LECTURE 10: UNIVERSAL GRAVITY, PART II

• How do Newton's laws of motion and gravity explain
  • ocean tides on the Earth?
  • orbits of comets?
  • gravitational effects of planets on each other?
• What experiment is needed to "weigh the Earth"?
• How could an "astronomer" around a distant star infer the existence of Jupiter?
• What is the relation between physics and astronomy?
• What does the "scientific revolution" teach us about science?

APPLICATION TO TIDES

• Moon pulls more strongly on near side of Earth than on center, more strongly on center than on far side.
• Therefore tends to "stretch" the earth into a (slight) oval.
• Hard to stretch solid earth, but liquid oceans are easier.
• Get "tidal bulge" in oceans, pointing roughly towards moon.
• Lags moon slightly because of friction, running into continents.
• As Earth rotates once per day, get two high tides and two low tides.
• Tidal effect of Sun is comparable to Moon.
• Get strong ("spring") tides when Sun and Moon align, reinforce each other.
• Get weak ("neap") tides when Sun and Moon are at right angles, partially cancel.
• Many complications due to geography, weather.

• "Friction" from ocean tides is gradually slowing rotation of the earth.
• Conservation of angular momentum means Moon is slowly getting further away (1-2 centimeters per year) to compensate.
• Earth tide on Moon is stronger, because Earth is more massive.
• Tidal friction has halted Moon's rotation relative to Earth, i.e., Moon's "tidal bulge" always points towards Earth, so no more friction.
• This is why we never see the far side of the Moon from Earth.

APPLICATION TO COMETS

• Comets moving under gravity of Sun.
• But come from far away, very elongated elliptical orbits.
• Turn rapidly when close to Sun.
• Newton used laws of motion and gravity to explain observed motions of comets, predict return of Halley's comet.

EFFECT OF PLANETS ON EACH OTHER

• Sun 1000 times more massive than Jupiter, which is most massive planet.
• Gravitational effects of planets on each other much smaller than effect of Sun.
• But not zero.
• Newton predicts: When Jupiter is "catching up" to Saturn, Saturn should slow down. When Jupiter has passed it, Saturn should speed up.
• Effect had already been seen, never understood.
• Newton's laws explain it precisely.
• Smoking gun evidence for universal gravity.

DISCOVERY OF NEPTUNE

• Planet Uranus discovered serendipitously in 1781, during telescopic survey of sky.
• Fifty years later, showing deviations from expected orbit.
• Two mathematicians show these deviations could be produced by gravity of a more distant planet.
• Predicted where the planet should be.
• Planet Neptune found within 1 degree of predicted position.

WEIGHING THE EARTH

• Can get size of Earth, distances of planets and Sun from precise observations and geometry.
• Can get relative masses of Sun and Earth by comparing acceleration of Earth to acceleration of Moon.
• Similarly, can get relative mass of Sun and Jupiter.

How can we get absolute masses (in kg)?

• Sounds easy.
• From Newton's law of gravity, we know: g = 9.8 m/sec² = G M_earth / R_earth².
• R_earth measured from geometry.
• Look up G in back of book.
• Solve for M_earth.

• Newton's problem: no book.
• Accelerations of planets, moons, etc. depend on GM_sun, GM_earth, GM_jupiter, etc., not G alone.
• To measure G, need to measure gravitational force between two objects whose mass is known independently, i.e., laboratory scale objects.
• Very hard, because gravity is very weak.
• Finally done by Henry Cavendish in 1798, beautiful experiment.
• Result: G = 6.67 x 10^-11 newton m² / kg² = 6.67 x 10^-11 m³ / (kg - sec²).

APPLICATION TO EXTRA-SOLAR PLANET SEARCHES

• Newton's 3rd Law: If Sun pulls on Jupiter, Jupiter also pulls on the Sun.
  (Other planets too, but Jupiter's effect is biggest.)
• Jupiter causes Sun to accelerate. But Sun is 1000 times more massive, accelerates 1000 times less.
• How could an astronomer around a distant star infer the existence of Jupiter?
• Too faint to see against the much brighter glow of the nearby Sun.
• But can watch for slight wobble of Sun.
• Small effect, requires very precise measurement.
• This is how we detect planets around other stars.

EVALUATION OF NEWTON'S ACHIEVEMENT

Hard to find enough superlatives.

• Simultaneously achieves giant advance in astronomy and physics.
• Each requires the other: need laws of motion and gravity to understand motions of planets and moon, but need motions of planets and moon to figure out and prove laws of motion and gravity.
• Has to invent major new branch of mathematics, calculus, to carry this out. Calculus is the mathematics of motion and change.
• Calculations are hard, but principles are simple and few: three laws of motion plus law of gravity.
• These explain observed motions of planets, tie them physically to motion of the moon and to falling objects on earth.
• Also explain much more: motion of Jupiter's moons, tides, comets, mutual gravitational effects of planets.
• Theory makes precise predictions (e.g., orbital deviations of Saturn, position of Neptune) that are confirmed by precise observations.

UNIVERSAL LAWS

• Perhaps most important of all, Newton gives unified explanation of terrestrial and celestial phenomena.
• Brilliant and persuasive realization of Kepler's idea: basic laws of physics apply throughout the universe.
• This idea underlies all of modern astronomy, proves astoundingly successful.
• Still the case that we use physics learned in laboratories on earth to understand planets, stars, galaxies, and the universe.
• Still the case that we use astronomical observations to learn about physics beyond the reach of terrestrial experiments.

Scientific Revolution: A Brief Summary

• Geocentric model of Aristotle. Complex, not highly accurate.
• Heliocentric model of Aristarchus. Simple, not highly accurate.
• Geocentric model of Ptolemy. Highly complex, accurate.
• Heliocentric model of Copernicus. Highly complex, accurate.
• Observations of Tycho: Undermined Aristotelian views, provided highly precise measurements of planetary positions.
• Kepler: Simple principles explain Tycho's data, very accurately. Idea of applying physical reasoning to celestial motions.
• Galileo: Discoveries with telescope support Copernican model. Substantial progress in understanding inertia, force, acceleration.
• Newton: Laws of motion and universal gravity explain Kepler's laws. Explain and predict many other phenomena.

LESSONS

What do we learn about science from the history of the scientific revolution?

• Scientific progress usually messy. Sometimes go right direction for wrong reason. Success may be hard to recognize at the time.
• Much more than collection of facts.
• Major advances in interpretations of facts require great creative leaps.
• Advances often enabled by new experimental or theoretical technology (e.g., Tycho's instruments, telescope, calculus).
• Occam's razor (seek the simplest explanation) is a powerful guide, but not always easy to follow.
• Most important principle is testing ideas against experiment and observation.
• Successful theories explain or predict phenomena beyond (often far beyond) their original scope. Do more than they were "designed" to do.