Observations on the AO-40 Orbit
Howard Long G6LVB
7 October 2002
Note: Originally published in Oscar News, and part-published in the AMSAT Journal
1.
Introduction
Since the launch of AO-40, and the final firings of both the 400N motor and the ATOS, AO-40 has provided many operators (this one included) with their first real DX opportunities. With this in mind, the author has often wondered why there are periods of excellent conditions followed by other periods of sub optimum operation.
For example, over the past few months, AO-40 has gone through some extended periods where the high gain antennas have not been pointing toward the Earth at apogee, making two-way transponder communication difficult if not impossible. With this in mind, the author spent some time analysing both this and other observations of AO-40’s behaviour. The purpose of this document is to describe both why these situations exist, and what can be expected in the future.
This article won’t be going into the mathematics of orbital mechanics, but some of the concepts will be described using diagrams. All of the background of this article is based on practical observation and trends in data generated by prediction programs.
The reader will need to be able to comprehend common AO-40 operating terms such as squint angle and ALON/ALAT. These terms are described in the excellent AO-40 mini-glossary at http://www.amsat-dl.org/journal/adlj40ge.htm.
Several tools were used to examine the data including Nova, InstantTrack, SQL Server, and Excel.
The predictions assume that there will be no additional solar panel deployment or 3-axis stabilisation on AO-40.
The four observations investigated in this document are:
· Short term repeating conditions – AO-40 and déjà vu
· Why AO-40 needs a regular attitude adjustment
· Is AO-40 always a night owl?
· I’m sure I used to get longer pass durations and higher elevations
2.
Short
term repeating conditions – AO-40 & déjà vu
The period of AO-40’s orbit is about 19 hours 6.5 minutes (see figure 1). This can be calculated either from prediction data by locating the times of consecutive perigees, or directly from the Keps.
Figure 1: Relative periods of AO-40 and Earth orbits
What’s interesting here (and is one of the things you notice after operating AO-40 for a few weeks), is that in four days a total of just over five orbits complete, and, at the observer, it appears that almost the same conditions exist as four days previously.
The differences occurring each four days:
(a) the same five orbits repeat each four days but are 27 mins, 25s earlier;
(b) apogee appears about 3.3º further east each five orbits.
These short term observations have slightly longer term implications. For example, if you discover that a particular set of good conditions exist for your QTH at a particular time, you’ll find that in general the same situation will occur in four days’ time. This is especially useful to know if you set your station up in your garden or portable because you know from recent successful operation where the dish was pointing.
On the other side of the coin, if a bad set of conditions are in place, such as anti-social hours even though AO-40 may be low in squint and the transponder is on, this condition too will continue to repeat.
Figure 2 identifies the similarities in four different parameters taken on three consecutive orbits, each orbit four days from the next.
Figure 2: Similarities in orbits four days apart from a ground station
3.
Why
AO-40 needs a regular attitude adjustment
Operators may be wondering why there are periods when AO-40 has to be manoeuvred from ALON/ALAT = 0/0, which means that it’s often difficult to make QSO’s, or hear and decode the beacon. The purpose of this section to explain the reason behind this off-pointing.
Normally, for tracking purposes, only the orientation of the spacecraft relative to the observation point on Earth is considered. For the purposes of explaining the ALON/ALAT attitude manoeuvres it’s necessary to change our conventional view and consider the position of the spacecraft relative to the Sun. This is because the attitude changes are required because of the orientation of the spacecraft relative to the Sun.
There are two reasons why these attitude manoeuvres are required:
(a) There is a spin-mode sun sensor on the spacecraft measuring up to ±45º. Beyond this, there is no easy way to measure the sun angle. Without being able to measure the sun angle, it is not easy to ascertain the attitude of the spacecraft (the ALON/ALAT) or maintain attitude and therefore control the spacecraft.
(b) Beyond about ±45º it’s not possible to support all the usual onboard systems such as the transponder and the RUDAK without entering negative power budget territory. When the sun angle is between ±45º, the spacecraft can be kept in a positive power budget, and the sun sensor can maintain and report attitude, so the high-gain antennas can point directly towards the Earth at apogee (ie, ALON=0 and ALAT=0).
