Animations of Retrograde Motion
|
Compass Directions Seasons Planet Motions in the Sky Motion and Newton's Laws |
Rising and Setting Moon Phases Kepler's Laws Gravity |
Time of Day Eclipses Models of the Universe |
Imagine you are looking down on the Earth from out in space. For a person standing at the place marked ``X'' north of the equator, what is the correct orientation of the directions?
Answer: 4. Hint: Maybe it helps to visualize looking at a globe:
which direction would "W" be from this perspective? Or you could try
and visualize yourself at the ``X''.
Imagine you are looking down on Earth's North Pole from out in
space. For a person standing at the place marked ``X'', what is the correct orientation of the directions?
Answer: 4. Hint: This is almost the exact same orientation as
in the previous question. ``N'' is the direction of the pole.
Imagine you are looking down on Earth's North Pole from out in
space. For a person standing at the place marked ``X'', what is the correct orientations of the directions?
Answer: 1. Hint: Imagine yourself at the ``X''. If you are
looking south, west will still be to your right.
Which direction does the person have to look to see the star shown below?
In what direction should you face to see this star when it is highest in the sky?
If you could see stars during the day, this is what the sky would look
like at noon on a given day. The Sun is near the stars of the
constellation Gemini. Near which constellation would you expect the
Sun to be located at sunset?
If you are standing at the North Pole, how would stars appear to move
around the sky?
If you are standing on the equator and looking east, stars will appear
to move...
If you look due north from San Diego, which picture shows how stars
would move across the sky during a night? (Remember the North
Star.)
Answer: 2. Hint: The North Star stands still in the sky. Stars
still have to rise (or get higher in the sky) to the east, and set (or
get lower in the sky) to the west.
Stars that never appear to set are called circumpolar. As you move
from Earth's equator toward the North Pole, the number of stars that
are circumpolar
For the person at position B in the diagram above, roughly what time
of day must it be?
Looking down on the Earth from above the North Pole, the Earth will
About what time of day would it appear to be for the person shown?
About what time of day would it appear to be for the person shown?
("NP" is the North Pole.)
On November 21st, which constellation will be on the opposite side of
the sky from the Sun?
Which of the people shown would see the Sun as being highest overhead?
In the diagram above, what season is it for person 1 in the northern
hemisphere?
Which of the following statements about the location of the Sun at
sunrise in the middle of winter is true?
As seen from your current location, when will an upright flagpole cast
NO shadow (because the Sun is directly above the flagpole)?
If the Sun is high in the sky to the southeast, what will the shadow
of a stick be like?
Which of the people shown would collect more sunlight?
If it is summertime right now, how does the altitude of the noontime
Sun change (if at all) as winter approaches?
The diagram below show possible ways of setting up Earth's orbit and
Earth's rotation axis. In the two cases, would the Sun appear to
change in size during a year?
The diagram above show possible ways of setting up Earth's orbit and
Earth's rotation axis. In the two cases, what season would it be in
the souther hemisphere if it is summer in the northern hemisphere?
Imagine the picture below shows the view of Earth from the Sun.
To someone in the northern hemisphere, what would day and night be like?
Imagine the picture below shows two views of Earth from the Sun.
To someone in the northern hemisphere, when would the
Sun be higher in the sky at noontime?
The pictures on the right side of the diagram below show views of the
Earth from the Sun. Which one corresponds to summer in the southern
hemisphere?
Answer: 3. Hint: Which one shows the southern hemisphere tilted
toward the Sun.
If the Earth is oriented as shown in the diagram, are there places where it
will be dark for more than 24 hours at a time?
What would seasons be like on the planet shown below?
The diagram below shows Earth and the Sun as well as 5 different possible
positions of the Moon. Which position of the Moon best corresponds with the
phase of the Moon shown in the box?
Answer: 4. Hint: The Moon's phases are caused by its own
shadow, not the Earth's shadow. At position 5, the Moon would also be
crescent, but with the lit portion on the right.
How much of the Moon's entire surface is illuminated by the Sun
during the phase shown in the box above?
How much of the Moon's illuminated surface is visible from Earth
during the phase shown in the box above?
The diagram below shows Earth and the Sun as well as 5 different possible
positions of the Moon. Which position of the Moon best corresponds with the
phase of the Moon shown in the box?
Answer: 2. Hint: At position 1 or 2, the Moon will appear more
than half lit. At position 1, the Moon would have the dark portion on
the left. You can try this out with a tennis ball and a strong light
bulb (your head plays the role of Earth.)
