Astronomy - Ch 3: Gravity & Motion
The image demonstrates
"Newton's cannon," a thought experiment how something can be forever "falling" but not hit Earth
Match each object with the force that would be needed to accelerate it to 5 m/s^2
0.750 N - A 0.150 kg baseball 500 N - A 100 kg person 15,000 N - A 3000 kg sport utility vehicle 1031 N - The Sun, with mass 2 × 1030 kg
Rank the following objects by how much inertia they have, from least (top) to most (bottom).
1. A leaf falling from a tree 2. A car driving on the highway 3. A house 4. The moon orbiting Earth 5. The Sun
Arrange the statements to show that the velocity of an orbiting moon can be used to measure the mass of a planet, even though the force to hold the orbit depends only on the moon's mass.
1. The moon must be in circular orbit 2. Since the moon is in circular orbit, the force of gravity provides the force that makes the moon orbit 3.F orbit = F gravity 4. Solving for V
The same force is applied to all the objects. Arrange them according to how much acceleration they experience, from the most (top) to the least (bottom).
1. ping pong ball 2. tennis ball 3. bowling ball 4. a golf cart
If quantity A is directly proportional to quantity B, then if B increases 10 times, A must increase___times
10
A planet with four times the mass and half the radius of Earth will have surface gravity ____ times stronger than Earth
16 - (It's 4 times stronger because of the mass, and (1/(1/2)2) = 4 times stronger because of the radius, for a total of 4 × 4 = 16 times stronger)
A planet with 9 times the mass and ______ times the radius of Earth will have the same surface gravity as Earth
3 - (3 squared is 9, and this gives 9 over 9 in the equation)
Match the escape velocity with the object. (Hint: Think about what escape velocity depends on.)
3 × 105 km/sec - A black hole (at the horizon) 617 km/sec - The Sun (at the surface) 42 km/sec - The Sun (at Earth's orbit) 11.2 km/sec - Earth (at the surface) 2.4 km/sec - The Moon (at the surface)
An astronaut in space swings a ball on a string in a circle. If the string breaks, the ball will
Move in a straight line - (The ball's inertia will keep it moving in a straight line)
A coconut falling from a tree is an example of
Newton's second law of motion - (The force of gravity causes the apple to accelerate)
Which idea or equation best explains the different accelerations (arrows) shown in the picture?
Newton's second law: a = F/m - (The same force accelerates a smaller mass more)
Select the planet that would have the same surface gravity as Earth.
One with nine times the mass and three times the radius. - (G=M/R so the changes cancel out)
As a rocket burns its fuel to accelerate, it gets less and less massive. If the force produced by the engine stayed constant, what does Newton's second Law tell us about the motion?
The acceleration would increase - (Acceleration is inversely proportional to mass, so if the mass decreased, the acceleration would increase)
A rocket is in orbit around Earth. This means
The force to hold the rocket in orbit is provided by gravity if the rocket fires its engine and changes its V, its orbit will change - (If V changes, FCircular would no longer equal FG and the orbit would change.)
If two planets have the same mass, but one has four times the radius of the other, how will their escape velocities compare?
The large planet will have one-half the escape velocity of the small planet - (radius is in the denominator of the escape velocity equation)
Two planets are experiencing the same force, but one is twice as massive as the other. Which planet has the highest acceleration?
The less massive planet - (acceleration is inversely proportional to mass)
Select all of the statements that correctly describe the constant G in Newton's universal law of gravity
The value of G is 6.67 × 10-11 Nm2/kg2 G is essentially a conversion factor. G is the same everywhere in the universe.
Why did ancient astronomers not make the connection between gravity and astronomical motion?
They did not understand that the same force at work on Earth also govern motion in space
Ancient scientists developed incorrect models of the Solar System because
They didn't properly understand friction or gravity Human perception does not sense Earth's motion
True or false: If astronomers know the period and semimajor axis of the orbit of a planet circling a nearby star and have some independent way to determine the mass of the star, they have enough information to determine the mass of the planet.
True - (Using Kepler's third law, they could find the sum of the star's and planet's masses. If they know the mass of the star, this could be subtracted to leave the mass of the planet)
The force to keep an object turning in a circle is given by F = m×V^2/d How much more force is required for a planet to keep a moon in an orbit of the same distance and speed if the moons mass were to double?
Twice as much force
Select the cases that correctly describe orbiting objects.
Two equally massive bodies orbit each other equally. When one object is very massive compared to the other object, the center of the balance point of the orbit can be inside the massive object. As a result of Newton's second and third laws, the smaller body moves more.
Identify the correct formula for escape velocity. Here, Vesc is the escape velocity, G is the gravitational constant and M and R are the mass and radius of the body to be escaped from.