To maintain the sun angle on the spacecraft between ±45º, the attitude (ALON/ALAT) is altered by using the magnetourquers. This means that the high-gain antennas now point away from the earth at apogee (ALON/ALAT ≠ 0/0), and this leads to significantly reduced (or occasionally no) useful transponder times.
Every 216 days or so (+/- a week), the cycle between ‘good’ and ‘bad’ sun angles repeats. For about half of these days, the sun angle will be between ±45º and ALON/ALAT may be maintained at 0/0, with the sun sensor providing useful data. A ‘bad’ sun angle is one where the incident angle of the sun on the spacecraft’s solar panels would be beyond 45º if the ALON/ALAT remained at 0/0. Figure 3 shows the long term repetition of these periods if ALON/ALAT was maintained at 0/0.
Figure 3: Sun angles on AO-40 if ALON/ALAT is held at 0/0. Good sun angles from AO-40’s perspective are between ±45º. Beyond this the spacecraft will suffer significantly reduced power budget and the spin-stabilised sun sensor will not provide data for attitude determination.
So now that these ‘bad’ sun angles exist, where does the off-pointing (adjusting ALON/ALAT from 0/0) help? To explain this, some diagrams will be needed. Firstly, it’s important to know how the sun angle is measured.
Figure 4: Sun angles on AO-40's solar panels
Referring to figure 4c, if the sun angle is zero, then the sun’s rays fall directly onto the solar panels and there is maximum power. As the angle increases or decreases away from 0°, the power decreases from the solar panels, and beyond ±45º, not only is it not possible to maintain sufficient power for all systems, but also the sun disappears from the sun sensor’s view.
Figure 5: Sun angles on AO-40 if ALON/ALAT is kept at 0/0 over part of the year. This also shows the slow precession of the orbit (0.1632° per day) where the ALON/ALAT co-ordinate system slowly turns.
Figure 6: Graphical representation of sun angles for the period under examination
Shown in figure 5 and figure 6 are representations of how sun angles would affect AO-40 over a period of time if ALON/ALAT is kept at 0/0. Between about 29 July 2002 and 15 November 2002, the sun angle would be in excess of 45º.
Also shown in figure 5 is the orbital precession of about 0.1632º per day, where the elliptical orbit itself slowly turns. If there were no orbital precession, the effect of sun angles would be synchronised with the Earth’s orbit, and there would be precisely two periods of poor sun angles per year. The orbital precession is primarily due to the Earth’s equatorial bulge. This is reflected in the Keplerian elements by a change in the RAAN parameter. The RAAN change moves ALON/ALAT coordinate system in space.
Figure 7: ALON/ALAT changes to keep sun angle under 45º
Figure 7 shows the attitude changes made to the spacecraft during the period 2 August 2002 to 17 November 2002 when sun angles were not optimum. It shows the changes made to the spacecraft’s attitude during this period in order to maintain sufficient sun on the solar panels and sun sensor.
Hypothetically, moving to three-axis stabilisation would still require off-pointing. However, because of the relatively rapid effects of three-axis stabilisation compared to magnetourquing, it might be possible to temporarily move the spacecraft to a more favourable position for an hour or two each orbit assuming that the batteries had sufficient charge to support this.
Had AO-40 assumed its designed inclination, under a spin stabilised scenario, these ‘bad’ sun angles would still occur, but would be far less apparent (OSCAR-13, for example, still had to be off-pointed on occasion).
4.
Is
AO-40 always a night owl?
Many operators have struggled bleary-eyed into the shack in the early hours to make QSO’s on AO-40. Back in September 2001, things were much more sensible. Long passes with great squint angles in the early evenings lasted for hours. Those were the days. So what happened?
Figure 8 is a plot of the times of day that apogee occurs for five years between July 2001 and July 2006. Looking at the times of day of apogee (when, assuming ALON/ALAT are 0/0, things will be optimum for the high-gain antennas), it can be seen that during September 2001 apogees were in the ‘core’ evening times between 17:00 and 00:00.
