The Vikram Samvat uses lunar months and solar sidereal years. Because 12 months do not match a sidereal year, correctional months (adhika māsa) are added or (occasionally) subtracted (kshaya masa). A lunar year consists of 12 months, and each month has two fortnights. The lunar days are called tithis.
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The Burmese calendar (, , or , ; Burmese Era (BE) or Myanmar Era (ME)) is a lunisolar calendar in which the months are based on lunar months and years are based on sidereal years. The calendar is largely based on an older version of the Hindu calendar, though unlike the Indian systems, it employs a version of the Metonic cycle. The calendar therefore has to reconcile the sidereal years of the Hindu calendar with the Metonic cycle's near tropical years by adding intercalary months and days at irregular intervals. The calendar has been used continuously in various Burmese states since its purported launch in 640 CE in the Sri Ksetra Kingdom, also called the Pyu era.
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Vikram Samvat (IAST: Vikrama Samvat; abbreviated V.S. (or VS) and B.S. (or BS); ) and also known as the Vikrami calendar, is the historical Hindu calendar in the Indian subcontinent. It is the official calendar of Nepal. In India it is used in several states. The calendar uses lunar months and solar sidereal years.
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Five synodic years is 2919.6 days. Thirteen sidereal years for Venus is 2921.1 days, and eight for Earth is 2922.05 days. The heliocentric longitude of Earth advances by 0.9856° per day, and after 2919.6 days, it has advanced by 2878°, only 2° short of eight revolutions (2880°). The 3.4° inclination of Venus's orbit is great enough to usually prevent the inferior planet from passing directly between the Sun and Earth at inferior conjunction.
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This was a good approximation, but not a perfect one, since 59 (sidereal) years are equal to 21550.1 days, while 730 (synodical) months equal 21557.3 days. The difference therefore amounts to seven days. In addition there are the interfering variations in the lunar orbit. However, a 59-year period had the advantage that it corresponded quite closely to an integer number of orbital revolutions of several planets around the Sun, which meant that their relative positions also repeated each Great Year cycle.
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On the sides of the stela are carved two portraits of his father in a non-Maya style, dressed as a Teotihuacan warrior, bearing the central Mexican atlatl spear-thrower not adopted by the Maya, and carrying a shield adorned with the face of the Mexican god Tlaloc. The reverse of the stela bears a lengthy hieroglyphic inscription detailing the history of Tikal, including the Teotihuacan invasion that established Yax Nuun Ayiin I and his dynasty. In the Early Classic period the Maya kings began to dedicate a new stela, or other monument, to mark the end of each kʼatun cycle (representing 7,200 days, just under 20 sidereal years). At Tikal, the first to do so was king Kan Chitam who ruled in the late 5th century.
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For a rigid Earth which is an oblate spheroid to a good approximation, the figure axis F would be its geometric axis defined by the geographic north and south pole, and identical with the axis of its polar moment of inertia. The Euler period of free nutation is (1) τE = 1/νE = A/(C − A) sidereal days ≈ 307 sidereal days ≈ 0.84 sidereal years νE = 1.19 is the normalized Euler frequency (in units of reciprocal years), C = 8.04 × 1037 kg m2 is the polar moment of inertia of the Earth, A is its mean equatorial moment of inertia, and C - A = 2.61 × 1035 kg m2. The observed angle between the figure axis of the Earth F and its angular momentum M is a few hundred milliarcseconds (mas). This rotation can be interpreted as a linear displacement of either geographical pole amounting to several meters on the surface of the Earth: 100 mas subtends an arc length of 3.082 m, when converted to radians and multiplied by the Earth's polar radius (6,356,752.3 m).
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