Vesc = (Square root of ) 2GM/R
What kind of object has an escape velocity equal to the speed of light?
a black hole
A planet's orbit around the Sun is a curved path. This implies that
a force acts on the planet - (If gravity weren't exerting a force, the path would be a straight line)
Match each equation with the appropriate law.
a3 = P2 - Kepler's third law F = m × a - Newton's second law FG = G {M×m/(d2)} - Newton's universal law of gravity FA on B = FB on A - Newton's third law
Near the surface of Earth, g = 9.8 m/s2. At a height of 6400 km above Earth's surface (one Earth radius), the acceleration of gravity would be
about one-quarter as much - (6400 km above the surface is twice as far from the center, and R is squared)
Select all of the statements that correctly describe the constant G in Newton's universal law of gravity.
G is essentially a conversion factor. G is the same everywhere in the universe. The value of G is 6.67 × 10^11 Nm2/kg2
Which fundamental force plays the most important role in shaping the structure of the Universe?
Gravity - (Gravity plays the most important role in forming planets, stars, and galaxies, and in the interactions of galaxies and dark matter that affect large-scale structure and the expansion of the Universe)
Select all that correctly describe Newton's contributions to understanding gravity.
He described the properties gravity must have it it were to control planetary motion. He was able to work out a mathematical description of gravity
In the absence of any forces, what keeps an object moving at constant speed?
Inertia - (Inertia is also the property that keeps a still object at rest)
Select all the choices that describe escape velocity
It's the speed required to escape a body's gravity It's equal to (Square root of) 2GM/R
The ball will move faster if the person
lets out some string and exerts the same force exerts a stronger force on the string
Observing the effect of gravity between a planet and its moon can allow us to determine the planet's
mass
The escape velocity from a celestial body depends on the___of the body and the___from the center of the body
mass radius
If you are using the equation at the right to calculate the mass of a star based on the motion of a planet and if the units of Newton's constant G are m3 kg-1 s-2, what should the units of d and P be?
meters and seconds
If one planet is larger (in size) than another, its surface gravity
might or might not be bigger - (It would depend on the densities of the two planets)
If two objects are accelerated to the same velocity, the more massive object requires___force
more - (Since a = F/m, for a bigger m you need a correspondingly larger F to get the same a)
The idea that a force exists between two bodies that depends on the product of their masses and the square of the distance between them was formalized by___and is known as the universal law of___
newton gravity
Two planets with the same mass orbit a Sun-like star. One has a semimajor axis three times as long as the other's. The force of gravity between the star and the closer planet is ____ the force of gravity between the star and the farther planet
nine times stronger than - (Since the closer planet is 1/3 the distance of the farther one, the gravitational force is nine (32) times as much)
Two planets with the same mass orbit a Sun-like star. One has a semimajor axis three times as long as the other's. The force of gravity between the star and the closer planet is___the force of gravity between the star and the farther planet
nine times stronger than - (Since the closer planet is 1/3 the distance of the farther one, the gravitational force is nine (3^2) times as much)
The force to keep an object turning in a circle is given by F = m×V^2/d. You swing a ball on a string. The same force is required to swing the ball three times as fast (3V) at distance d as is required to swing it at speed V at ____ the distance.
one-ninth - (V ⇒ 3V makes the force go up 9 times (V is squared and on top). d ⇒ 1919d would have the same effect (d is not squared and is on the bottom of the fraction)
Newton's___law of motion states that the___acting on an object must be the product of the___acceleration of the object.
second force mass
A gun fires a dart, and the dart appears to be accelerated much more strongly than the gun. This is an example of Newton's___law
second - (Newton's second law states: "The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object." This gives us the equation F = ma)
A gun fires a dart, and the dart appears to be accelerated much more strongly than the gun. This is an example of Newton's___law.
second - (Newton's second law states: "The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object." This gives us the equation F = ma)
Based on the equation, we can conclude that moons that are farther out from a planet have
slower orbital speeds
Newton's law of inertia states that a moving body maintains a constant___moving in a___line, unless a___acts on it.
speed straight force
Reducing the separation of two bodies to one-fourth its original value will cause the gravitational force between them to become ____ times ____. (Select two choices.)
stronger 16
___is the term for the acceleration of gravity near a body's surface.
surface gravity
The Moon orbits Earth, but a falling apple hits the ground. This is because
the Moon also has a "sideways" (compared to falling) velocity - (If the apple were moving sideways (at a right angle to the direction toward Earth) at a very high rate of speed, it too would orbit!)
