Jan 31 2021.
The objective of this project is to assess orbit choices for an orbiting calibration source. There are two things we desire: 1) satellite is in the shadow of the Earth, so that we avoid reflected sunlight issues, and 2) angular rate not to exceed 30 arcsec/sec, i.e. twice the sidereal rate, so that large telescopes can track the source easily. Two limiting cases that don't work: i) geosynch orbits put source at fixed azimuth and elevation (angluar rate =0) but except for equinox these objects are in the sunlight, ii) low earth orbits, few 100 km above surface, are in shadow but have really high angular rate as seen from observatory.
...
** Need to be sure to include the apparent parallax due to motion of the Earth's surface, under the satellite.
Parallax makes it seem to move faster than background stars, in opposite direction. Typical parallax rate is 3 to 5 arcsec per sec. If we have orbital rate of ~20 arcsec per sec going the other way, it's locked to the stars. So do we want 15 or 20 arcsec/sec?
steps:
- pick an ellipticity between 0.5 and 0.9
- for semi-major axis "a" ranging from 7,000 km to 20,000 km
- figure out where the focus of ellipse is, call that "c"
- compute distance to center of mass when satellite is at apogee, which is r=c+a
- compute linear speed at that point in the orbit, using expression above
- compute apparent angular rate from orbital motion, in radians per sec that is v/r
- convert to arcsec per sec
- compute apparent parallax due to rotation of the Earth
- compute inclination of orbit needed to attain sun-synch precession
- produce plots of
- apogee speed vs a
- apogee angular rate vs a
- parallax at apogee vs. a
...
So technically, we want a dusk to dawn orbit! At some orbit that is Molnya like such that the angular rate issue is resolved. See new wiki page for details
Precession - In astronomy, precession refers to any of several gravity-induced, slow and continuous changes in an astronomical body's rotational axis or orbital path. Precession is a change in the orientation of the rotational axis of a rotating body. In an appropriate reference frame it can be defined as a change in the first Euler angle, whereas the third Euler angle defines the rotation itself. The sun synchronous orbit slowly precesses around Earth to always be in the dark at a given time over a part of the planet. Formula for precession is here: Sun-synchronous orbit - Wikipedia
Why does it do precession? - It's mostly physics magic! The Earth's rotation causes it to bulge slightly at the equator, which means the Earth is trying to twist the Orbit over on to its side. How this causes the orbit plane to rotate isn't very intuitive, but you can recreate the same effect by spinning up an old bike wheel and holding it on one side of the hub while it is upright. For the Earth's rotation to cause exactly the right rate of precession, we just have to periodically tweak the orbital inclination and altitude. We use around 20kg of fuel per year for this, and that's mainly to tweak the inclination. If we tried to make the orbit turn through the year without the help of the equatorial bulge, we'd burn through our 300kg fuel budget within a few hours!
...
Angular rate - rate at which the thing moves across the sky. Angular velocity is the rate of velocity at which an object or a particle is rotating around a center or a specific point in a given time period.
Sidereal day just refers to when the earth completes one revolution relative to itself in a vacuum. a solar day it when the same spot on earth faces the sun again. the sidereal rate is the rate at which the earth spins on its axis, and consequently the rate at which the 'fixed' stars appear to move in the sky.A sidereal day – 23 hours 56 minutes and 4.1 seconds – is the amount of time needed to complete one rotation, so there are 4 minutes left that carry over. sidereal time at any given place and time will gain about four minutes against local civil time, every 24 hours, until, after a year has passed, one additional sidereal "day" has elapsed compared to the number of solar days that have gone by.
Using sidereal time, it is possible to easily point a telescope to the proper coordinates in the night sky. Briefly, sidereal time is a "time scale that is based on Earth's rate of rotation measured relative to the fixed stars. This is because you are measuring and going by the absolute rotation of the Earth so the stars must be in the same place every day, not shifted around ever 4 minutes.
In the picture of the sun and distant star above: Sidereal time vs solar time. Above left: a distant star (the small orange star) and the Sun are at culmination, on the local meridian m. Centre: only the distant star is at culmination (a mean sidereal day). Right: a few minutes later the Sun is on the local meridian again. A solar day is complete.
the sidereal rate is the rate at which the earth spins on its axis, and consequently the rate at which the 'fixed' stars appear to move in the sky.
equinox - the time or date (twice each year) at which the sun crosses the celestial equator, when day and night are of equal length (about September 22 and March 20).
The umbra (Latin for "shadow") is the innermost and darkest part of a shadow, where the light source is completely blocked by the occluding body. An observer within the umbra experiences a total eclipse. The penumbra (from the Latin paene "almost, nearly") is the region in which only a portion of the light source is obscured by the occluding body. An observer in the penumbra experiences a partial eclipse. https://mysite.du.edu/~jcalvert/astro/shadows.htm
However, the umbra and penumbra of course aren't just triangles, they're cones; and as such, treat them. Question is : are earth and the sun in the same plane?
- What is the sunlight intensity vs. distance from Earth (umbra vs. penumbra), in the shadow? What is angular size of shadow as seen from observatory? https://en.wikipedia.org/wiki/Umbra,_penumbra_and_antumbra
- this matters because if we are in the penumbra, some sunlight will come through, defeat the purpose of being a calibration source; or we'd have to subtract that intensity, technically, to get a good reading.
- Is there a strobed-source approach that would work, if we could make a constant-integrated-photon-flux-per-pulse strobed source? What about scintillation?
- wdym?
apparent parallax - an apparent change in the position of an object resulting from a change in position of the observer. astronomy the angle subtended at a celestial body, esp a star, by the radius of the earth's orbit
Parallax makes it seem to move faster than background stars, in opposite direction.
ellipticity vs eccentricity
The orbital eccentricity of an astronomical object is a dimensionless parameter that determines the amount by which its orbit around another body deviates from a perfect circle. A value of 0 is a circular orbit, values between 0 and 1 form an elliptic orbit, 1 is a parabolic escape orbit, and greater than 1 is a hyperbola. Orbital eccentricity - Wikipedia
For elliptical orbits eccentricity e can also be calculated from the periapsis and apoapsis since rp = a(1 − e) and ra = a(1 + e), where a is the semimajor axis. look at wikipedia
Linear speed is the measure of the concrete distance travelled by a moving object. it would be the tangent of the circle in this case.
refs
Adaptive optics guide star and calibration satellite, ORCAS:
...