Tag Archives: spaceflight

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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Dispersion of CubeSats in a “flock”

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.

Four satellites were released on July 13, 2018 from a device on the ISS called the NanoRacks CubeSat Deployer. They were ejected at about 1.5 m/.s (3 mph.) Initially they were spaced about 10 to 50 cm (4 to 20 inches) apart. They quickly moved ahead of the ISS together in a cluster as the distance between them more gradually increased over time. EQUiSat, the satellite built by Brown Space Engineering (BSE) students, is the second from the right.

Four CubeSats shortly after deployment on July 13th
Four CubeSats shortly after deployment on July 13th. Credit: NASA

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.

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Tracking “flocks” of CubeSats

A satellite built by undergraduate students from Brown Space Engineering (BSE) was launched by NASA and has been operating in low earth orbit since July 2018. Objects in orbit are tracked by the Space Surveillance Network.  Measurements of the position and velocity are made using optical telescopes, radar ranging, and radio reception. This data is then used to calculate the orbit. Once or twice per day a file is published for each tracked object that can be used to predict the motion a day or two in the future.  The file is called a two-line element set (TLE) and contains numbers that describe the elliptical shape of the orbital path and where the object is at a given moment. Here is a sample TLE for the ISS: the International Space Station.

ISS (ZARYA)
1 25544U 98067A   98324.28472222 -.00003657  11563-4  00000+0 0  9996
2 25544 051.5908 168.3788 0125362 086.4185 359.7454 16.05064833    05

Each object is given a unique designation that includes the year and number of launch followed by a letter for each piece that is in a separate orbit. The first module of the ISS (called Zarya, the Russian word for “dawn” or “sunrise”) was the 67th launch of 1998 and is cataloged as 1998-067-A. Any piece that becomes detached, either by accident or intentionally, is given a new designation to independently track it. A tool bag that floated away from an astronaut became known as 1998-067-BL and the BSE satellite named EQUiSat released by the astronauts is designated 1998-067-PA. All of the objects discussed below are considered “loose pieces” of the ISS and I’ll refer to them using just the trailing letter designation.

Doppler shift graph of radio transmissions
Doppler shift measurements of the EQUiSat radio transmissions  made by an amateur radio operator. Each vertical line is a data packet reception and the smooth curve is the best fit of the measurements to the predicted orbit. Credit: cgbsat / SatNOGS

On July 13th EQUiSat was one of four small satellites released from the ISS. The first TLE files were published three days later. There was some early confusion about which TLE corresponded to which satellite. EQUiSat was initially identified as NZ on July 17 but was later found to be better matched to PA on July 22. The remainder of this post is a detailed analysis of the computed orbital elements in the published TLE files.

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