Download a. What do we mean by a light year?

Astronomy 110-5
Quiz1 – Answers
Fall, 2005
1. a. What do we mean by a light year?
The distance light travels in one year. Distance = Velocity X Time, with the velocity equal
to the speed of light ( 3 × 108 m/sec ) and the time equal to one year( ∼ 3 ×107 sec ) the distance
covered is one light year ( 9 ×1015 m or ~13 trillion miles).
b. Why does looking further into the universe mean we are looking back further in time?
Since light travels at a finite speed it takes a finite time to cover any distance. Therefore the
information it brings to us is about the time the light was emitted, not when the light was
observed. If a star is 10 light years away, light takes ten years to make the trip and tells us
about the star ten years ago. The further away we look the longer light takes to make the trip
and the further back in time we are seeing.
2. a. Describe three different levels of structure in the universe?
Structure in the universe is hierarchical. Stars gas and dust tend to cluster to form galaxies,
galaxies tend to cluster to form clusters of galaxies and clusters of galaxies are found in
super-clusters of galaxies.
b. How are stars in a constellation related?
Stars in a constellation are not related at all other than the fact that they appear to be within
the angular boundaries of a given constellation. In general they are not physically close or
related in any way like mass, age or type.
3. Describe how you would make your own celestial sphere?
I would identify the one pole I can see and mark its location on the sphere. I would then
mark the stars in the vicinity of the pole on the sphere in their correct angular orientations
with respect to each other. I would extend the map over all the stars that are visible to me
over the year by adding them in their correct angular positions on the sphere.
What measurements would you have to make?
The measurements you have to make are the relative angular positions of a given star with
respect to the stars around it. The locations of any two stars on my celestial sphere have to
be the same angular separation when measured from the center of the sphere as the stars
they represent are in the sky. We can imagine shrinking ourselves to a point at the center of
the sphere and then marking the stars on the sphere as they are seen through the sphere.
Could you do it all in one night? One month? How long would it take?
No it takes at least one year to see all the stars that can be seen from any position on the
Earth. Then we would have to repeat the whole exercise for the southern Hemisphere - so
two years is the minimum time. If we had a very clear sky all the way down to the horizon we
could imagine taking one all-sky image at the North Pole and one at the South Pole and then
processing the data to make a complete celestial sphere with only two nights of work. You
can see all-sky images at www.concam.net.
4. a. Describe the coordinate system we use to identify points on Earth.
On earth we use latitude and longitude. Latitude measures the angular distance we are
north or south of the equator as measured from the center of the Earth. Lines of latitude are
parallel to one another and form circles whose radius decreases as we approach the poles.
Longitude measures how far east or west we are from an arbitrary pole-to-pole cut through
the earth going through Greenwich England (the Prime meridian). Lines of longitude are
great circles – they each cut the earth in half.
b. How do we extend this coordinate system to the sky?
The, equator, north, and south poles are projected onto the sky (as seen by an observer at the
center of the Earth). We then define a star's position by whether it is north or south of the
celestial equator (declination) and its right ascension, its position east or west of one
intersection of the celestial equator with the ecliptic (the vernal equinox).
5. Define the ecliptic? Explain why a point on the ecliptic is both a date and a direction in
the sky.
The ecliptic is the apparent path the Sun makes around the earth in the course of a year.
Since we map out the ecliptic by plotting the sun's position relative to the celestial sphere as
it moves across over the year any point on the ecliptic is, by definition a point on the sky –
i.e. a direction in space. I also represents the date that the sun will be at the point on the sky.
6. Define the zenith and the horizon.
The zenith is the direction directly overhead for a given observed. It is an extension of the
direction of the radius of the earth onto the night sky. The horizon is the plane tangent to the
earth at the observer's location. It is the boundary between what can and cannot be observed
in the sky at that location.
Show how different observers on the earth have a different horizon.
Because the earth is a sphere its local tangent plane tilts continuously as we move north or
south of the equator. Moving from the equator to 30 degrees north latitude, for example tilts
our horizon by 30 degrees with respect to where it was at the equator. Note that observers at
the north and south poles have the same horizons but the sense is reversed. What is visible in
the night sky for one is blocked by the earth for the other.
