6) Estimation: Making estimates is a practice that gives important guidance to scientists. Your
friend, who likes astrology, tells you the position of Jupiter at your birth is gravitationally
significant because Jupiter has over 300 times the mass of Earth. So, you decide to estimate the
relative gravitational force at your birth of: Jupiter; the doctor who delivered you; and a nearby
mountain. The relevant part of Newton’s law of gravity is M/r2, where M is the mass of the
attracting object and d is its distance. (The other two terms of the law, your mass and the
gravitational constant G, don’t change in each case.)
Make a table and compute the relative gravitational attraction on you by the nearby mountain,
the delivery doctor, and Jupiter:
Object Mass (kg) Distance (km) Relative force (M/d2) (kg/km2)
Mountain (typical) 3 1014 30 ?
Doctor 100 2 10-4 ?
Jupiter 1.6 1027 8 108 ?
Which had the most force on you?
4.4 Short Answer Questions
1) You are alone in space and your tether brakes and you are floating motionless relative to your
spaceship, which is located a frustrating 10 meters away. You spacesuit has no jet pack and you
have no air to spare. All you have is your wrench. How do you return to your ship?
2) State Newton’s three laws of motion.
3) Energy generated by solar panels is intermittent, but can be stored by using it to pump water
uphill into a reservoir (called Pumped Storage Hydroelectricity). The water is later released
downhill to power turbines generating electricity for periods of darkness or high demand (when
it can be sold for more). In this scenario, what is the original type of energy and what type is
being stored?
4) Imagine another solar system, with a star of the same mass as the Sun. Imagine the planets are
just like those of our system, but are placed in the reverse order: going outward from the star
there is Neptune, Uranus, Saturn, Jupiter, Mars, Earth and Venus. The distances remain the
same. E.g., in the new system, Neptune is located the same distance from the star as our Mercury
is from our Sun, etc. How would the orbital periods of each planet change?
5) Suppose it takes 6 seconds for a watermelon to fall to the ground after being dropped from a
tall building. If there were no air resistance, so that the watermelon would fall with the
acceleration of gravity, about how fast would it be going when it hit the ground?
6) A person trying to get something out of a narrow mouth bottle such as a ketchup bottle or
sticky pill bottle might be seen shaking the bottle violently up and down. Explain how they are
employing both Newton’s 1st and 2nd laws.
7) A coasting hybrid car accelerates down a hill. The driver applies the car’s “regenerative”
brakes, which slow the car while turning a small electrical generator. The generator sends energy
to the battery, reversing its chemical reaction, recharging it. What three types of energy are
involved?
8) In the sci-fi film Gravity, a pair of tethered astronauts jet through space. When, in desperation,
they attach themselves to a floating object, one astronaut sacrifices himself by detaching from
the tether to prevent it from tearing. Under which of these cases would force be felt on the
tether? 1) The pair are in free fall, not attached to any object. 2) The moment the two attach
themselves to an object having a different velocity than their own. 3) During a period after the
attachment, when the object and the two astronauts are all stationary with respect to each other.
9) Briefly explain why Earth feels a greater tidal force from the Moon than from the Sun, even
though it feels a greater total gravitational force from the Sun. Recall that the tidal force depends
on the difference between the force strength on either side of Earth.
10) Explain what synchronous rotation is. What is it caused by? Give an example.
4.5 Mastering Astronomy Reading Quiz
1) The difference between speed and velocity is that ________.
A) they are expressed in different units
B) velocity also includes a direction
C) velocity is the same as acceleration but speed is different
D) velocity is calculated using a physics equation
2) The acceleration of gravity on Earth is approximately 10 m/s2 (more precisely, 9.8 m/s2). If
you drop a rock from a tall building, about how fast will it be falling after 3 seconds?
A) 30 m/s
B) 10 m/s
C) 30 m/s2
D) 10 m/s2
E) 20 m/s
3) As a gas cloud in space shrinks, it
A) spins slower.
B) spins faster.
C) spins at the same rate as it did before it shrank.
4) Suppose you lived on the Moon. Which of the following would be true?
A) Your weight would be less than your weight on Earth, but your mass would be the same as it
is on Earth.
B) Both your weight and your mass would be less than they are on Earth.
C) Your mass would be less than your mass on Earth, but your weight would be the same as it is
on Earth.
D) You would feel weightless. The Moon has no atmosphere and no atmospheric pressure, and
therefore no gravity pushing downward.
