Lecture 3 ASTR 111 – Section 002

Terms Apogee/Perigee Subtend Parsec, light-year, AU Parallax Solar and Sidereal time Small angle formula Ecliptic Zenith Tropic of Cancer, Capricorn, Artic and Antarctic Circle Equinox, Solstice Zodiac

Notes on Lecture Notes Sent out Tuesday afternoon/evening I suggest that you print them out and bring them to class I will also post PowerPoints If you have problems with the file, email me!

Outline Quiz Discussion Rotation – review generally The Seasons – finish lecture tutorial The Moon in its orbit Math Review – converting units and scientific notation

#3 In class, we estimated the angular separation of two points on the screen that were separated by 10 feet. Suppose that these two points were separated by 1 AU. How far away from the screen would you need to walk so that the dots appeared to subtend 1 arc-second?

B A

Gods-eye view Observer’s view “

#4 How many light-years are in 10 parsecs? How many parsecs are in 5 light-years?

Units conversion Start with a relationship like 1 degree = 60 arcminutes To convert from degrees to arcminutes, set up a ratio so the unit you want to get rid of cancels Example: how many arcminutes is 0.5 degrees?

Units conversion Start with a relationship like 1 parsec = 3.26 light-years To convert from parsec to light years, set up a ratio so the unit you want to get rid of cancels Example: How many light-years are in 5 parsecs?

#6 In the image, suppose that a star in the constellation Cygnus appears exactly at an observer's zenith (the dotted line) at 8 pm local time. After 24 solar hours have passed, where would the constellation appear to be?

Outline Quiz Discussion Rotation – review generally The Seasons – finish lecture tutorial The Moon in its orbit Math Review – converting units and scientific notation

Thinking about rotation With parallax, we learned that the position of a near object relative to a distant object can change if the observer moves. With rotation, the time it takes for the position of a near object to change relative to a distant object can be different if the observer moves.

Thinking about rotation In the last lecture I had you do an experiment with a quarter to illustrate this point: When one object “B” rotates about another object, the number of times it rotates with respect to something in the distance depends on if “B” is rotating on its axis.

Slippage Meaning When you skid a tire, there is slippage – same part of tire always touches ground When you roll a tire, there is no slippage – different parts of tire touch ground

George B looking straight to the left (at a distant object) B Table

I can get him across the table by “skidding” or “slipping” – the 9 always touches the table. In this case he always is looking to the left at the distant object. B Table

Instead of “skidding” or “slipping”, he can “roll” Instead of “skidding” or “slipping”, he can “roll”. On a flat table, he will look at same place in distance after 1 revolution – or after he has “rolled” the distance of his circumference B Table

Group Question Rotate B around A with slippage. How many times does George B look straight to the left? With slippage, the 9 on the top quarter always touches the bottom quarter Rotate B around A without slippage (like a gear). How many times does George B look straight to the left? Without slippage, first the 9 in the 1993 on the top quarter touches the bottom quarter, then 1 then the “In God We Trust”. B A (A is glued to the table)

Group Question B A One time Two times Rotate B around A with slippage. How many times does George B look straight to the left? With slippage, the 9 on the top quarter always touches the bottom quarter Rotate B around A without slippage (like a gear). How many times does George B look straight to the left? Without slippage, first the 9 in the 1993 on the top quarter touches the bottom quarter, then 1 then the “In God We Trust”. One time B A Two times (A is glued to the table)

With slippage A B The nine on B always touches A

Without slippage B B A B B Note: George B only looks directly at George A’s center one time right about here B “rolls” on A, in the same way a tire rolls on the ground. B B A B B George B is looking to the left again here!

Summary When the coin slipped across the table, it did not rotate at all. When a coin slipped around another coin, it rotated once with respect to the “distance”. When a coin rolled across a table the distance of its circumference, it rotated once. When it rolled the same distance, but around another coin, it rotated twice with respect to the “distance”.

