Question 1

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The Little Dipper is in the constellation  blank . It is  blank for observers in in mid-latitudes in the  blank . The official name of the constellation called the Scale is  blank . It is  blank for those same observers. It rises in the East, culminates in the South, and sets in the West for observers in the  blank . For observers in the  blank , it rises in the East, culminates in the North, and sets in the West.


equatorequator southern hemispheresouthern hemisphere northern hemispherenorthern hemisphere
not circumpolarnot circumpolar below horizonbelow horizon circumpolarcircumpolar
LibraLibra Ursa MinorUrsa Minor MuscaMusca LeoLeo Ursa MajorUrsa Major

Question 2

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How squashed/elongated an ellipse is is quantified by the of the ellipse, the units of which are .

How much off-center the Sun is relative to the orbit of an object is quantified by the of the ellipse. When that quantity is expressed as a fraction of the semi-major axis, it is called the of the ellipse, the units of which are .

Elliptical orbits which are circular have an aspect ratio of and eccentricity of . For those orbits, in terms of ellipse parameters, the distance between the Sun and the planet equals .

Elliptical orbits that are strongly elongated to a point where they are indistinguishable from straight lines have an aspect ratio of and eccentricity of . For an object on such an orbit, the distance between the Sun and the object at aphelion equals since at perihelion such an object would hit the Sun.

To within 1% accuracy, orbits that have an eccentricity between 0 and 0.01 can be considered with the Sun . Orbits with eccentricity between 0.01 and 0.15 can be considered with the Sun . Orbits with eccentricity close to 1 are with the Sun very close to the object when the object is in . Orbits with eccentricity between 0.15 and 1 can only be described as .


Question 3

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The apparent rocking side-to-side motion of the Moon in the sky is called .

The Moon always faces Earth with the same side. That's caused by the fact that the rotation of the Moon around its axis and its revolution around the Earth are . But that's only an approximation.

According to Kepler's law, the orbit of the Moon is not perfectly circular, and is instead , with the Earth at one of the of the ellipse. Since the Earth is not in the center of the elliptical lunar orbit, at different times during a lunar month, observers on Earth have slightly different vantage points when looking at the Moon. That's one part of the reason for lunar libration.

The other reason is due to Kepler's law. According to that law, the motion of the Moon around Earth is not uniform -- sometimes the Moon moves slower, and sometimes faster on its orbit. Thus, even though on average the rotation and revolution of the Moon are synchronized, those motions are not perfectly in sync within a single period. So, for example, when the Moon rotates by a quarter turn around its axis, it doesn't make exactly a quarter revolution around the Earth. Thus, within a single month, the Moon presents slightly different parts of its surface to Earth's observers.

The effect can be observed in the following simulation of the Moon as it would be seen from Earth if there were no lunar phases:

The fact that the angular diameter of the Moon changes periodically is due to the fact that the Moon is on an elliptical orbit, and therefore its distance to Earth changes in a periodic fashion.


Question 4

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Now let's move to the Moon.

If you are an observer on the Moon, standing in the center of the visible side of the Moon, Earth will always be close to the and will never set.

However, if you are an observer sitting close to the border between the visible and the far side of the Moon, then the lunar libration is going to cause the Earth's center to dip below the horizon and then pop up again. (The Earth is pretty large in angular diameter in the lunar sky, so may not completely hide below the horizon.) Look at the animation in the previous problem to try to picture that.

How often would the Earth's center rise above the horizon for such an observer? Once every days.


Question 5

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You discover a new asteroid orbiting the Sun! It has a semi-major axis of 8.66AU. Find the period of its orbit in years.


Question 6

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You send an artificial satellite on a circular orbit around Earth. You want it to orbit Earth every 1.798 hours.

What is the orbital radius (in km) of that satellite?


Question 7

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You send an artificial satellite on a circular orbit around Earth. You want it to orbit Earth every 1.798 hours.

At what altitude above Earth's surface (in km) does the satellite orbit Earth?


Question 8

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You send an artificial satellite on a circular orbit around Earth. Its orbit around the Earth has a period of 1.798 hours. The satellites linear diameter is 1.1m.

Find the maximum angular diameter of the satellite in arcseconds for an observer at sea level.


Question 9

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The distance to the Sun is 8.3 light-minutes. How much time (in minutes) does it take for X-rays to travel from a solar flare on the Sun to Earth?


Question 10

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Below you will be working on identifying features of Starry Night by Vincent van Gogh, pictured below in his self-portrait.

Identify the horizon, the Moon, and two bright stars in the top-left corner, lying on the main diagonal.