How much of the Moon's illuminated surface is visible from Earth
during the phase shown in the box above?
What does the Moon's
phase look like from the northern hemisphere of Earth (the part of
Earth facing you in the figure below)?
Answer: 2. Hint: Can you see more than half of the lit side
from Earth?
What would the Moon's
phase look like from the northern hemisphere of Earth (the part of
Earth facing you in the figure below)?
Answer: 4. Hint: Look at the diagram upside-down (like your point of
view on the side of Earth facing the Moon).
For a person on Earth, at what time would the Moon be highest overhead
when the Moon is at the position shown?
If the Moon is positioned as shown below, about what time would it be
overhead?
If the Moon is positioned in its orbit as shown below, at what time
would it be highest overhead?
If the Moon is positioned as shown below, about what time would the
Moon rise?
If the Moon is positioned as shown below, about what time would the
Moon set?
What is the phase of the Moon when it is in the position shown above?
Which phase of the Moon rises in the east as the Sun rises in the east?
What would the Moon's phase look like if it was in the position shown?
Answer: First row on the right. Hint: The Moon has to be a
crescent, roughly midway in phase between third quarter and
new. Try figuring out where the Moon has to be for us to see the other
phases shown.
Many people incorrectly believe that Earth's shadow causes Moon
phases. If this incorrect belief were true, then which location would
produce the Moon phases shown in the upper right corner of the figure
below?
Answer: 2. Hint: The Moon would only go into the Earth's
shadow when it is on the opposite side of the Earth from the Sun.
Typically though we see new Moon when it is at position 4, and
we are looking at the Moon's shadowed side.
What does the Moon's phase have to be if there is a solar eclipse?
What phase does the Moon have to be for there to be a lunar eclipse?
At what times is it possible to see a lunar eclipse from Earth?
Match the appearance of the solar eclipse (the numbered choices) with
the place you would have to be to see it (the letters) in the figure below.
Answer: A: 4. B: 2. C: 1. D: 3. Hint: How do the dashed lines
help tell you whether you can see the top or bottom edges of the Sun?
What would the Moon look like (from Earth) when it is at the positions
(A and B) shown?
An observer on Earth sees a total lunar eclipse. At the same time, if
someone is standing on the Moon facing the Earth, what would they see?
Where would you look to see a planet rise when it is in retrograde motion?
A planet moving in retrograde motion will, over the course
of one night, appear to
A planet is moving in retrograde motion. Over the course
of several nights, how will the planet appear to move relative to
the background stars?
If Venus and the Sun are on separate merry-go-rounds, but both are making
one circle of the Earth in exactly the same amount of time, what
would we see from Earth over time?
If Venus and the Sun are on separate merry-go-rounds (as pictured in
the previous question), but Venus' merry-go-round makes one circle of
the Earth in slightly less time than the Sun's merry-go-round does,
what would we see from Earth over time?
In the heliocentric model shown below,
where would a planet have to be to be seen overhead by a person at
midnight on Earth?
Answer: 7. Hint: To see something as being high overhead, you
have to be looking away from the center of the Earth. Where would a
person have to be standing for it to be midnight on Earth?
In the picture above, at roughly what time would the planet at
position 5 be roughly overhead (high above the horizon)? (Earth
rotates counterclockwise from this point of view.)
The picture shows the solar system today. Which planet will be highest
overhead at around midnight?
The picture shows the inner solar system today. When would Venus (V)
be highest overhead? (Earth rotates counterclockwise in this view.)
If you lived on Venus and you monitored Earth's position in
the sky over the course of several years, what would you see?
If you lived on another planet and you watched Earth's position in
the constellation sover the course of several years, which ones would
see Earth do retrograde motion? (Give all correct answers.)
Answer: 1. Hint: If the orbit is any kind of oval, the Sun will
NOT be at the center of the oval.
Mars moves in an elliptical orbit around the Sun. The location of
the Sun relative to this ellipse is
The picture below shows the orbit of a planet around the Sun with the
planet in different positions. Rank the planet's speed when it is at
the different positions in order from fastest to slowest.
The Earth is a few percent closer to the Sun in January than it is
in July. What does this fact mean for the lengths of the seasons?
If a small weather satellite and the large International Space Station
are orbiting Earth at the same altitude above Earth's surface, which
object takes longer to orbit once around Earth?