5) In which of the following cases would you feel weightless?
A) while falling from a roof
B) while parachuting from an airplane
C) while accelerating downward in an elevator
D) while walking on the Moon
6) Which of the following statements is not one of Newton’s Laws of Motion?
A) What goes up must come down.
B) The rate of change of momentum of an object is equal to the net force applied to the object.
C) In the absence of a net force acting upon it, an object moves with constant velocity.
D) For any force, there always is an equal and opposite reaction force.
7) Compare the acceleration the Moon experiences due to the Earth’s gravity and the acceleration
the Earth experiences due to the Moon’s gravity.
A) The acceleration of the Earth is greater than the acceleration of the Moon.
B) The acceleration of the Moon is greater than the acceleration of the Earth.
C) The accelerations are equal and opposite.
8) Compare the force of gravity on the Moon due to the Earth, and the force of gravity on the
Earth due to the Moon.
A) The force on the Moon is greater than the force on the Earth.
B) The force on the Earth is greater than the force on the Moon.
C) The forces are equal and opposite.
9) When a spinning ice skater pulls in his arms, he spins faster because ________.
A) his angular momentum must be conserved, so reducing his radius must increase his speed of
rotation
B) there is less friction with the air
C) there is less friction with the ice
D) there exists an unbalanced reaction force
10) All of the following hypothetical planets orbit a star with the same mass as the Sun (one solar
mass). Which one has the shortest orbital period? (If two objects would have the same orbital
period to within a difference of less than 1%, consider them as having identical periods.)
A) Planet A: one Earth mass and 1 AU from the star
B) Planet B: two Earth masses and 1 AU from the star
C) Planet C: two Earth masses and 2 AU from the star
D) Planets A and B
E) Planets B and C
11) If one drops a golf ball and a bowling ball simultaneously from the same height above the
ground, what will happen? Neglect the effects of wind or air resistance.
A) The golf ball and the bowling ball will hit the ground at the same time.
B) The bowling ball will hit the ground before the golf ball.
C) The golf ball will hit the ground before the bowling ball.
12) Absolute zero is ________.
A) 0 Kelvin
B) 0° Celsius
C) 0° Fahrenheit
D) 100° Celsius
13) What does temperature measure?
A) the average kinetic energy of particles in a substance
B) the average mass of particles in a substance
C) the total potential energy of particles in a substance
D) the amount of infrared radiation emitted by an object
14) In the formula E = mc2, what does E represent?
A) the mass-energy, or potential energy stored in an object’s mass
B) the kinetic energy, also known as Einsteinium
C) the radiative energy carried by light
D) the gravitational potential energy of an object held above the ground
E) the electric field produced by a charge
15) Consider a star with 2 planets. The mass of planet A is the same as the mass of planet B. The
orbit of Planet A is on average, closer to the star than the orbit of Planet B. Which of the
following statements is true?
A) Planet A is moving slower than Planet B.
B) Planet A moves with the same speed as Planet B.
C) The relative orbital speeds depend on the masses of the planets.
D) Planet A is moving faster than Planet B.
16) What is the difference between a bound orbit and an unbound orbit around the Sun?
A) An object on a bound orbit follows the same path around the Sun over and over, while an
object on an unbound orbit approaches the Sun just once and then never returns.
B) A bound orbit is an orbit allowed by the universal law of gravitation, and an unbound orbit is
not.
C) An object on a bound orbit has a gravitational attraction to the Sun, while an object on an
unbound orbit does not.
D) A bound orbit is circular, while an unbound orbit is elliptical.
17) Why is Newton’s version of Kepler’s third law so useful to astronomers?
A) It can be used to determine the masses of many distant objects.
B) It tells us how rapidly a planet spins on its axis.
C) It tells us that more-distant planets orbit the Sun more rapidly.
D) It explains why objects spin faster when they shrink in size.
18) What do we mean by the orbital energy of an orbiting object (such as a planet, moon, or
satellite)?
A) Orbital energy is the sum of the object’s kinetic energy and its gravitational potential energy
as it moves through its orbit.
B) Orbital energy is the object’s kinetic energy as it moves through its orbit.
C) Orbital energy is a measure of the object’s speed as it moves through its orbit.
D) Orbital energy is the amount of energy required for the object to leave orbit and escape into
space.
19) Which statement must be true in order for a rocket to travel from Earth to another planet?
A) It must attain escape velocity from Earth.
B) It must carry a lot of extra fuel.