But during our last period of ALON/ALAT=0/0 between (May-July 2002), things became rather less convenient. Apogees are either during the day (when many amateurs are at work) or in the early hours.
Figure 8: Apogee times at G6LVB (IO91vl)
On the bright side, December 2002, January 2003 and February 2003 look like bumper months for apogee occurring during convenient times here at G6LVB. These months also coincide with low sun angles too, so ALON/ALAT=0/0.
As the graph shows, these periods, although cyclical, are not quite as constant in frequency as some of other observations. There is, of course, also a degree of subjectivity when determining when good and bad times occur.
5.
I’m
sure I used to get longer pass durations and higher elevations
A few months ago, the author posted a note on the AMSAT-BB saying that he didn’t think AO-40 was as good as it used to be. Well, it appears that although he couldn’t quantify it at the time, there may have been something in what was said. Back in the days when the transponder was first switched on, at the G6LVB latitude of 51.5º North, regular maximum elevations of 35º or more were encountered. As time has progressed, maximum elevations of only 20 to 25º have become the norm.
Initial analysis of the prediction data generated from Nova’s Keplerian model (figures 9 and 10) shows that the sub satellite point at apogee is oscillating between 7.6º north and 7.6º south. At the time of writing (September 2002), apogee is currently at about 7.6º South, leading to the lower maximum elevations in the Northern Hemisphere as well as shorter pass times.
Ground stations in the Southern Hemisphere will correspondingly experience their highest elevations during the time of Southern apogees, and similarly have maximum pass duration at this time.
A Northern sub satellite point at apogee is also reflected in a Southern sub satellite point at perigee. It is convention that rather than describing this variation as a change in the apogee in Keps, it is described at perigee by the ‘argument of perigee’ parameter, or ArgP. This variation in ArgP is primarily because of the Earth’s equatorial bulge.
Figure 9: Maximum elevation of AO-40 attained at G6LVB (51.5º North), and the corresponding apogee sub satellite point latitude, using the Keplerian model
Figure 10: Averaged pass duration at G6LVB (51.5º North)
The Keplerian model used in Nova does not consider the perturbation effects of the Sun and Moon on highly elliptical orbits such as that of AO-40, which makes some significant differences in longer term predictions. Using alternative software techniques (the same techniques which have previously predicted AO-13’s re-entry to the day) Stacey Mills W4SM has determined that these perturbations will in fact lead to inclinations between 5° and 10°, maximising in the medium term in the Northern Hemisphere at 10° in spring 2004 (see figure 11).
This will mean that there will be correspondingly higher elevations and slightly longer pass durations in the Northern Hemisphere.
Figure 11: W4SM's inclination predictions including solar & lunar perturbations
6.
What
does this all mean?
Here’s the low down.
· Because of the apparent repetition of similar conditions every four days, it makes it quite easy to predict in the short term when similar good or bad conditions for operating AO-40 will occur.
·
AO-40 will continue to require to have ALON/ALAT adjusted
away from 0/0 on a repeating cycle which lasts every 216 days or so. This is
because of angle of the sun on the spacecraft. For about half of this 216 day
cycle, ALON/ALAT can be kept at around 0/0. For the remaining time the attitude
will be adjusted in order to (a) keep sufficient sun on the solar panels and
(b) allow the sun sensor to maintain attitude and provide attitude data to keep
the spacecraft under control.
·
Periods of convenient and then inconvenient hours of
AO-40 transponder operations during good ALON/ALAT will continue to occur, with
the length of these periods being several months at a time.
·
About every three years or so, AO-40’s apogee sub
satellite point varies in latitude from 5°-10° South to 5°-10° North and back
to 5°-10° South again. When apogee is in the opposite hemisphere to the
observer, pass durations and maximum elevations will reduce correspondingly.
When all four sub-optimal situations are in place, such as during September & October 2002 in the Northern Hemisphere, operators should consider taking a visit to the mast for some deserving antenna maintenance.
Acknowledgements:
Stacey Mills W4SM
Jerry Brown K5OE