ap physics - history of measuring the solar system

who was aristarchus?

a greek astronomer, the first to hypothesize that the earth spins on its axis and revolves around the sun.

what was the argument against aristarchus’s hypothesis?

stellar parallax - critics argued that the positions of stars would vary if when observed from opposite ends of earth’s orbit, but no such shift was observed.

what was aristarchus’s counterargument?

the stars were simply too far for there to be any observable parallax to be seen from the earth.

who was eratosthenes?

a greek astronomer & mathematician who measured the circumference of the earth

what was eratosthenes’s method?

at noon on the summer solstice, a stick was placed in syrene, which was directly under the sun and therefore had no shadows casted on it. another stick was placed in alexandria at the same time and the angle of the shadow formed was measured, which was estimated to be around 7 degrees. this is about 1/50th of 360, indicating that the distance between alexandria & syrene was around 1/50th the circumference of the earth.

who was ptolemy?

a greek astronomer who proposed an earth-centric model that accounted mathematically for the movement of celestial bodies against “unmoving stars,” explaining irregularities in their motion that are referred to as “retrograde motion”

what was ptolemy’s model?

he proposed an epicycle in which there would be times when the epicycle velocity would oppose or add to the orbital velocity, seemingly changing its direction

copernicus’s model

proposed simpler, sun-centric model that explained motion of the “heavens” — explained retrograde motion by theorizing that some planets have a larger orbit than earth and are slower in their orbit

kepler’s achievements

published 1st book since copernicus that defended his theory — 3 laws of planetary motion:

• 1st law: the law of orbits — all planets move in elliptical orbits, w/ sun at 1 focus

  • aphelion — max radius from sun

  • perihelion — min radius from sun

  • eccentricity — (distance between foci)/(length of major axis)

• 2nd law: the law of areas — as a planet orbits, it sweeps out equal areas in equal times

• 3rd law: the law of periods — R³/T² = constant

  • R = average radius of ellipse = semi major axis

galileo’s observations

1. observed that jupiter had moons, demonstrating that not everything orbits the earth (evidence against earth-centric model)

2. observed a complete range of phases for venus, from 0 to 100% illumination

   1. in the earth-centric model, venus moves in an epicycle, meaning it could never be more than 50% illuminated

cassini’s accomplishments

1st to measure parallax shift of mars, resulting in a measurement of distance to mars:

• by measuring the angle from each location (cayenne and paris) and the baseline distance, geometry & trigonometry can be used to find d (distance to mars)

• once d was found, it could be used in kepler’s 3rd law to find the distance from earth to the sun

• this method was used to find the distance of all planets to the sun as well as all stars less than 500 light years away

newton’s accomplishments

• used kepler’s 2nd law & galileo’s ideas of uniform motion (inertia) to infer that there must be a force pulling the planets towards the sun rather than pushing them around it — also recognized that the force that pulls objects down at earth’s surface could result in a body continually falling toward it forever (orbit), and termed this force a gravitational force

• law of universal gravitational — every object in universe attracts every other object

cavendish’s accomplishments

1st to perform experiment that allowed a measurement of G

• Fg caused small masses to move towards large masses & twist quartz fiber, reaching a new equilibrium position where the elastic force in the fiber equals Fg

• deflection of laser shows how far the fiber has been twisted, and once the instrument is calibrated, the result allows G to be found