C) It must have very large engines.
D) It must be launched from space, rather than from the ground.
20) Approximately where is it currently high tide on Earth?
A) on the portion of Earth facing toward the Moon and on the portion facing away from the
Moon
B) only on the portion of Earth facing the Moon
C) wherever it is currently noon
D) at the equator at the closest point to the Moon
21) Consider the gravitational force between the Sun and Earth. Which of the following
statements describes the situation the best?
A) The gravitational force experienced by the Sun is equal and opposite to the gravitational force
experienced by the Earth.
B) The acceleration experienced by the Sun due to the Earth is equal and opposite to the
acceleration experienced by the Earth due to the Sun.
C) Both of these statements are true.
4.6 Mastering Astronomy Concept Quiz
1) Which of the following represents a case in which you are not accelerating?
A) driving in a straight line at 60 miles per hour
B) going from 0 to 60 miles per hour in 10 seconds
C) slamming on the brakes to come to a stop at a stop sign
D) driving 60 miles per hour around a curve
2) Suppose you drop a 10 kilogram mass object and a 5 kilogram mass object on the Moon, both
from the same height at the same time. What will happen?
A) Both objects will hit the ground at the same time.
B) The 10 kilogram object will hit the ground before the 5 kilogram object.
C) The 5 kilogram object will hit the ground before the 10 kilogram object.
D) Both objects will float freely since they are weightless on the Moon.
3) Why are astronauts weightless in the Space Station?
A) because the Space Station is constantly in free-fall around the Earth
B) because they are in a vacuum and floating in their spacesuits
C) because there is no gravity so far from Earth
D) because the Space Station is moving at constant velocity
4) A planet is orbiting a star. Which of the following statements is true for the acceleration and
gravitational forces experienced by the star and the planet?
A) The acceleration of the planet is much more than the acceleration of the star, but the force on
the star is the same but opposite the force on the planet.
B) The force on the star is much smaller than the force on the planet, but the accelerations are
about equal.
C) The acceleration of the planet is much more than the acceleration of the star, and the force on
the planet is much more than the force on the star.
5) Suppose you are in an elevator that is traveling upward at constant speed. How does your
weight compare to your normal weight on the ground?
A) It is the same.
B) It is greater.
C) It is less.
D) You are weightless.
6) Imagine a spaceship in orbit around a planet. Its engine suffers a severe malfunction, and
explodes. What is the most physically realistic depiction of this event?
A) The spacecraft breaks in half and begins to sink down into the planet, like a sinking aircraft
carrier.
B) The spacecraft breaks apart, and the pieces continue to orbit the planet.
C) The spacecraft burns up in a giant fireball.
7) Suppose the Sun were suddenly to shrink in size but that its mass remained the same.
According to the law of conservation of angular momentum, what would happen?
A) The Sun would rotate faster than it does now.
B) The Sun’s rate of rotation would slow.
C) The Sun’s angular size in our sky would stay the same.
D) This could never happen, because it is impossible for an object to shrink in size without an
outside torque.
8) Suppose you kick a soccer ball straight up to a height of 10 meters. Which of the following is
true about the gravitational potential energy of the ball during its flight?
A) The ball’s gravitational potential energy is greatest at the instant when the ball is at its highest
point.
B) The ball’s gravitational potential energy is greatest at the instant it returns to hit the ground.
C) The ball’s gravitational potential energy is always the same.
D) The ball’s gravitational potential energy is greatest at the instant the ball leaves your foot.
9) Suppose you heat an oven to 400°F and boil a pot of water. Which of the following explains
why you would be burned by sticking your hand briefly in the pot but not by sticking your hand
briefly in the oven?
A) The water can transfer heat to your arm more quickly than the air due to its density.
B) The water has a higher temperature than the oven.
C) The molecules in the water are moving faster than the molecules in the oven.
D) The oven has a higher temperature than the water.
10) Which of the following scenarios involves energy that we would typically calculate with
Einstein’s formula E = mc2?
A) A small amount of the hydrogen in a nuclear bomb (an H-bomb) becomes energy as fusion
converts the hydrogen to helium.
B) An object accelerated to a great speed has a lot of kinetic energy.
C) A mass raised to a great height has a lot of gravitational potential energy.
D) A burning piece of wood produces light and heat, therefore giving off radiative and thermal
energy.
11) How does a rocket launch upwards? Choose the statement that best describes why a rocket
goes up.
A) By expelling gas downwards, the rocket is propelled upwards.
