3.3-Copernican Revolution

Copernican Revolution

• story of the origin of modern science

• the dramatic change, initiated by copernicus, that occurred when we learned that earth is a planet orbiting the sun rather than the center of the universe

Copernicus

• tables of planetary motion based on the ptolemaic model had been noticeably inaccurate

• tried Aristarchus’s sun-centered idea, first proposed more than 1700 yrs earlier-recognized the much simpler explanation for apparent retrograde motion offered by a sun-centred system

• discovered simple geometric relationships that allowed him to calculate each planets orbital period around the sun and its relative distance form the sun in terms of the earth-sun distance-success convinced him that the sun-centered idea must be correct

What was problematic about the copernicus model?

• primary problem was that he held fast to the ancient belief that heavenly motion must occur in perfect circles

• forced him to add numerous complexities to his system (including circles on circles) to get it to make decent predictions

• complete model was no more accurate and no less complex than the ptolemaic model

Tycho

• First person to make accurate observations within less than 1 arcminute of the sky (naked eye)

• 1563-observed a widely anticipated alignment of Jupiter and Saturn

  • occurred nearly 2 days later than the date copernicus had predicted-compiled careful observations to improve the predictions

  • 1572-observed a “nova”-its lack of observable parallax led him to conclude that the nova was much farther away than the moon-contradicted the ancinet greek belief in unchanging heavens

  • inability to detect stellar parallax led him to conclude that the earth was stationary and must be at center of solar system (but recognized that other planets go around sun)

Kelper

• he believed that planetary orbit should be perfect circles-tried to match circular motions to Tychos observations

• found a circular orbit that matched all of Tychos observations of mars position along the ecliptic (east-west) to within 2 arcminutes-the model didn’t correctly predict mars positions north or south of the ecliptic

• he attempted to find a unified model with a circular orbit-he found that some of his predictions differed from tychos observations by as much as 8 arcminutes (1/4th the angular diameter of the full moon)

• the small discrepancies finally led Kelper to abandon the idea of circular orbits

Kelpers key discovery

planetary orbits are not circles-but an ellipse

• came up with a model that could predict planetary motions with far greater accuracy than Ptolemy’s earth-centered model

Ellipse

a type of oval that happens to be the shape of bound orbits. an ellipse can be drawn by moving a pencil along a string whose ends are ties to 2 tacks; the locations of the tacks are the foci (singularfocus) of the ellipse

• long axis: major axis, each half is called a semimajor axis, the length of the semimajor axis is particularly important

• short axis: minor axis

Eccentricity

• by altering the length of string the same, you can draw ellipses of varying eccentricity

• a quantity that describes hoe much an ellipse is stretched out compared to a perfect circle

• a circle is an ellipse with 0 eccentricity, and a greater eccentricty means a more elongated ellipse

Kelpers laws of Planetary motion

• Kelpers 1st law: the orbit of each planet around the sun is an ellipse with the sun at 1 focus 

• Kelpers 2nd law: as a planet moves around its orbit, it sweeps out equal areas in equal times 

  • This means that a planet travels faster when it is nearer to the sun and slower when it is farther from the sun 

• Kelpers 3rd law: more distant planets orbit the sun at slower average speeds, obeying the relationship p2=a3

  • p=orbital period in years

  • a=avg. Distance from sun in AU

  • 1^2=1^3 is earth

  • Recognize the formula- 2AU do 2x2x2=a 8^2 for p-recognize simple numbers 

1st law

• a planets distance from the sun varied during its orbit

• closest point=perihelion

• farthest point=aphelion

• length of semimajor axis=average of a planets perihelion and aphelion

2nd law

a planet moves faster in the part of its orbit near the sun and slower when farther from the sun, sweeping out equal areas in equal times

• “sweeping” is an imaginary line connecting the planet to the sun, and keeping the areas equal means that the planet moves a greater distance (and hence is moving faster when it is near perihelion than it does in the same amount of time near aphelion)

3rd law

relates orbital time (period), we can use the law to calculate a planets average orbital speed, confirming that more distant planets orbit the sun more slowly

more distant planets move more slowly…

led kelper to suggest that planetary motion might be the result of a force from the sun (gravity)

An asteroid orbits the sun at an average distance a=4 AU. How long does it take to orbit the sun?

• A. 4 yrs, b. 8 yrs, c. 16 yrs, d. 64 yrs

• Remember that p2=a3

b

3 objections to copernican view

1. Aristotle had held that Earth could not be moving because, if it were, objects such as birds, falling stones, and clouds would be left behind as earth moved along its way

2. the idea of noncircular orbits contradicted Aristotles claim that the heavens-the realm of the sun, moon, planets, and stars-must be perfect and unchanging

3. no one had detected the stellar parallax should occur if earth orbits the sun

Galileo diffused 1st objection

• used experiments with rolling balls to demonstrate that a moving object remains in motion unless a force acts to stop it

• explained why objects that share earths motion through space should stay with earth rather than falling behind

Galileo diffused 2nd objection

• saw sunspots in the sun-considered imperfections

• moon has mountains and valleys like the imperfect earth by noticing the shadows cast near the dividing line between light and dark portions of the lunar face

• elliptical orbits, was not so objectionable

Galileo diffused 3rd objection

• based on his estimates of the distances of stars, Tyco believed that his naked eye observations were sufficiently precise to detect stellar parallax if earth did in fact orbit the sun

• have to show that stars are more distant than Tycho had thought

• saw that the Milky Way resolved into countless individual stars-helped argue that the strs were far more numerous and more distant

2 of Galileos earliest discoveries through his telescope

• 4 moons orbiting Jupiter, not earth-showed moons can orbit a moving planet like Jupiter

• observed that venus goes through phases in a way thta makes sense only of it orbits the sun and not earth