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2

For an astronomical view, rather than a geometrical one: The shape of an orbit and the position of a body on that orbit are defined by six orbital elements https://en.wikipedia.org/wiki/Orbital_elements I would appreciate anyone who can insert the diagram ,with attribution, from the referenced Wikipedia article) Of interest here is the true anomaly, an angle ...


5

In geometry these terms are used for a circular segment: Let R be the radius of the arc which forms part of the perimeter of the segment, θ the central angle subtending the arc in radians, c the chord length, s the arc length, h the sagitta (height) of the segment, and a the area of the segment. Source So arc length is the curved distance and chord length ...


3

Perhaps you are looking for a relationship in the form of (or wondering whether such a relationship exists): Nmin(A_cap,n) = μ(n) * (A_Earth/A_cap) A_cap: area of an instantaneous coverage by a single satellite, constant in time (circular orbits), modelled as a spherical cap. Nmin: smallest number of satellites in a practical constellation that can provide ...


6

Some notes on your approach, which I believe is a good one as a first order approximation. Doing this I belive I'm overestimating the number of satellites I would rather say it has to be an underestimate. Circles do not perfectly tile. To achieve a 1-fold coverage, for instance, there must be some overlap, requiring $\frac{2\pi}{3\sqrt{3}} \approx 1.21$ ...


4

I'm not able to address your entire question, but I think I can answer questions 2 & 3. Are any actually tracked? Are any specific orbits known? Or would a spacecraft have to go out there and scour the orbits of old nuclear reactors looking for them? Have any individual droplets ever been detected by any means, or are they strictly deduced to exist? It ...


4

The latitude of your launch site would be the optimal inclination, as the relative inclination between the LEO orbit and Moon's orbit matters very little for delta-v cost. A lunar transfer orbit is very long and skinny, so at lunar encounter, the spacecraft's velocity (< 200m/s) is much less than the Moon's velocity (> 1km/s), which means that its ...


5

Long term, and it must be in LEO? There are many things to consider: any LEO orbit's plane will drift, due to the shape of the Earth, so no orbit will stay aligned with the Moon's inclination. You likely want a somewhat high-inclination orbit, so that your normal trajectory to the Moon arcs far north or south, thus avoiding the worst of the Van Allen belts. ...


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