# Astronomy (Notes)

### Time

MST is measured from the vernal equinox. This precesses & a correction
yields the Stellar Day, 23h 56m 4.098 903 691s.

The International Earth Rotation and Reference Systems Service, IERS,
is the best source of data.

### Time of Orbit

M primary's mass
m satellite's mass
G gravitational constant
a semi-major axis
e eccentricity
T orbital period
r separation
C circumference

Average orbital speed, Va = (2πa/T)v(1 - 1e^{2}/4 - 3e^{4}/64 - 5e^{6}/256 - 7e^{8}/16384...)
Instantaneous speed, V = v[Gm(2/r - 1/a)]
If e is low & m << M, Va = 2πa/T, or Va = v(Gm/a)
If e is low & m <<<< M, Va = v(Gm/r)
If e is low & m & M are comparable, Va = v[G(M + m)/r]
C = (2πa)[1 - (1/2)^{2}e^{2}/1 - (1.3/2.4)^{2}e^{2}/3 - (1.3.5/2.4.6)^{2}e^{2}/5...]
So average r = a[1 - (1/2)^{2}e^{2}/1 - (1.3/2.4)^{2}e^{2}/3 - 1.3.5/2.4.6)^{2}e^{2}/5...]
With such low values of e in the solar system, r = a.

### The Earth

Earth bulges at the equator. South of the equator the bulge is ~ 15m
higher than it is north of the equator. The south pole is ~ 30m closer to the
centre of the earth than the north pole. The circumference of Earth at the
equator is about 40,075 km, but from pole-to-pole - the meridional
circumference - Earth is only 40,008 km around.

### Constellations

Capricornus 19 JAN 15 FEB Leo 10 AUG 15 SEP
Aquarius 16 FEB 11 MAR Virgo 16 SEP 30 OCT
Pisces 12 MAR 18 APR Libra 31 OCT 22 NOV
Aries 19 APR 13 MAY Scorpius 23 NOV 29 NOV
Taurus 14 MAY 19 JUN Ophiuchus 30 NOV 17 DEC
Gemini 20 JUN 20 JUL Sagittarius 18 DEC 18 JAN
Cancer 21 JUL 9 AUG

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