NASA wants to launch a spacecraft to go out to the planet Mars
(without stopping there), and then come back. If the spacecraft
never uses rockets after it leaves Earth, how long will it take the
satellite to make its orbit?
How long will it take the spacecraft to make a complete orbit around
the Sun compared to the time it takes Mars to complete an orbit?
A newly discovered asteroid is observed orbiting the Sun at an average
distance of 4 astronomical units (AU). How long will it
take to orbit the Sun?
The figure below shows a portion of Copernicus' model of the
universe. If Venus was in the positions given by letters, what phases
would you see through a telescope from Earth?
A car is travelling along a straight, flat road at constant speed.
The car's
A car is travelling at constant speed around a curve. The car's
Beaker is riding on a cart and is not wearing a seatbelt. The chair hits a wall and
stops. What is the best description of what happens to Beaker?
Is there a net (unbalanced) force acting in the following situations?
The pictures below show boxes (that are initially at rest) and the
forces that are acting on them. In each case, what is going to happen
to the box?
Which of the following diagrams best represents the forces acting on
a ball hanging from a string?
Answer: 3. Hint: Newton's First Law -
the ball is not moving, so there can be no net force. Gravity is
pulling down, and the string exerts a force pulling upward.
Which of the following diagrams best represents the forces acting on
a cart sitting still on a table?
Answer: 3. Hint: Newton's First Law -
the cart is not moving, so there can be no net force. Gravity is
pulling down, and the table exerts a force pushing upward from below.
You are late for class and driving too fast when you enter into a
sharp right turn. The tires lose their grip on the road. What is
probably going to end up happening?
A ball is rolling in a straight line as shown in the figure below
(from the view of someone standing over the table). If it is struck on
the left side, what is going to happen to its motion?
At the same instant, in which direction is there a net force acting?
I swing a ball on a string counterclockwise above my head (as seen
from above in the picture below). At the point shown, I suddenly release
the string. Which of the paths below would the ball most closely follow
when released?
Answer: 2. Hint: Newton's First Law - once the net force (the
pull on the string) is gone, the ball will travel in a straight line
in the direction it was travelling.
Answer: B. Hint: Newton's First Law - once the net force
(exerted by the track) is gone, the marble will travel in a straight
line in the direction it was travelling.
The space shuttle fires its engine. What forces act on the space
shuttle?
A red cart is going to hit a pair of blue carts with a spring-loaded
pusher. (The pair of blue carts has twice the mass of the red cart.)
After the hit, which cart will have accelerated (sped up) more?
Suppose you are an astronaut taking a space walk to fix your
spacecraft with a hammer. Your tether line breaks and the jets on your
backpack are out of fuel. How could you return to your spacecraft
without the help of someone else?
An asteroid is moving through space at constant velocity. At the time
shown, a rocket that is attached to the asteroid starts to fire
continuously toward the bottom of the screen. Which of the paths would
the asteroid most closely follow as the rocket fires?
Answer: C. Hint: Newton's Third Law tells you about that gas
being shot downward will exert a force upward on the rocket and
asteroid. If the rocket is firing continuously, then it will cause the
asteroid to move on a curved path because the force continues to
accelerate the asteroid upward.
A compact car and a large truck collide head-on and stick
together. Which vehicle exerts the largest force during the collision?
A compact car and a large truck collide head-on and stick
together. Which vehicle undergoes the largest acceleration during the
collision?
If the planet is moving with the velocity shown in blue, what will the
Sun's gravitational force (red) be doing to the planet at the point
shown?
Answer: B. Hint: Compare to the strength of planet D's
force. Planet A is 16x more massive, but 4 times further away, so
those factors cancel - its force is the same as planet D. Planet C
will exert a smaller force than D - the distance reduces the force
more than the larger mass increases it. Planet B has a large enough
mass that its force is larger than planet D's force (10/9ths, to be
exact.)
You and your friend measure the strength of the force of gravity
acting on both of you when you are on the surface of Earth. Your friend has 3 times as much mass as you do. The force on your friend is
Answer: 3. Hint: Gravitational force is stronger the more mass is
involved: 3 times stronger if there is 3 times more mass in one of the
objects.
An astronaut measures the strength of the force of gravity acting on him
when he is on the surface of Earth and when he is 10 times farther away
from the center of Earth. How do they compare?
