Formula Sheet: Earth, Moon, and the Sun

C is the circumference (in km), π is approximately 3.14, and r is the radius of the Earth (≈ 6371 km). It determines the distance around the Earth.

v is the speed (in km/h), d is the distance (circumference of the Earth), and t is the time (24 hours). It shows the speed at which the Earth rotates.

D is the day duration (in hours), and Δh is the change in hours due to seasonal tilt. It illustrates how day length varies across seasons.

I is the intensity (in W/m²), P is the power (watts), and A is the area (in m²). It explains how sunlight intensity varies per unit area.

F is the gravitational force (in N), G is the gravitational constant (≈ 6.67 × 10⁻¹¹ N m²/kg²), m1 and m2 are the masses (in kg), and r is the distance between their centers (in m). It describes the gravitational pull between Earth and the Moon.

T is the time taken for one revolution of Earth around the Sun. It shows the relationship between the Earth's orbit and the calendar year.

θ is the angle of Earth's axial tilt. This tilt is what causes the change in seasons as Earth revolves around the Sun.

This condition describes that during a solar eclipse, the apparent sizes of the Moon and Sun from Earth are similar due to their distances.

Indicates that during a lunar eclipse, the Earth’s shadow falls on the Moon, blocking the sunlight.

This formula shows the adjustment of timekeeping based on the variations in Earth's rotation, accounting for the time that daylight appears.

E represents energy (in joules), m is mass (in kg), and c is the speed of light (≈ 3 × 10⁸ m/s). This formula shows how mass can be converted into energy, a fundamental idea in physics.

V is voltage (volts), I is current (amperes), and R is resistance (ohms). It defines the relationship between current and voltage in a circuit.

ρ is density (kg/m³), m is mass (kg), and V is volume (m³). It relates the mass of an object to its volume, useful in comparing celestial bodies.

W is weight (in newtons), m is mass (in kg), and g is acceleration due to gravity (≈ 9.81 m/s² on Earth). This equation describes the gravitational force on an object.

T is the period of revolution (in seconds), r is the radius of orbit (in m), and G is the gravitational constant. It describes how orbiting bodies move around each other.

This law states that the square of the orbital period (T²) of a planet is proportional to the cube of the semi-major axis of its orbit (r³), illustrating the relationship between revolution times and distances.

ω is angular velocity (in rad/s), θ is the angle in radians, and t is time (in seconds). This shows how quickly the Earth rotates or orbits.

E is energy of a photon (in joules), h is Planck’s constant (≈ 6.626 × 10⁻³⁴ Js), and f is frequency (in Hz). Relates energy with the solar radiation we receive.

KE is kinetic energy (in joules), m is mass (in kg), and v is velocity (in m/s). Useful to calculate energy of orbiting objects like Earth.

PE is gravitational potential energy (in joules), m is mass (in kg), g is acceleration due to gravity, and h is height (in meters). Describes how height affects energy in gravitational fields.