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Greek Astronomy - The Spherical Earth

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Greek Astronomy - The Spherical Earth

● In addition to this eclipse-based observation of the Earth's sphericity A spherical Earth was also supported by– distant ships disappearing over

the horizon

– change in the altitude of the pole stars with changing location, and visibility of southern stars that were otherwise invisible at more northerly locations.

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Eratosthenes and the Size of the Earth● On the same day separated locations show Noon shadows of

different length indicating an angular difference in the altitude of the Sun.– Assuming a spherical Earth one can calculate it's circumference knowing

this angle difference and the physical distance between the two sites.

4Aristarchus and the Relative Distances of the Moon and Sun

● Half moon occurs close enough to 90 degrees around the Moon's orbit that the Sun must be substantially further away than the Moon.– Since they have the same angular size – the Sun must be much bigger than

the Moon and Earth.

– A big Sun naturally motivates the heliocentric model (250 B.C.).

In the illustration above is noticeably less than 90o requiring a relatively nearby Sun.

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The Lunar Crater Aristarchus

● Very bright!

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The Dogma of the Time

The lack of observable stellar parallax (either geocentric/diurnal or annual) combined with the sensation that the Earth was stationary led to an Earth-centered view of the Universe.

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The Dogma of the Time

The lack of observable stellar parallax (either geocentric/diurnal or annual) combined with the sensation that the Earth was stationary led to an Earth-centered view of the Universe.

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Explaining Retrograde Motion

The Greek astronomer Ptolemy (85-165 A.D.) successfully created a model that explained the complex observed planetary motion in the context of the dogmatic restrictions of the time.

All motions were perfect circles.

The rate of motion was constant and unchanging.

Explain this????

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Prior to the Renaissance

Ptolemy solved the problem of retrograde motion by postulating spheres embedded within spheres (more than 40) all turning at uniform speed.

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Prior to the Renaissance

Ptolemy solved the problem of retrograde motion by postulating spheres embedded within spheres (more than 40) all turning at uniform speed.

Even more complexity... constant angular motion about the “equant” (point Q).

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Prior to the Renaissance

Alfonso X, King of Castille in the 13th century noted, “If the Lord Almighty had consulted me before embarking on the creation, I should have recommended something simpler.”

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Prior to the Renaissance

This statement captures the essence of “Occam's Razor” - the simplest explanation for a phenomenon is usually right.

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Copernicus

It wasn't until more than a thousand years later that the Heliocentric model advocated by Aristarchus was revived.

Copernicus asserted that things would be much simpler with the Sun in the center.

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Copernicus

Specifically, the Copernican model made the explanation of retrograde motion simple and obvious.

http://www.lasalle.edu/~smithsc/Astronomy/retrograd.html

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Planetary Configurations

● Superior vs. inferior planets

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Planetary Configurations

● Inferior planets

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Planetary Configurations

● Inferior planets

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Inferior Planets as “Evening Stars”

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Planetary Configurations

● Superior planets

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Synodic vs. Sidereal Orbital Periods

● Sidereal orbital periods reference the orbit to the Universe (the true orbital period).

● Synodic period measures the time from opposition to opposition.

1P sid

= 1PEarth

+ 1P syn

1P syn

= 1P sid

− 1P Earth

for Inferior Planets

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Synodic vs. Sidereal Orbital Periods

● The synodic period of distant (almost stationary planets) is not much longer than a year.

● Near Earth asteroids can have synodic periods of decades.

1P sid

= 1PEarth

− 1P syn

1P syn

= 1PEarth

− 1P sid

for Superior Planets

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Copernicus

It wasn't until more than a thousand years after Aristarchus that the Heliocentric model was revived.

Copernicus asserted that things would be much simpler with the Sun in the center.

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Renaissance Astronomy

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Galileo

Began a longstanding tradition of quick application of new technology to enable astounding astronomical discoveries.

He put the telescope to astronomical use within a couple of years of its invention – just over 400 years ago

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Galileo

Began a longstanding tradition of quick application of new technology to enable astounding astronomical discoveries.

These observations were the first to provide strong direct observational support for the Copernican heliocentric mode.

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Galileo: Craters on the Moon, Spots on the Sun

The Heavens weren't perfect, in fact they could be downright terrestrial.

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Galileo: Phases of Venus

Venus showed phases that changed over time and that were consistent with the Copernican model.

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Galileo: Jupiter's Moons

Galileo discovered four satellites in orbit around Jupiter, and obeying Kepler's Harmonic Law.

I should disclose and publish to the world the occasion of discovering and observing four Planets, never seen from the beginning of the world.... I noticed three little stars...near the planet...arranged exactly in a straight line... When I turned again to look [a few nights later]... I found a very different state of things.

I therefore concluded... that there are three stars in the heavens moving about Jupiter, as Venus and Mercury around the Sun.

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Galileo: Jupiter's Moons

Any object could serve as the center of motion – so why not the Sun. Jupiter was an example of the Solar System in miniature.

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Galileo and Neptune

Another notebook page shows an object that moved with respect to the background stars over a few nights.

Galileo made a note of it but did not follow up.

It was Neptune...

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Galileo and Supernovae

Galileo, Tycho, and Kepler all observed supernovae and recognized that, because they didn't show parallax, these objects were part of a changing celestial sphere.

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Galileo and the Church

Galileo died a prisoner, having been under house arrest imposed by the Inquisition for a decade.

Although characterized by many as a conflict between science and religion, the details are much more complex.

Many in the Church accepted Galileo's conclusions and even confirmed the observations for themselves.

Many refused to look through a telescope and were compelled to enforce the longstanding dogma of a stationary Earth.

Galileo had both friends and enemies. He was a stubborn, irascible, and outspoken character who was successful and popular. His enemies were thus well-motivated to plot his demise.

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I have been told by a friend of mine, a priest who is very fond of you, that a gang of ill-disposed men, who are envious of your virtue and merits, met at the residence of the Archbishop of Florence, and put their heads together in a mad quest for some means by which they could damage you, either with regard to the motion of the Earth or otherwise. One of them asked a preacher to state from the pulpit that you were asserting outlandish things. The priest, seeing the animosity against you, replied as a good Christian and a member of a religious order ought to do. I write this that your eyes may be open to the envy and malice of these evildoers.

In 1992, Pope John Paul II expressed formal regret for the handling of the Galileo affair and acknowledged that the church had made errors.

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Galileo's tomb at Santa Croce

Galileo – a Catholic perspective

Galileo biography