Gravity

Core Concept: Gravity is a universal attractive force between all material bodies that curves straight-line motion into elliptical orbits.
Mathematical Expression: $F_{\text{gravity}} = G \frac{M_1 M_2}{R^2}$
- Force is directly proportional to the product of masses ( $M_1$ and $M_2$ ) and inversely proportional to the square of separation distance ( $R$ ).
Surface Gravity vs. Orbital Acceleration:
- Objects at Earth's surface accelerate downward at $9.8\,m/s^2$ .
- The Moon, located $60$ Earth radii away, experiences an acceleration reduced by $\left(\frac{1}{60}\right)^2 = \frac{1}{3600}$ , resulting in $\approx 0.00272\,m/s^2$ .
Mass vs. Weight: Mass is intrinsic and constant, whereas weight varies with local gravitational strength.

Perihelion & Aphelion: Points in a solar orbit where an object is closest (moves fastest) and farthest (moves slowest) from the Sun, respectively.
Perigee & Apogee: Corresponding closest and farthest points for bodies orbiting Earth.
Satellites vs. Moons: Satellites are human-made orbiting objects, while moons are natural satellites.

Planetary Orbits: The eight major planets move in low-eccentricity elliptical orbits near the ecliptic plane. Orbital speed decreases with distance from the Sun (e.g., Mercury moves at $48\,km/s$ vs. Neptune at $5\,km/s$ ).
Asteroids: Small rocky bodies mostly located in the asteroid belt ( $2.2\,AU$ to $3.3\,AU$ ) between Mars and Jupiter with stable, lower-eccentricity orbits.
Comets: Small bodies with highly eccentric orbits ( $e \ge 0.8$ ) that spend most of their time slowly in the outer solar system and accelerate rapidly near perihelion.