Understanding Newton's Law of Universal Gravitation
Newton's law of universal gravitation states that every particle in the universe attracts every other particle with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. The formula is F = G (m1 m2) / r², where G is the gravitational constant. This law applies to planetary motion by describing the attractive force between the Sun and planets, which keeps them in stable orbits rather than flying off into space.
Key Principles in Planetary Motion
The law underpins Kepler's three laws of planetary motion. Kepler's first law (elliptical orbits) arises because the gravitational force provides the centripetal force needed for curved paths. The second law (equal areas in equal times) reflects conservation of angular momentum under this inverse-square force. The third law (T² ∝ a³, where T is orbital period and a is semi-major axis) directly follows from balancing gravitational force with orbital velocity, showing how larger orbits take longer periods.
Practical Example: Earth's Orbit Around the Sun
Consider Earth orbiting the Sun. The Sun's mass (about 1.989 × 10^30 kg) exerts a gravitational force on Earth (5.972 × 10^24 kg) at an average distance of 1 AU (1.496 × 10^11 m). Using F = G (M_sun m_earth) / r², this force equals the centripetal force mv²/r, resulting in Earth's elliptical path with a period of 365.25 days, demonstrating how the law predicts stable planetary orbits.
Importance and Real-World Applications
This application revolutionized astronomy by unifying terrestrial and celestial mechanics, enabling predictions of planetary positions for navigation and space exploration. Today, it's crucial for satellite orbits, mission planning like NASA's Voyager probes, and understanding exoplanets. Misconceptions, like gravity only acting on Earth, are clarified: it's a universal force governing all cosmic motion.