What to know When thinking about rotation, you need to account for rotation about its own axis and rotation about another object. The number of times you see something in the distance will be different than the number of times you look at the object that you are rotating around.

Someone in back of room (distant object) Top view of classroom Someone in back of room (distant object) Stage Student Instructor

Or Sidereal Time = star time Sidereal Day = the length of time it takes for a star to repeat its position in the sky. Solar Time = sun time Solar Day = the length of time it takes the sun to repeat its position in the sky.

Sidereal Time = star time Solar Time = sun time At 1, line points at sun and distant star Line 1 goes through sun and distant star

Sidereal Time = star time At 2, 24 sidereal hours since 1, line is now pointing at distant star only Sidereal Time = star time Solar Time = sun time Line 1 goes through sun and distant star At 1, line points at sun and distant star Line 1 goes through sun and distant star

Sidereal Time = star time At 2, 24 sidereal hours since 1, line is now pointing at distant star only Sidereal Time = star time Solar Time = sun time Which is longer? Sidereal day Solar day At 1, line points at sun and distant star At 3, 24 solar hours since 1, line points at sun only

Sidereal Time = star time At 2, 24 sidereal hours since 1, line is now pointing at distant star only Sidereal Time = star time Solar Time = sun time Which is longer? Sidereal day Solar day by ~ 4 min. At 1, line points at sun and distant star At 3, 24 solar hours since 1, line points at sun only

Key A solar day is longer than a sidereal day This means it takes longer for the sun to repeat its position in the sky than a distant star

Which way is Andromeda at 8:00 pm local time for the person in California? West East Vertical West East Vertical

Where is Cygnus 24 sidereal hours later? West East Vertical

Where is Cygnus 24 solar hours later? West East Vertical West East Vertical

Outline Quiz Discussion Rotation – review generally The Seasons – finish lecture tutorial The Moon in its orbit Math Review – converting units and scientific notation

What causes the seasons? Distance of the sun from earth Tilt of Earth with respect to the ecliptic Both None of the above Primarily 2., but with a small contribution from 1.

What causes the seasons? Distance of the sun from earth Tilt of Earth with respect to the ecliptic which causes Change in length of time sun is visible Change in height of sun in sky Both None of the above Primarily 2., but with a small contribution from 1.

The ecliptic is the imaginary plane that the Earth moves on as it rotates around the sun

The Celestial Sphere Sometimes it is useful to think of the stars and planets as moving along a sphere centered on Earth

Figure 2-16 The Sun’s Daily Path Across the Sky This drawing shows the apparent path of the Sun during the course of a day on four different dates. Like Figure 2-10, this drawing is for an observer at 35° north latitude.

Important! The angle of the light to the ground. Figure 2-17 Tropics and Circles Four important latitudes on Earth are the Arctic Circle (661⁄2° north latitude), Tropic of Cancer (231⁄2° north latitude), Tropic of Capricorn (231⁄2° south latitude), and Antarctic Circle (661⁄2° south latitude). These drawings show the significance of these latitudes when the Sun is (a) at the winter solstice and (b) at the summer solstice. Important! The angle of the light to the ground.

Figure 2-17 Tropics and Circles Four important latitudes on Earth are the Arctic Circle (661⁄2° north latitude), Tropic of Cancer (231⁄2° north latitude), Tropic of Capricorn (231⁄2° south latitude), and Antarctic Circle (661⁄2° south latitude). These drawings show the significance of these latitudes when the Sun is (a) at the winter solstice and (b) at the summer solstice.

Figure 2-17 Tropics and Circles Four important latitudes on Earth are the Arctic Circle (661⁄2° north latitude), Tropic of Cancer (231⁄2° north latitude), Tropic of Capricorn (231⁄2° south latitude), and Antarctic Circle (661⁄2° south latitude). These drawings show the significance of these latitudes when the Sun is (a) at the winter solstice and (b) at the summer solstice.