A person measures the strength of the force of gravity acting on him
when he is on the surface of Earth, and compares it to the force acting on
his friend (who is twice as massive) when his friend is 10 times farther away
from the center of Earth. How do they compare?
An astronaut goes on the first mission to Mars. Mars has a mass that
is only about one-tenth the mass of the Earth, and it is about half
the size of Earth (so that she is closer to the center of the planet
when she is standing on the surface). How will her weight on Mars
compare to her weight on Earth?
Consider a person standing in an elevator that is accelerating upward.
The upward force exerted by the elevator floor on the person is
the downward weight of the person.
Answer: 1. Hint: Gravity (the weight) is pulling down. To have
a net force (and thus, to accelerate the person) upward, the floor
must exert a force on the person that is larger than gravity.
Load and fire a cannonball with a speed of 6 km/s in the animation
here. What will happen if
we increase the speed of the cannonball to 8 km/s?
A spacecraft hovers near a small asteroid (with the help of its rocket)
as they are both moving toward the right. Which of the paths would
the asteroid most closely follow as time goes on?
Answer: E. Hint: The spacecraft will exert a downward
pull on the asteroid (in the diagram) that will slowly start
to accelerate the asteroid downward.
J. P. Adams, D. J. Loranz, E. E. Prather, and
T. F. Slater. Lecture Tutorials for Introductory Astronomy --
Instructor's Guide, 2002 (Prentice Hall). E. Mazur. Peer
Instruction: A User's Manual, 1997 (Prentice Hall).
Answer: 1. Hint: Visualize the star's place on the dome - which compass direction is it closest to?
Answer: 2. Hint: The North Star shows you which direction is
north, and the star gets highest on the dome opposite the North Star.
Rising and Setting
This is what the sky would look like at noon on a given day. Where
would you expect the Sun to be located at sunset?
Answer: 2. Hint: "Rises in the east, sets in the west"
Answer: 3. Hint: "Rises in the east, sets in the west". Even
though we often don't pay attention to them, the stars are doing
almost the exact same thing as the Sun.
Answer: 3. Hint: Imagine standing at the North Pole in the diagram.
All of the stars in the diagram circle around over your head.
Answer: 3. Hint: Try using the diagram above, and imagine
standing on the black line with your head pointing away from the
center of Earth. How would the stars appear to move?
Answer: 1. Hint: All stars are circumpolar at the North Pole,
and none are at the equator.
Time of Day
For the person at position B, what direction would he have to look to
see the Sun on the horizon?
Answer: 3. Hint: If that person is facing into the paper, he is looking south. Then would his left hand be east or west?
Answer: 4. Hint: If the Sun is on the horizon in the east, it
is sunrise, right?
Answer: 2. Hint: "Rises in the east, sets in the west"
Answer: 3. Hint: "Rises in the east, sets in the west"
Answer: 4. Hint: The person is on the night side of
Earth. Remember that the person on the Earth will rotate
counterclockwise from this point of view.
Seasons
On October 21st, which constellation is behind the Sun?
Answer: 3. Hint: Find where Earth is in its orbit in October, and
find the direction you need to look from Earth to see the Sun.
Answer: 6. Hint: Find where Earth is in its orbit in November, and
look in the opposite direction from the Sun.
Answer: 3. Hint: "Overhead" is a direction pointing
directly away from the center of the Earth.
Answer: 4. Hint: He is in the northern hemisphere, which is
tilted away from the Sun.
Answer: 3. Hint: During winter, the northern hemisphere is
tilted away from the Sun. which makes the Sun appear to go lower
across the sky. This also means that we see less of the Sun's circle
around the sky from our position on Earth.
Answer: 5. Hint: In the United States, we are not close enough to
the equator that the Sun can ever be overhead.
Answer: 3. Hint: The shadow points exactly opposite the
direction of the Sun. How long is your shadow at sunset? Noon?
Answer: 1. Hint: Look at which person is exposing the most body
area to the sunlight coming from directly above.
Answer: 2. Hint: Remember which hemisphere (the northern or
southern one) is tilted toward the Sun in summer and in winter.
Answer: 4. Hint: Think about how big an object appears to you if it is close or far away.
Answer: 4. Hint: How much of all of the Sun's light is falling
in the two hemispheres?
Answer: 1. Hint: For a person in the north (especially at the
North Pole) they stay on the lit side for more than half of a day.
Answer: 1. Hint: On Earth, the Sun is highest in the sky
in the places that are facing most toward the Sun.
