Earth, Moon, and the Sun – Formula & Equation Sheet
Essential formulas and equations from Curiosity, tailored for Class 7 in Science.
This one-pager compiles key formulas and equations from the Earth, Moon, and the Sun chapter of Curiosity. Ideal for exam prep, quick reference, and solving time-bound numerical problems accurately.
Key concepts & formulas
Essential formulas, key terms, and important concepts for quick reference and revision.
Formulas
Circumference of Earth: C = 2πr
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.
Speed of Rotation: v = d/t
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.
Day Duration Variation: D = 24 + Δh
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.
Solar Intensity: I = P/A
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.
Force of Gravity: F = G(m1*m2)/r²
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.
Revolution Period: T = 365.25 days
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.
Tilt Angle: θ = 23.5°
θ is the angle of Earth's axial tilt. This tilt is what causes the change in seasons as Earth revolves around the Sun.
Solar Eclipse Condition: d_{Moon} ≈ d_{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.
Lunar Eclipse Condition: d_{Earth} > d_{Moon}
Indicates that during a lunar eclipse, the Earth’s shadow falls on the Moon, blocking the sunlight.
Length of Solar Day: 24 hours - (mean solar time)
This formula shows the adjustment of timekeeping based on the variations in Earth's rotation, accounting for the time that daylight appears.
Equations
E = mc²
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.
Ohm’s Law: V = IR
V is voltage (volts), I is current (amperes), and R is resistance (ohms). It defines the relationship between current and voltage in a circuit.
Density: ρ = m/V
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.
Weight: W = mg
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.
Period of Revolution: T = 2π√(r³/GM)
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.
Kepler’s Third Law: T² ∝ r³
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.
Angular Velocity: ω = θ/t
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.
Energy: E = hf
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.
Kinetic Energy: KE = 1/2 mv²
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.
Potential Energy: PE = mgh
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.
