Original Notes CalSat Research

Some notes I need to write because I am new to this stuff:

• Altitude (alt.), sometimes referred to as elevation (el.), is the angle between the object and the observer's local horizon. For visible objects, it is an angle between 0° and 90°.
  • Alternatively, zenith angle may be used instead of altitude. The zenith angle is the complement of altitude, so that the sum of the altitude and the zenith angle is 90°.
• Azimuth (az.) is the angle of the object around the horizon, usually measured from true north and increasing eastward. Exceptions are, for example, ESO's FITS convention where it is measured from the south and increasing westward, or the FITS convention of the Sloan Digital Sky Survey where it is measured from the south and increasing eastward.

The horizontal coordinate system is sometimes called other names, such as the az/el system,^[4] the alt/az system, or the alt-azimuth system, from the name of the mount used for telescopes, whose two axes follow altitude and azimuth

Sun Synchonous - This orbit is a special case of the polar orbit. Like a polar orbit, the satellite travels from the north to the south poles as the Earth turns below it. In a sun-synchronous orbit, though, the satellite passes over the same part of the Earth at roughly the same local time each day (for example, the satellite always shows up at midnight over Cambridge, allowing for easy calibration over it). This can make communication and various forms of data collection very convenient. For example, a satellite in a sun-synchronous orbit could measure the air quality of Ottawa at noon. From the perspective of the sun, the orbit looks exactly the same and does not change as the earth revolves around it. Look at the picture from the perspective of the sun.

However, this means that other areas of the world cant use this calibration quite like the designated area can. 

There is a special kind of sun-synchronous orbit called a dawn-to-dusk orbit. In a dawn-to-dusk orbit, the satellite trails the Earth's shadow. When the sun shines on one side of the Earth, it casts a shadow on the opposite side of the Earth. (This shadow is night-time.) Because the satellite never moves into this shadow, the sun's light is always on it (sort of like perpetual daytime). Since the satellite is close to the shadow, the part of the Earth the satellite is directly above is always at sunset or sunrise. That is why this kind of orbit is called a dawn-dusk orbit. This allows the satellite to always have its solar panels in the sun. 

Sun-synchronous polar orbit - YouTube - really great video; it should be noted that the orbit of the satellite is LEO, and goes around every 90 minutes around earth, so it would eventually go in front of a lot of parts of earth since the period is so fast; however if we had a molnya orbit we could make it stationary such that we calibrate using a known source about that same 24 hour period. 

The inclination is the angle the orbital plane makes when compared with Earth's equator. why do sun synchronous orbit have high inclinations? because it requires less thrust to precess the right amount? Look at sun syncronous wiki for inclination info

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.

Another way to see how this effect works is to hold your hand out in front of you and look at it with your left eye closed, then your right eye closed. Your hand will appear to move against the background.

This effect can be used to measure the distances to nearby stars. As the Earth orbits the Sun, a nearby star will appear to move against the more distant background stars. Astronomers can measure a star's position once, and then again 6 months later and calculate the apparent change in position. The star's apparent motion is called stellar parallax.

There is a simple relationship between a star's distance and its parallax angle:

d = 1/p

The distance d is measured in parsecs and the parallax angle p is measured in arcseconds.

This simple relationship is why many astronomers prefer to measure distances in parsecs.

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 r_p = a(1 − e) and r_a = 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.

 - we'd be at the focus of the ellipse, and the ellipse is the orbit of the satellite; the fourth picture is the side view of what would be going on, with earth being M. The angular rate at apoapsis needs to be about 15 arcsec/sec, and the period in total needs to be about 24 hrs.