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a. I hope this is the case, but if it is, it would seem to be a huge oversight on STK's part; I'll take your word for it. There For it to be off that much in the gif seems wrong. To note, there is a distinction made here in STK (Satellites - Propagators - Two-Body, J2 Perturbation & J4 Perturbation (agi.com)):
- J2Perturbation includes the point mass effect as well as the dominant effect of the asymmetry in the gravitational field (i.e. the J2 term in the gravity field, representing North/South hemisphere oblateness); J4 additionally considers the next most important oblateness effects (i.e., the J2^2 and J4 terms in addition to J2). None of these propagators model atmospheric drag, solar radiation pressure or third body gravity; they only account for a few terms of a full gravity field model.
- These propagators are often used in early studies (where vehicle data is usually unavailable for producing more accurate ephemeris) to perform trending analysis: J2 Perturbation is often used for short analyses (weeks) and J4Perturbation often for long analyses (months, years).
Even thenwhen i implemented this, it doesn't look like it makes much of a difference when I simulate it with J4.
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- There is also a cool constraint feature in STK that lets you ensure you only compute access for orbits that are above a certain angular rate. As for whether you can see the angular rate, I have not been able to find that property on STK yet.
- There is also a cool constraint allowing you to limit it to times above a certain elevation angle:
- From STK(Introduction to STK (agi.com)): "You know that when you are on the ground trying to see something in space the lower you look along the horizon the more atmosphere you have to look through and the better the chance that something will be in the way. To help avoid the elevation angle problem, STK allows you to put an elevation angle constraint on a ground-based location. A good typical minimum elevation is 6-8 degrees, but it can be more depending on the area, the surrounding terrain, and even buildings."
- There are also a list of other constraints you can impose on Access times (a full list is here:Constraints - Basic (agi.com))
- Notable ones include elevation angle, elevation rate, altitude, and line of sight.
ORBIT 1
a = 15100 km, e = 0.55, inc = 169 deg
I still filtered for evenings from 17:30 to 6:30, so that still cut off some times.
As you can see, the times for access are now much more realistic (on the order of 10 minutes). We still could not see Antarctica, and we can barely see Greenland. With this new constraint, there is a gap in times in Cambridge in April and October, and a gap in times in July in Chile. Access numbers are noted below for this. Quite good access frequencies for this orbit, as noted in the chart below the plots.
ORBIT 2
Next, I did a = 12000 12717 km, e = 0.3, inc = 169 deg
There is no access for Greenland or for Antarctica. However, there is quite good access for Cambridge and Chile . (~2 accesses a day)
ORBIT 3
Next, I did a = 12000 12717 km, e = 0.3, inc = 23.5 deg
No Antarctica access, per usual. This is the solution we want, but it performs very poorly for some months of the year, sadly. That isn't to say we can't launch two satellites to cover dead zones of the other, though? Plus, since we've seen that times for access haven't gone down for the other satellites when we implement the penumbra/umbra constraint, I'd say it doesn't even matter that we don't put it in the plane of the ecliptic (would you agree)?
So I'm glad that issue was resolved. IF these results look good to you, one constraint was implemented, giving us more valid results.
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One final thing I want to do is change the eccentricity for the plane of the ecliptic solution (I arbitrarily set it to 0.3=ecc) to see if there is a lower angular rate solutiondecided to do was optimize for the smallest angular rate given some fixed inclination = 157.5 deg (23.5 deg giving the same solution), by varying the value of a first then varying the value of eccentricity. This is because the orbit solution for a = 12717 km, e = 0.3, inc = 23.5 deg was an unoptimized solution; when I wrote my own code for it, I was now able to optimize for the a and ecc that gives the smallest angular rate. The plots for these results are shown below. (These solutions are implemented with the constraint that the perigee value should be at least 400 km above Earth).
The two solutions to take from this are:
eccentricity solution: (the ang_rate is off by a factor of 1000 because of the way units work in PoliAstro, the actual value is 87.22 arcsec/sec)
semi-major solution:
I must say that the two solutions look very similar to each other, with very similar eccentricities and semi major axes; this is expected, as I just parameterize one of the values. So, it will just be said that the solution is:
a = 14600, ecc = 0.532, inc = 157.5 or inc = 23.5, with an angular rate close to 87.2 arcsec/sec
In the gif, you can see the two orbits from this optimized solutions, the only difference being the inclination.
The orange orbit is the a = 14600, ecc = 0.532, inc = 157.5 solution
The blue orbit is the a = 14600, ecc = 0.532, inc = 23.5 solution
The purple orbit is the a = 15100, ecc = 0.55 inc = 169 solution from earlier for reference
I then graphed the access times for these orbits, given the constraints of being in the penumbra/umbra and being only between the hours of 17:30 to 6:00.
ORBIT 4
a = 14600 km, e = 0.532, inc = 23.5 deg
Orbits have a number of gaps in some months, as the others. Orbit frequency is about once per day, like the other orbits. Barely access Greenland; however, this is the first satellite to access Antarctica on a semi-consistent basis(72 over a year) , which is interesting.
ORBIT 5
a = 14600 km, e = 0.532, inc = 23.5 deg, J$ Pertubation
In order to prove that there is minimal difference between J2 and J4 perturbations, I ran the same python script on a J4 perturbed orbit, as shown below. The motivation for this was to show that the gifs are not erroneous, even when using the right settings (J4 is meant for months long simulations). This is the same exact orbit as orbit 4, except J4 perturbed. The numbers are almost exactly the same, save for a couple more or less orbits seen in some locations.
ORBIT 6
a = 14600 km, e = 0.532, inc = 157.5 deg
This orbit has the most number of accesses for the shown locations of all locations calculated, but no accesses for Greenland or Antarctica.
Based off of these plots and numbers, these are a promising sign toward making a satellite calibration target with a CubeSat. Given the infrequencies of some of the orbit accesses, it would probably be best to use satellites in different orbits to achieve maximum coverage, especially since satellites are fairly inexpensive.