2.3 Newtonian physics and gravitation

Newtonian physics laid the groundwork for understanding motion and gravity. It introduced laws that explain how objects move and interact, from apples falling to planets orbiting the sun. These principles gave cosmologists their first mathematical toolkit for describing how the universe works at large scales.

That said, Newtonian physics has real limits. It falls short in explaining phenomena like Mercury's orbital drift or the behavior of light near massive objects. Recognizing those limits is what eventually paved the way for Einstein's theories and our modern understanding of space and time.

Newtonian Physics and Gravitation

Key concepts of Newtonian physics

Newton published his three laws of motion and his law of universal gravitation in the Principia (1687). Together, they describe how forces cause objects to move and how gravity acts between any two masses in the universe.

• Newton's first law (law of inertia): An object at rest stays at rest, and an object in motion keeps moving at a constant velocity, unless an external net force acts on it. This is why a hockey puck slides across ice until friction slows it down, and why planets keep orbiting rather than stopping in space.
• Newton's second law: Force equals mass times acceleration, expressed as $F = ma$. Here $F$ is the net force on an object, $m$ is its mass, and $a$ is its acceleration. A larger force produces a larger acceleration, and a more massive object requires more force to accelerate at the same rate.
• Newton's third law: For every action, there is an equal and opposite reaction. Forces always come in pairs. A rocket pushes exhaust gases downward, and those gases push the rocket upward with equal force.
• Law of universal gravitation: Every object with mass attracts every other object with mass. The force is given by $F = G \frac{m_1 m_2}{r^2}$, where $G$ is the gravitational constant ($6.674 \times 10^{-11} \, \text{N m}^2/\text{kg}^2$), $m_1$ and $m_2$ are the two masses, and $r$ is the distance between their centers. Notice that the force drops off with the square of the distance: double the distance and the gravitational pull falls to one-quarter.

Mathematical framework for celestial motion

Newton showed that Kepler's empirical laws of planetary motion could be derived mathematically from his laws of motion and gravitation. This was a huge deal because it unified terrestrial and celestial physics under one framework.

• Kepler's three laws describe planetary orbits: (1) planets travel in ellipses with the Sun at one focus, (2) a line from the Sun to a planet sweeps out equal areas in equal times, and (3) the square of a planet's orbital period is proportional to the cube of its semi-major axis. Newton proved all three follow directly from the inverse-square law of gravity.
• Orbital mechanics treats celestial motion as a balance between gravitational pull and inertia. A planet's inertia wants to carry it in a straight line, while gravity curves its path into an ellipse. Near the Sun, a planet speeds up as gravity does more work; farther away, it slows down.
• Tides result from the gravitational pull of the Moon and Sun on Earth's oceans. The Moon has a stronger tidal effect than the Sun despite being far less massive, because tidal force depends on how close the attracting body is (it falls off with the cube of the distance, not the square).
• Orbit types depend on an object's velocity relative to the Sun's gravitational pull:
  1. Elliptical orbits are closed paths. Most planets and short-period comets follow these.
  2. Parabolic orbits are open paths where an object has exactly escape velocity. Some long-period comets approximate this.
  3. Hyperbolic orbits are open paths where an object exceeds escape velocity and passes through the solar system only once, like the interstellar object 'Oumuamua.

Implications for universal understanding

Newton's framework carried deep philosophical implications about the nature of space, time, and predictability.

• Absolute space: Newton assumed space is a fixed, unchanging backdrop. Motion happens within this background, and it provides a universal reference frame, like an invisible 3D coordinate grid that exists whether or not anything occupies it.
• Absolute time: Time flows at the same rate everywhere, for everyone, regardless of motion or location. Two perfectly synchronized clocks would always agree, no matter where you placed them. (Einstein later overturned this assumption.)
• Deterministic universe: If you knew the exact position and velocity of every particle in the universe at one moment, Newton's laws would let you predict the entire future. The mathematician Laplace captured this idea with his thought experiment known as Laplace's demon, an intellect that could calculate everything that would ever happen.
• Clockwork universe: This analogy compares the cosmos to a perfectly engineered machine. Once set in motion, it runs according to fixed, predictable laws, like the gears of a clock. The regular orbits of the solar system seemed to confirm this picture.

Limitations in astronomical explanations

Despite its power, Newtonian gravity fails in several important situations, and recognizing these failures drove cosmology forward.

• Precession of Mercury's orbit: Mercury's closest approach to the Sun (its perihelion) shifts slightly with each orbit. Newtonian gravity predicts most of this shift due to the gravitational tugs of other planets, but it's off by about 43 arcseconds per century. Einstein's general relativity accounts for this discrepancy exactly, and it was one of the theory's first major confirmations.
• High-speed and high-gravity regimes: Newtonian physics breaks down when objects move at speeds approaching the speed of light or when gravitational fields become extremely strong. Near black holes or neutron stars, you need general relativity to get accurate predictions.
• Dark matter and dark energy are concepts that go beyond anything Newton could have anticipated:
  1. Dark matter was proposed to explain why galaxies rotate faster than Newtonian gravity predicts based on visible mass alone. Galaxy rotation curves show that outer stars orbit too quickly unless there's unseen mass holding them in.
  2. Dark energy was hypothesized to explain why the expansion of the universe is accelerating rather than slowing down, as Newtonian gravity would suggest. It accounts for roughly 68% of the total energy content of the universe.