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Brilliant

Gravitational Physics

via Brilliant

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Overview

Here we lay out Newton's law of gravity and crack open the universe of consequences that spring from it. On the journey we'll come to understand planetary phenomena like tides and atmospheres, the rich geometry of heavenly bodies and their motion, and the engineering considerations of space travel.

By the end of this course, you’ll be able to code simulations to explore applied problems using Python, derive pieces of general relativity, and understand where Newton’s law starts to buckle.

Syllabus

  • Introduction to Gravity: Get acquainted with the basics of gravitation through a series of thought experiments and test them against real astronomical data.
    • Explore: Mass Dependence: An apple clocked Newton on the head, and his theory of gravity was born.
    • Explore: Distance Dependence: Discover the form of gravitational force by observing the cycle of the Moon.
    • Apply: Heavenly Orbits: Use data from the moons of Jupiter to complete the gravitational force law.
    • The Strength of Gravity: Decide where to place a sensitive gravitational experiment so Earth's gravity doesn't interfere.
  • Newtonian Gravity: Newton's greatest idea unified the physics of the heavens and Earth. Here we introduce Newton's theory, and then take him to meet Einstein.
    • Cavendish's Experiment: You don't need a planet to see gravity at work — just build a torsion pendulum in your garage.
    • Atmospheric Thickness: Predict the height of the atmosphere on a neutron star — with shockingly good accuracy.
    • Escape Velocity: Throw a ball fast enough from Earth, and it'll never return. What can this teach us about black holes?
    • Ocean Tides: The tide goes in, the tide goes out — and there's never a miscommunication.
    • Gravitational Redshift: This particle physics thought experiment points the way toward Einstein's general theory of relativity.
    • Gravity is Acceleration: Find out why astronauts don't experience the effects of gravity in orbit.
  • Gravitational Fields: Here we reimagine the force of gravity as a Universe-filling field, and develop powerful methods to solve hard problems.
    • Gravitational Energy: Get a firmer grasp on gravity using an energy approach.
    • Gravitational Pendulum: How long would it take to fall through the center of the Earth, from one side to the other?
    • Full Field of a Spherical Shell: The gravitational field of a spherical planet is extra simple.
    • Gauss' Law: Inverse-square force fields come equipped with a powerful mathematical tool.
    • Hunting for Resources: Use Gauss' Law to hunt for deposits of oil and ore beneath Earth's surface.
    • What if Earth was Flat?: Hold onto your coffee mug and steer clear of the mountain of ocean water.
    • Why Planets are Smooth: What is the gravitational field of a potato? And why aren't planets shaped like this?
  • Keplerian Orbits: The eternal dance of celestial bodies in the night sky spawned science as we know it. In this chapter, we develop the tools to predict them.
    • Circular Orbits: Join Lonely Walter as he plays catch with himself.
    • The Two-body Problem: Why does Earth orbit the Sun, and not the other way around?
    • Equations of Orbital Motion: These two equations describe a universe of possibilities.
    • Rotational Symmetry: Kepler's Second Law expresses a hidden symmetry in gravitational systems.
    • Orbits in a Gravity Well: If the gravitational field were a surface, what would it look like?
    • Bound Orbits: To escape the Sun, a planet needs extra energy. But why don't planets fall into the Sun?
    • Elliptical Orbits: Kepler's First Law says that planets follow elliptical orbits around the Sun, but Newton gave the proof.
    • Hohmann Transfer Orbits: Someone put a bus on an orbit to Mars, but you've got to get a running start to hop on.
    • Orbital Periods: Use everything you've learned so far to plan a mission to Mars.

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