Lecture 5

ASTR 111 – Section 002

Outline

1. Quiz Discussion

2. The Moon in its orbit review

3. Gravitation and the Waltz of the Planets – through section 4.3 of text.

The great debate

• Geocentric – Earth is fixed and everything rotates around it.

• Heliocentric – The sun is fixed and everything rotates around it.

The resolution of this question is one of the great examples of the scientific method

The great debate

• Geocentric – Earth is fixed and everything rotates around it.

• Heliocentric – The sun is fixed and everything rotates around it.

The resolution of this question is one of the great examples of the scientific method

Parallax• Apparent

change in an objects position due to a change in the line of sight

• In astronomy we use Apparent and Actual in many contexts. Parallax is one example.

Side note: What is wrong with this picture (from text)?

• What if the nearby object is moving too?

• That is, moving at a speed comparable to the speed of Earth in its orbit?

Typical observations

Projection (in context of celestial sphere)

• Connect point on celestial sphere with a line to the center of Earth. Where line intersects Earth’s surface is where celestial point projects onto Earth’s surface.

• Need two points + a projection point

UP

Top View

If U is fixed and P rotates CCW, what does U see on the wall?

1. Beam traces a line from left to right

2. Beam does not move

3. Beam traces a line from right to left

Will U ever see P reverse directions with respect to the distance stars?

1. Yes

2. No

If U is fixed and P rotates 90o CCW, what does U see on the wall?

1. Beam traces a line from left to right

2. Beam does not move

3. Beam traces a line from right to left

If P is fixed and U rotates 90o CCW, what does U see on the wall?

1. Beam traces a line from left to right

2. Beam does not move

3. Beam traces a line from right to left

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6

78 9

1

Distant “stars”

• In this diagram, are the Republicans to the East or West?• At points 1-8, an observer on Earth will see the planet in

front of a different “star”. Label them below:1. Rush Limbaugh2. 3. 4. 5. 6. 7. 8.

• During which intervals was the planet moving “to the right” and which “to the left”? When was the planet in retrograde motion?

Typical observations

4-5-6 = retrograde motion (westward against background stars)

1-2-3-4 and 6-7=8-9 = protograde (direct) motion (eastward against background stars)

Occam’s Razor

Occam’s Razor

• Law of parsimony

• When all things are equal, choose the theory or model that is simpler or requires fewer assumptions

• As a group, write down two theories for a given phenomena. One theory should not be parsimonious.

Copernicus devised the first comprehensive heliocentric model

• Copernicus’s heliocentric (Sun-centered) theory simplified the general explanation of planetary motions

• In a heliocentric system, the Earth is one of the planets orbiting the Sun

• The sidereal period of a planet, its true orbital period, is measured with respect to the stars

Copernicus devised the first comprehensive heliocentric model

• Some planets always observed near Sun while looking in the sky.

• Some planets are sometimes observed at night and sometimes opposite the Sun.

Inferior planets

superior planets

A planet’s synodic period is measured with respect to the Earth and the Sun (for example, from one opposition to the next)

Copernicus’ heliocentric model was not widely accepted. Why?

• Predictions

• Occam’s razor

Theme• Need. More. Data.

• Need. “Satisfactory”. Mathematical. Theory.

If the Earth was in motion (heliocentric), parallax of nearby stars should appear to shift throughout the year

If the Earth was in motion (heliocentric), parallax of nearby stars should appear to shift throughout the year

If Earth is fixed (geocentric), parallax does not change)

• I measure the angular separation of two dots on the screen from the four corner chairs in this room. Describe what happens to my measurement of the angular separation.

• I sit in the middle of the room and measure the angular separation of two dots on the screen. Someone rotates the walls of the building by 90 degrees. What happens to my measurement of the angular separation?

If Earth is fixed, then parallax angle of stars does not change throughout the year

The heliocentric model

Earth rotates around Sun; stars and Sun are fixed

If Earth is fixed, then parallax

angle of stars changes throughout the year

• Brache did not find a difference in the parallax angle. Did he prove the heliocentric model was incorrect?

One more problem with the geocentric model

• One of Galileo’s most important discoveries with the telescope was that Venus exhibits phases like those of the Moon

• Galileo also noticed that the apparent size of Venus as seen through his telescope was related to the planet’s phase

• Venus appears small at gibbous phase and largest at crescent phase

There is a correlation between the phases of Venus and the planet’s angular distance from the Sun

Galileo’s discoveries with a telescope stronglysupported a heliocentric model

• The invention of the telescope led Galileo to new discoveries that supported a heliocentric model

• These included his observations of the phases of Venus and of the motions of four moons around Jupiter