground station at Ladd Observatory. Traveling at a speed of 27,600 km/h (17,100 mph) it takes only 92 minutes to orbit the Earth. The same 1998-067 object label suffixes are used as in the last post: NZ, PA, PB, and PC. EQUiSat is PA and EnduroSat is NZ. RadSat-g and MemSat failed to transmit signals and so they can’t be distinguished based on radio transmissions. I suspect that RadSat-g corresponds to the leading PC and MemSat is the trailing PB.
The first pair of diagrams shows the distance between the “flock” of satellites and the ISS on July 16th. This was the first day that orbital elements were published for the CubeSats. It took 3 days before they were separated from the ISS by enough distance that their position could be measured. They lead the ISS by about 400 km (250 miles. ) But they are too close together to be distinguished from each other and each individual satellite can not yet be tracked accurately enough for long term predictions. The tracking is good enough to predict passes above a ground station for the next day or so.