Newtonian Gravity: Crash Course Physics #8

Introduction to Newton's Transformative Impact

  • Isaac Newton fundamentally transformed physics.

  • His three laws of motion describe movement.

  • Understanding of gravity was scarce before Newton's contributions.

  • Scientists recognized dropped objects fell to the ground and observed orbital motions.

  • The connection between falling objects and celestial orbits was unknown.

Newton's Initial Thoughts on Gravity

  • Newton's realization sparked by an apple falling from a tree.

  • Proposed that gravity pulls objects down (the apple) and potentially affects larger bodies (Earth).

  • Speculated gravitational force could also affect celestial bodies like the Moon.

  • The Moon's orbit explained: it is constantly pulled towards the Earth but moves sideways, maintaining its orbit.

Developing the Law of Universal Gravitation

  • Newton sought an equation to describe gravitational force affecting both terrestrial and celestial objects.

  • Recognized that gravitational force is influenced by the mass of the objects and their distance apart.

Role of Distance in Gravitational Force

  • Objects near Earth (e.g., apples) accelerate under gravity at approximately 10 m/s².

  • The Moon experiences much less acceleration ( o approximately 1/3600th of the apple) due to its distance.

  • The gravitational force diminishes with increasing distance, specifically inversely proportional to the square of the distance between objects.

Role of Mass in Gravitational Force

  • Gravitational force is stronger with larger masses.

  • The equation for gravitational force is derived: proportional to the product of the two masses divided by the distance squared.

  • Small gravitational forces between common objects require a constant, called G, to scale the calculations appropriately.

Newton's Law of Universal Gravitation Equation

  • The complete equation: F = GMm/r², where:

    • F = gravitational force

    • G = gravitational constant (initially a placeholder)

    • M and m = masses of the two objects

    • r = distance between the centers of the two objects

  • The gravitational constant G was later determined to be approximately 6.67 x 10^-11 N*m²/kg².

Compatibility with Kepler's Laws

  • Newton ensured his law of gravitation aligned with Kepler's three laws of planetary motion.

Kepler's First Law

  • Orbits of planets are elliptical, with the Sun at one focus.

  • Applies to moons, including Earth's natural satellite.

Kepler's Second Law

  • Law of equal areas: a line from a planet to the Sun sweeps out equal areas in equal time intervals.

  • Example: Earth's varying distances from the Sun still yield equal area sweeps.

Kepler's Third Law

  • The cube of the semi-major axis of a planet's orbit divided by the square of its orbital period remains constant across planets.

  • Both Kepler's ratios (approximately 3.34 or 3.35) confirmed by observational data.

Newton's Explanations of Orbital Deviations

  • Unlike Kepler, Newton explained orbital deviations due to gravitational interactions among celestial bodies.

Newton's Second Law of Motion and Gravitational Acceleration

  • A net force equals mass times acceleration (F = ma) principles apply.

  • Gravitational acceleration derived from gravitational equations includes mass of larger objects and distance.

  • Gravitational acceleration on Earth, small g, can be expressed as:

    • g = G * Earth's mass / Earth's radius²

Application: NASA's Mars Exploration

  • NASA tests spacesuits by simulating Martian gravity.

  • Gravitational acceleration on Mars calculated using:

    • g = G * Mars's mass / Mars's radius²

  • Result: Mars's surface gravity approximates 3.7 m/s², about 38% of Earth's.

Conclusion

  • Newton's contributions remain foundational, even several centuries later.

  • His law of universal gravitation and motion calculations continue to be applicable today in modern physics and space exploration.