The sidereal period of a planet is the time it takes to complete one orbit around the Sun, as seen from a fixed point in space. The formula for calculating the sidereal period is $$T = \frac{2\pi}{\sqrt{\frac{G M}{a^3}}}$$, where $$G$$ is the gravitational constant, $$M$$ is the mass of the Sun, and $$a$$ is the semi-major axis of the planet's orbit.

The synodic period of a planet is the time it takes for the planet to return to the same position relative to the Sun and Earth. The formula for calculating the synodic period is $$T = \frac{1}{\frac{1}{T_1} + \frac{1}{T_2}}$$, where $$T_1$$ is the sidereal period of the planet and $$T_2$$ is the sidereal period of the Earth.

The elongation of a planet is the angle between the planet and the Sun, as seen from the Earth. The formula for calculating the elongation is $$\epsilon = \arccos{\frac{\cos{\lambda_p} - \cos{\lambda_s}}{\sin{\lambda_p}\sin{\lambda_s}}}$$, where $$\lambda_p$$ is the ecliptic longitude of the planet and $$\lambda_s$$ is the ecliptic longitude of the Sun.

The declination of a planet is the angle between the planet and the celestial equator, as seen from the Earth. The formula for calculating the declination is $$\delta = \arcsin{\sin{\lambda_p}\sin{\epsilon}}$$, where $$\lambda_p$$ is the ecliptic longitude of the planet and $$\epsilon$$ is the obliquity of the ecliptic.

The right ascension of a planet is the angle between the vernal equinox and the planet, as seen from the Earth. The formula for calculating the right ascension is $$\alpha = \arctan{\frac{\sin{\lambda_p}\cos{\epsilon}}{\cos{\lambda_p}}}$$, where $$\lambda_p$$ is the ecliptic longitude of the planet and $$\epsilon$$ is the obliquity of the ecliptic.

The planetary periods are the time it takes for a planet to complete one orbit around the Sun. The formula for calculating the planetary periods is $$P = \frac{2\pi}{\sqrt{\frac{G M}{a^3}}}$$, where $$G$$ is the gravitational constant, $$M$$ is the mass of the Sun, and $$a$$ is the semi-major axis of the planet's orbit.

The transits are the time it takes for a planet to pass in front of the Sun, as seen from the Earth. The formula for calculating the transits is $$T = \frac{1}{\frac{1}{P_1} + \frac{1}{P_2}}$$, where $$P_1$$ is the sidereal period of the planet and $$P_2$$ is the sidereal period of the Earth.

The progressions are the time it takes for a planet to move one degree in longitude. The formula for calculating the progressions is $$P = \frac{2\pi}{\sqrt{\frac{G M}{a^3}}}$$, where $$G$$ is the gravitational constant, $$M$$ is the mass of the Sun, and $$a$$ is the semi-major axis of the planet's orbit.

The planetary aspects are the angles between the planets, as seen from the Earth. The formula for calculating the planetary aspects is $$\theta = \arccos{\frac{\cos{\lambda_1} - \cos{\lambda_2}}{\sin{\lambda_1}\sin{\lambda_2}}}$$, where $$\lambda_1$$ is the ecliptic longitude of the first planet and $$\lambda_2$$ is the ecliptic longitude of the second planet.

The planetary houses are the twelve divisions of the zodiac, as seen from the Earth. The formula for calculating the planetary houses is $$H_i = \frac{360\degree}{12} + \frac{i - 1}{12}360\degree$$, where $$i$$ is the number of the house.

The planetary rulerships are the associations between the planets and the signs of the zodiac. The formula for calculating the planetary rulerships is $$R_i = \frac{360\degree}{12} + \frac{i - 1}{12}360\degree$$, where $$i$$ is the number of the planet.

The planetary dignities are the strengths of the planets in the signs of the zodiac. The formula for calculating the planetary dignities is $$D_i = \frac{360\degree}{12} + \frac{i - 1}{12}360\degree$$, where $$i$$ is the number of the planet.

The planetary debilities are the weaknesses of the planets in the signs of the zodiac. The formula for calculating the planetary debilities is $$W_i = \frac{360\degree}{12} + \frac{i - 1}{12}360\degree$$, where $$i$$ is the number of the planet.

The planetary exaltations are the strongest positions of the planets in the signs of the zodiac. The formula for calculating the planetary exaltations is $$E_i = \frac{360\degree}{12} + \frac{i - 1}{12}360\degree$$, where $$i$$ is the number of the planet.

The planetary falls are the weakest positions of the planets in the signs of the zodiac. The formula for calculating the planetary falls is $$F_i = \frac{360\degree}{12} + \frac{i - 1}{12}360\degree$$, where $$i$$ is the number of the planet.