Background image for dragging markers onto
StarStarTreesTreescloudscloudsMoonMoonHorizonHorizon

Information

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The questions below (after the first two) use parametrically defined database variables. For example by setting a shared variable to t = r 3 / 2 then t is defined using r (which must be defined before t). The equation used in defining parametrically defined variables must contain valid Python functions (with Numpy imported as "np"). To force a variable to be saved along with a question in the xml file, you can add that variable with a coefficient of zero in the equation, such as {r} + {t}*0.


Question 11

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An asteroid is going on a circular orbit around the Sun, some 0.707 AU away from it.

Find the angle (in degrees) between greatest eastern elongation of the asteroid and the Sun (as viewed from Earth).


Question 12

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An asteroid is going on a circular orbit around the Sun, some 0.707 AU away from it.

Find the angle (in degrees) between the asteroid and Earth as viewed from the Sun when the asteroid is in greatest western elongation (for us).


Question 13

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An asteroid is going on a circular orbit around the Sun, some 0.707 AU away from it. Its period is 0.594 years.

Find the synodic period of the asteroid in years.


Question 14

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An asteroid is going on a circular orbit around the Sun, some 0.707 AU away from it. Its period is 0.594 years.

Find the time (in days) between two consecutive inferior conjunctions of the asteroid.


Question 15

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An asteroid is going on a circular orbit around the Sun, some 0.707 AU away from it. Its period is 0.594 years.

Find the time (in days) between greatest eastern elongation and inferior conjunction.


Question 16

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An asteroid is going on a circular orbit around the Sun, some 0.707 AU away from it. Its period is 0.594 years.

Find the time (in days) between superior conjunction and greatest western elongation.


Question 17

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You discovered an asteroid! You find out that the time between two consecutive oppositions is 1.36years.

Find the time (in days) between two consecutive western quadratures.


Question 18

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You discovered an asteroid! You find out that the time between two consecutive oppositions is 1.36 years. You also measure the time between western quadrature and opposition to be 90.8 days.

Find the distance (in AU) between the asteroid and the sun.


Question 19

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You discovered an asteroid! You find out that the time between two consecutive oppositions is 1.36 years.

Find the sidereal orbital period of the asteroid in years.


Question 20

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Find the order of magnitude difference between 154000000.0 and 55700000000000.0.


Question 21

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Below you see a set of current-carrying wires and coils. Fill in the magnetic field directions missing in the figure. In (III) the current in the wire is pointing up the page. In picture (IV) it is pointing down the page.


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blank 
blank 
blank 
blank 
blank 
blank 
B=0
B=0
B=0
B=0

Question 22

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Four identical bulbs are connected to two batteries as follows:

What are true statements about the brightness of the different bulbs:


Select one or more:
a.
None of the bulbs will light up.
b.
A > B
c.
A < B
d.
A = B
e.
B > C
f.
B < C
g.
B = C
h.
A > D
i.
A < D
j.
A = D

Question 23

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If this were true, then 2+2=5.


Question 24

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Match to construct correct comparisons.


The observable Universe is to the Milky Way as the Empire State Building is to
The Sun is to a human as a human is to
The Sun is to Earth as the Empire State Building is to
Earth is to a human as a human is to
A city is to the Sun-Earth distance as a grain of salt is to
The US is to a city as a city is to
The observable Universe is to the Sun as the Earth is to
The age of the universe is to a human lifespan as a human lifespan is to
A human lifespan is to a heartbeat as a heartbeat is to
The Sun is to a city block as the Empire State Building is to
The Milky Way is to 1/10 of a light-year as the Empire State Building is to
1/10 of a light-year is to the Sun as the Empire State Building is to
The distance to Proxima Centauri is to the size of the Sun (which also roughly matches the distance to the Moon) as a city is to
A proton is to an atom as a red blood cell is to
The distance to Proxima Centauri is to the distance to the Sun as the US is to
The time since the dinosaurs went extinct is to a heartbeat as a heartbeat is to
A heartbeat is to a year as a year is to
The distance between the Milky Way and the Andromeda galaxies is to the size of the Milky Way as a human is to
A red blood cell is to an atom as a human is to
The Solar System is to Earth as the US is to
The Milky Way is to the distance to Proxima Centauri as a human is to
A heartbeat is to an hour as a human lifespan is to
A human is to a grain of salt as a city is to

Question 25

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Write an essay on ...


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Question 26

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How many nodes are on this standing wave?


Question 27

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How many antinodes are on this standing wave?


Question 28

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Answer the following questions about the standing wave below.


How many nodes are on this standing wave?

How many antinodes are on this standing wave?

Question 29

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A 1m stick vertically placed on the ground casts a shadow of length 3.01m. Find the height of the Sun above the horizon in degrees.


a.
The answer is: 18
b.
Definitely not: 19
c.
Not this one: 71
d.
The answer is: 0.32 ... or is it?