Answer: 4. Hint: Draw in where the line between day and night would be.
Even if the Earth is rotating, what part of Earth stays in the dark?
Answer: 1. Hint: As a planet orbits the Sun, its axis will
always point in the same direction. This planet will have one of its
hemispheres lit by the Sun for months at a time, but half a year later
that same hemisphere will be in darkness for months at a time (and the
other hemisphere would be lit).
Moon Phases
For more practice, see the Lunar
Phase Quizzer animation.
Answer: 3. Hint: We are only seeing part of illuminated side of the
Moon, but it is still there...
Answer: 2. Hint: Most of the lit side is facing away from us (and is
on the side of the Moon facing away from us).
Answer: 4. Hint: In this case, most of the lit side is on the
side of the Moon facing toward us.
Answer: 3. Hint: You have to be in the middle of the nighttime
side of Earth for you head to be pointing at the Moon.
Answer: 4. Hint: You would have to be standing in lower left
part of Earth for your head to be pointing toward the Moon. According
to the way the Earth is rotating, that would be between midnight and
sunrise (6 am).
Answer: 2. Hint: You have to be on the upper right portion of
Earth to see the Moon nearly overhead, which puts you on the lit side
of Earth, past noon. This is just like earlier questions about when
constellations rise and set.
Answer: 2. Hint: The Moon is highest overhead at sunrise
(person standing at the bottom of Earth), so the Moon would rise about
6 hours earlier.
Answer: 1. Hint: The Moon would be overhead at about 3 pm
(person standing at upper right part of Earth), so the Moon would set
about 6 hours later.
Answer: 1. Hint: You would see less than half of the lit side
from Earth, and since the Moon orbits counterclockwise from the point
of view of the picture, it must be waning (appearing to get more
full).
Answer: 4. Hint: If it rises at the same time as the Sun, the
Sun must be on the opposite side of the Moon from us.
Eclipses
If we make the Earth the size of a basketball (12 in. across), then if
the Moon is also made the same scale, it should be about 3
in. across. How far from Earth should the Moon be on this scale?
Answer: 4. Hint: The distance between them is about 30 times
the size of the Earth... far out (literally)!
Answer: 1. Hint: How do the Earth, Sun, and Moon have to be oriented?
Answer: 3. Hint: How do the Earth, Sun, and Moon have to be oriented?
Answer: 1. Hint: When a lunar eclipse is occuring, anyone on
the nighttime side of Earth could potentially see it.
Answer: 4. Hint: A total eclipse on the Moon means that no
sunlight is reaching it.
Planet Motions in the Sky
If you carefully watch over several nights, how will the Moon apear to
move compared to stars in constellations?
Answer: 2. Hint: This is different than rising and setting! If
you can forget about the Earth's rotation as the Moon moves around the
Earth, it goes counterclockwise around the diagram and would be in
front of different stars over time.
Answer: 1. Hint: Everything rises in the eastern half of
the sky, and set in the western half because of Earth's rotation. The
retrograde motion doesn't matter here.
Answer: 1. Hint: The Earth's rotation is much quicker than
the planet's motion through the sky, and the rotation is what makes
things rise in the east and set in the west.
Answer: 1. Hint: Relative to the stars, a planet normally moves
from west to east. Retrograde motion (relative to the stars) is in
the opposite direction.
Answer: 2. Hint: If the two merry-go-rounds circle in the same amount
of time, it is just as if the two merry-go-rounds were attached.
Answer: 1. Hint: Venus' merry-go-round is moving faster in this
case, so it would catch up with the Sun.
Answer: 2. Hint: A person would have to be on the lit side of the
Earth in the lower right for the planet to be overhead.
Answer: 5. Hint: This is the only planet on the opposite side of
Earth from the Sun. (To see Saturn , you would have to look in the
same direction as the Sun...)
Answer: 1 Hint: You have to be on the daytime side of Earth
(the side facing the Sun) in the morning (the Earth would have
recently rotated you off the nighttime side of Earth.)
Answer: 3. Hint: From the point of view of someone on Venus, Earth
is a superior planet (it has a larger orbit than Venus). Thus, it will
act in the same way that Mars acts when we view it from Earth.
Answer: 1,2. Hint: From the point of view of someone on Mercury
or Venus, Earth is a superior planet (has a larger orbit), and will do
retrograde motion on occasion.