The two circled yellow arrows point to the same line of latitude. Figure 2-17 Tropics and Circles Four important latitudes on Earth are the Arctic Circle (661⁄2° north latitude), Tropic of Cancer (231⁄2° north latitude), Tropic of Capricorn (231⁄2° south latitude), and Antarctic Circle (661⁄2° south latitude). These drawings show the significance of these latitudes when the Sun is (a) at the winter solstice and (b) at the summer solstice. The two circled yellow arrows point to the same line of latitude. The right arrow is perpendicular to surface. The left arrow is less than perpendicular to surface.

Thinking about light It is often useful to think of photons as very small particles. When I point a flashlight at you, you are getting hit with a bunch of little pellets. Suppose you were hit by 10 pellets in an area the size of a quarter. How does this compare with getting hit with 10 pellets over an area the size of a book?

Figure 2-13 Solar Energy in Summer and Winter At different times of the year, sunlight strikes the ground at different angles. (a) In summer, sunlight is concentrated and the days are also longer, which further increases the heating. (b) In winter the sunlight is less concentrated, the days are short, and little heating of the ground takes place. This accounts for the low temperatures in winter.

See Seasons Lecture Tutorial at end F

Outline Quiz Discussion Rotation – review generally The Seasons – finish lecture tutorial The Moon in its orbit Math Review – converting units and scientific notation

Eventually we want to be able to explain …

A simple model Moon executes circular orbit Moon orbit is in Earth’s ecliptic plane

What is wrong with this picture?

Fill in the dark and light parts of the Moon for A-D (from this perspective) From the perspective of someone on Earth what position of A-E best fits the Moon view in the lower-left-hand corner? In the blank boxes below, sketch how the Moon would appear from Earth from the four Moon positions that you did not choose for Question 2. Label each box with a letter. A E Sun’s rays Earth D B C View of Moon from Earth at one of the positions (A-E) above.

Shade in the part of the Moon that is not illuminated by the sun when it is at positions F-I. Which Moon position (F-I) best corresponds with the Moon phase shown in the lower-left corner? How much of the Moon’s surface is illuminated by the sun during this phase? How much of the Moon’s illuminated surface is visible from Earth for this phase of the Moon? G Sun’s rays F H Earth I View of Moon from Earth from one of the positions (F-I) above.

Model can explain the phases of the Moon The phases of the Moon occur because light from the Moon is actually reflected sunlight As the relative positions of the Earth, the Moon, and the Sun change, we see more or less of the illuminated half of the Moon.

What does the Earth look like from the Moon at Full Moon New Moon First Quarter Third Quarter

What are 2 observations simple model does not predict?

What are 2 observations simple model does not predict? Why there are not eclipses every month Why there are “annular” and “total” eclipses

Eclipses occur only when the Sun and Moon are both on the line of nodes

What are 2 observations simple model does not predict? Why there are not eclipses every month Why there are “annular” and “total” eclipses of the sun

Solar eclipses can be either total, partial, or annular, depending on the alignment of the Sun, Earth, and Moon

Lunar eclipses can be either total, partial, or penumbral, depending on the alignment of the Sun, Earth, and Moon

Question If you were looking at Earth from the side of the Moon that faces Earth, what would you see during A total lunar eclipse? A total solar eclipse?

The Moon’s rotation always keeps the same face toward the Earth due to synchronous rotation

Time and the Moon Two types of months are used in describing the motion of the Moon. With respect to the stars, the Moon completes one orbit around the Earth in a sidereal month, averaging 27.32 days. The Moon completes one cycle of phases (one orbit around the Earth with respect to the Sun) in a synodic month, averaging 29.53 days.

sidereal month, averaging 27.32 days. sidereal day – 23 hr 56 min synodic (lunar) month, averaging 29.53 days. solar day – 24 hr

Question On a certain date the Moon is in the direction of the constellation Gemini as seen from Earth. When will the Moon next be in the direction of Gemini? One year later? 366.2425 days later? One sidereal month later? One synodic month later?