When we say that "the sun rises out of the eastern horizon" explain what is really
happening.
The earth is rotating counterclockwise when we look down onto the North Pole. Therefore,
for a given observer, it is always his eastern horizon that leads the rotation and will rotate
past the sun first (dawn). We take the earth to be standing still and talk about the sun rising.
7. Where in the sky is the full moon at midnight?
The full moon rises as the sun sets so in the middle of the night it will be overhead.
Why don't we see an eclipse every full and new moon?
The plane of the moon's orbit it tilted by about 5 degrees with respect to the ecliptic.
Therefore, to see an eclipse not only must the earth, moon and sun be aligned in three
dimensions. Full and new moon assure that they are lined up as we look down on the ecliptic
plane, but because of the tilt of the moon's orbit the moon can be above or below the earthsun line at that moment. To have an ecplipse we must have a full or new moon and the moon
must be also crossing the ecliptic plane.
8. At the North Pole all stars are circumpolar. Explain why this is true.
At the North Pole the observer's horizon plane is at right angles to the spin axis of the earth.
That means that as the earth spins it does not wobble at all. So whatever stars are above the
observer's horizon plane are always above her horizon plane since the plane never changes
its orientation. The trajectories of stars over the course of the evening are circles in the sky
parallel to the horizon.
How is the Arctic Circle defined?
As we move further north of the equator the seasonal variation in day night difference
becomes more extreme until at the latitude of the Arctic Circle we reach a latitude on the
earth where on the day of the solstice the sun either does not rise or set at all . This only
occurs on the day of the solstice at the Arctic Circle but as we move further north it occurs
for a period of time around the solstice that increase as we get closer to the poles. Finally,
at the poles, the day night cycle is six months long since the only thing that can move the
poles from darkness to daylight is the orbital motion of the earth itself.
9. Describe two ways in which Galileo's observations refuted classical Greek assumptions
about the nature of the solar system?
Galileo led several attacks on the classical notions of the laws of nature and the structure of
the solar system:
a. His observations of Jupiter showed that other objects in the universe can be
centers of rotation.
b. His observations of the moon and sun showed that they are not perfect spheres.
c. His studies of the acceleration of gravity showed that the classical concepts of
gravity were wrong.
d. His studies of motion led the way to Newton's first law and showed that the solar
system did not need to be constantly driven to stay in motion.
10. State and illustrate Kepler's second law? How would Newton explain the physical basis
behind this law?
Kepler's second law states that as each planet moves abut the sun the radius joining the
planet to the sun sweeps out equal areas in equal time. (See pictures in lecture notes) Newton
proved that this was true by showing that in the absence of outside forces angular momentum
of the planet was conserved. That means that it speeded up when it was closer to the sun and
slowed down when it was further from the sun. The angular momentum turned out to be
proportional to the rate at which the sun-planet radius swept out area so that if angular
momentum was conserved Kepler's second law had to follow.
11. State and illustrate Newton's third law?
For every action there is an equal and opposite reaction. You cannot apply a force without
feeling a force. If you try to hit something you hurt your hand.
What is the difference between mass and weight?
Mass is an intrinsic property. It represents a bodies resistance to being accelerated and it is
independent of the circumstances – where, when etc. Weight is the force of attraction on an
object as a result of gravity caused by other masses. Your weight will change on the moon or
mars relative to the Earth but not your mass.
12. Are the tides higher at the full moon or the quarter moon? Why are there two high tides a
day?
Both the moon and the sun create a tidal bulge of land and sea on the earth because the tidal
forces they create apply a stretching force to the earth. When the earth moon and sun are
lined up in any order the stretching force, and the tidal bulges from the moon and sun add up
to create higher tides. Because the stretching pulls roughly along the line joining the earth
to the sun or moon, bulges are created in each case on both sides of the earth. Therefore any
point on the earth will rotate through two bulges in 24 hours giving two high and low tides a
day.