Kepler's Laws
NASA wants to launch a spaceship from Earth (inner circle) to Mars
(outer circle) and immediately come back. Which of the pictured orbits
is possible according to Kepler's first law?
Answer: 2. Hint: Think about Kepler's First Law of planetary motion.
Answer: 1. Hint: Think about Kepler's Second Law of planetary motion.
Answer: 2. Hint: Think about Kepler's Second Law of planetary
motion. Is the Earth moving faster around its orbit in January or
July?
Answer: 3. Hint: Kepler's Third Law says that the time it takes
an object to orbit (its period) only depends on its distance from the
object it is orbiting.
Answer: 3. Hint: Think about Kepler's Third Law of planetary motion.
Answer: 2. Hint: Think about Kepler's Third Law of planetary motion.
Answer: 3. Hint: Use Kepler's Third Law of planetary motion.
Models of the Universe
The figure below shows a portion of Ptolemy's model of the
universe. What phases would you see for Venus when it is at the
positions given by letters if you are using a telescope on Earth?
Motion and Newton's Laws
A car is sitting still on a road. The car's
Answer: 1. Hint: If the car is not moving and staying that way,
both will be zero.
Answer: 2. Hint: The car is moving, but the velocity is not changing
(neither speed nor direction.
Answer: 4. Hint: The direction of the car's velocity is changing.
Answer: 1. Hint: Newton's First Law... he keeps moving in a straight line
at constant speed.
Answers: 1: Yes; 2: Yes; 3: No; 4: Yes; 5: Yes. Hint: If an
object is accelerating, there must be an unbalanced force.
Answer: A: 1. B: 3. C: 5. D: 2. Hint: Newton's First Law -
the box will move in the direction of the net force.
Answer: 2. Hint: Newton's First Law - friction with the
road is need to keep the car in the turn.
Answer: 5. Hint: The acceleration of the ball is in the same
direction as the force points.
I am swinging a ball on a string counterclockwise around my head (as
seen from above in the picture below). At the instant shown, In which
direction is the ball's velocity pointing?
Answer: 3. Hint: At the instant shown, the ball is moving from right
to left across the top of the circle.
Answer: 1. Hint: The ball has has gotten as far toward the top
of the diagram as it is going to get, so I must be pulling toward the
bottom of the diagram.
I roll a marble around a circular track that has a section cut out.
When the marble reaches the end of the track, what path will it take?
Answer: 2. Hint: There is a second force
acting on the gas. That is what Newton's Third Law is referring
to.
Answer: 1. Hint: Newton's Third Law tells you about the forces
on the red and blue carts, but you also need to consider Newton's
second law to determine the effect of the forces.
Answer: 2. Hint: Newton's Third Law.
Answer: 3. Hint: Newton's Third Law.
Answer: 1. Hint: Newton's Second Law tells you about the amount
of acceleration for objects with different masses. The forces on the
two vehicles are the same (see previous question).
Answer: Part a: 1., Part b: 2. Hint: The direction of the force tells the story: it
is pulling in roughly the same direction the planet is moving (causing
it to speed up), and is pulling somewhat toward the right hand side
(making the planet start turning that way). This could make it go around
the orbit shown below.
Gravity
A hypothetical planet system has planets in equally-spaced circular
orbits. The planet masses are given in terms of the mass of the
innermost planet. Which of the planets exerts the greatest
gravitational force on the star?
as the force on you.
Answer: 2. Hint: Gravitational force decreases with distance,
and it decreases as the square of the distance.
Answer: 4. Hint: As in the previous question, the (10 times)
larger distance would reduce the force to 1/100th of the force on him,
but his friend's larger mass makes the force twice as large as it
would have been if they were the same mass.
Answer: 3. Hint: Because Mars has a smaller mass, there is less
gravitational force (1/10th as large as Earth because of that
alone). However, because Mars is smaller than Earth, a person on the
surface is closer to all of the mass of Mars, which makes the
gravitational force larger (4 times larger than it would be
otherwise).
Answer: 2. Hint: For 6 km/s the cannonball gets close to half way around the
Earth before crashing. A little extra upsh will get the cannonball into a
circular orbit. Once the cannonball is able to get halfway around Earth, it
will be able to get the rest of the way around --- the lowest point of its orbit will
miss Earth's surface. For slower cannonballs, the lowest point in the orbit is
inside the Earth - CRASH!
Some of the questions above are taken from the following
sources:
Last update: February 20, 2013