B) By expelling gas downwards, which pushes against the ground, the rocket is propelled
upwards.
C) By expelling gas, the rocket loses mass; because it is lighter, it rises up.
12) Suppose that the Sun shrank in size but that its mass remained the same. What would happen
to the orbit of the Earth?
A) Earth’s orbit would be unaffected.
B) The size of Earth’s orbit would shrink, and it would take less than one year to orbit the Sun.
C) Earth’s orbit would expand, and it would take more than one year to orbit the Sun.
D) Earth would change from a bound orbit to an unbound orbit and fly off into interstellar space.
13) Imagine another solar system, with a star of the same mass as the Sun. Suppose a planet with
a mass twice that of Earth (2MEarth) orbits at a distance of 1 AU from the star. What is the
orbital period of this planet?
A) It would not be able to orbit at this distance.
B) 1 year
C) 2 years
D) It cannot be determined from the information given.
14) Imagine another solar system, with a star more massive than the Sun. Suppose a planet with
the same mass as Earth orbits at a distance of 1 AU from the star. How would the planet’s year
(orbital period) compare to Earth’s year?
A) The planet’s year would be shorter than Earth’s.
B) The planet’s year would be longer than Earth’s.
C) The planet’s year would be the same as Earth’s.
D) An orbit at a distance of 1 AU would not be possible around a star more massive than the
Sun.
15) Newton showed that Kepler’s laws are ________.
A) natural consequences of the law of universal gravitation
B) seriously in error
C) actually only three of seven distinct laws of planetary motion
D) the key to proving that Earth orbits our Sun
16) The astronauts feel weightless in the International Space Station, which orbits the Earth once
every 90 minutes. Why?
A) because there is no gravity in space
B) because they are moving so fast
C) because the gravity from the Moon cancels out the gravity from Earth
D) because they and the space station are both falling around the Earth
17) When NASA’s New Horizons spacecraft passed by Jupiter, its speed increased (but not due
to firing its engines). What must have happened?
A) Jupiter must have lost a very tiny bit of its orbital energy.
B) New Horizons must have dipped through Jupiter’s atmosphere.
C) Jupiter’s rotation must have sped up slightly.
D) Jupiter captured an asteroid during the period New Horizons passed by, as accurately
predicted in NASA’s mission plan.
18) Suppose you are in an elevator that is traveling upward at constant speed. How does your
weight compare to your normal weight on the ground?
A) It is the same.
B) It is greater.
C) It is less.
D) You are weightless.
19) Which of the following best describes the origin of ocean tides on Earth?
A) Tides are caused by the difference in the force of gravity exerted by the Moon across the
sphere of the Earth.
B) The Moon’s gravity pulls harder on water than on land, because water is less dense than rock.
C) Tides are caused by the 23.5-degree tilt of the Earth’s rotational axis to the ecliptic plane.
D) Tides are caused on the side of the Earth nearest the Moon because the Moon’s gravity
attracts the water.
20) At which lunar phase(s) are tides most pronounced (for example, the highest high tides)?
A) both new and full moons
B) both first and third quarters
C) full moon only
D) new moon only
21) Which of the following best explains why the Moon’s orbital period and rotation period are
the same?
A) The Moon once rotated faster, but tidal friction slowed the rotation period until it matched the
orbital period.
B) The Moon was once closer to Earth, but the force of gravity got weaker as the Moon moved
farther away.
C) The law of conservation of angular momentum ensured that the Moon must have the same
amount of rotational angular momentum as it has of orbital angular momentum.
D) The equality of the Moon’s orbital and rotation periods is an extraordinary astronomical
coincidence.
22) As an interstellar cloud of hydrogen gas shrinks in size, its rate of rotation
A) increases, because its angular momentum is conserved.
B) decreases, because its angular momentum is conserved.
C) increases, because its total energy is conserved.
D) increases, because the force of gravity strengthens as the cloud shrinks.
E) decreases, because the force of gravity strengthens as the cloud shrinks.
23) As an interstellar cloud of hydrogen gas shrinks in size, its temperature increases
A) because gravitational potential energy is converted to thermal energy.
B) because kinetic energy is converted to radiative energy.
C) because thermal energy is converted to radiative energy.
24) Consider the elliptical orbit of a comet around the Sun. Where in its orbit is the comet
moving the fastest?
A) when it is farthest from the Sun
B) when it is closest to the Sun
C) It is always moving at the same speed.