You release a ball that rolls downhill on a curving ramp. This is considered "accelerated motion" because
the ball's direction is changing - (Acceleration produces a change in speed, direction, or both) the ball's speed is changing - (Acceleration produces a change in speed, direction, or both)
The green arrow pointing along the string represents
the force on the ball from the string - (To keep the ball going in a circle, there must be a force acting to change the ball's direction)
A rocket ship in space fires its engine. The force that accelerates it is from
the reaction to rocket fuel exploding out the back of the ship - (The force pushing on the ship forward is equal and opposite to the force accelerating the burning fuel out the back)
Two asteroids, R and S, orbit each other. R is 10 times the mass of S. Compared to the gravitational force exerted by R pulling S toward R, the gravitational force exerted by S pulling R toward S is
the same - (Gravity is between two masses and depends on both of them. Each pulls on the other with the same strength but in opposite directions (Newton's third law)
Match the correct missing words with each statement.
the same as - A truck falling off a bridge will experience an acceleration that is ____ a pebble that falls off. larger than - The pull of gravity from Earth on a truck is ____ that on a pebble. smaller than - Very far from Earth's surface, the acceleration of gravity is ____ it is close to the surface
Astronomers might use the modified version of Kepler's third law to determine
the total mass of a binary star system the mass of a Kuiper belt dwarf planet and its moon the mass of a nearby star with planets
The force needed to keep an object moving in a circle (not necessarily an orbit) depends on
the velocity of the object the object's mass the radius of the circle
A gun fires a dart, and the dart and the gun experience forces in opposite directions. This is an example of Newton's___law
third
Newton's___law of motion is that two interacting bodies produce a pair of equal and opposite forces on each other
third
An orbit that is nine times farther from a black hole will have a circular velocity that is _____ than the closer orbit
three times slower - (If d increases by a factor of nine, V must decrease by 9‾√9 = 3)
If the period and separation of binary stars are known, then a modified version of Kepler's third law can be used to determine the system's
total mass - (the third law relates mass, separation, and period)
If the same force acts on one cart with a mass of 5 kg and another with a mass of 10 kg, the 5 kg cart will be accelerated___as much as the 10 kg cart
twice - (For the same force, half the mass will result in twice the acceleration)
Compared to the gravitational force between two bodies with masses of 100 kg and 200 kg, the gravitational force between two bodies the same distance apart with masses of 100 kg and 400 kg is
twice as much - (Force is directly proportional to the product of the masses. Since one doubled and one stayed the same, the product doubled)
A dropped apple falls because of the force of gravity between it and Earth. Compared to the downward force on the apple, the force on Earth is
upward and equal
Astronauts sometimes train in water tanks because the buoyancy of water exerts a force that opposes the pull of Earth's gravity. In the tank, the ___of the astronauts and their equipment decreases, but the___which affects how hard it is to move them, stays the same.
weight inertia
Compared to being on Earth, on Mars your
weight will be different and your mass the same - (Weight depends on the pull of gravity. Mass depends on how much matter is in an object)
If the gravitational force between Earth and the Moon were suddenly switched off, the Moon's motion
would be a straight line - (In the absence of a force, inertia keeps the Moon moving straight)
You apply a 12 N force to a 3 kg mass. The acceleration it produces is
4 m/s^2
Select all that represent an object undergoing an acceleration.
A car braking to a stop - (Any change in velocity is an acceleration) A ball falling off a table - (The falling ball is accelerated by gravity) A car turning a corner at 88 km/hr - (A change in direction is an acceleration)
Select all the examples below where the net force is zero.
A spacecraft in deep space coasting at constant velocity. - (With no acceleration from its rockets, or gravity from nearby objects, the net force on the spacecraft is zero) Two people pushing on opposite sides of a box with equal strength. A box sitting on a table. - (Earth's gravity pulling down on the box is balanced by the force of the table pushing up on the box)
Match the terms and definitions.
Acceleration - A change in speed, direction, or both Velocity - The speed and direction of an object Mass - The amount of matter in an object Force - Something that causes a change in speed, direction, or both
Select all of the objects that (essentially) maintain a constant velocity.
An apple sitting on a table A hockey puck sliding on the ice
True or false: in the diagram, the force of gravity exerted by the planet on the moon is stronger than the force of gravity exerted by the moon on the planet
False
Earth continues to orbit the Sun in a generally circular path because of inertia.
False - (Only motion in a straight line at a constant speed is described by inertia; changes of direction (circular motion) or speed require the action of a force)
True or false: in the diagram, the force of gravity exerted by the planet on the moon is stronger than the force of gravity exerted by the moon on the planet.
False - (using Newton's law of gravity shows that the two forces are equal. Remember F = GMm/r^2; for both forces, the masses and distance are the same.
If all objects on Earth are acted on by the force of gravity (giving them weight), how is it that an object can remain stationary (be at constant velocity)?
For an object to remain stationary, gravity must be balanced by other forces. - (No net force ⇒ no change in velocity)
Match the constants and variables on the left to the equations they apply to on the right
G - Newton's law of gravity P - Kepler's third law of planetary motion a - Newton's second law of motion
Who was the first person to suggest that gravity is what keeps the planets in their orbits around the Sun?
Robert Hooke
While driving at a high speed, you suddenly slam on the brakes. An unsecured bag on the seat will
Slide forward due to its inertia - (There is no force acting to stop the bag's motion)
Select the cases in which the object undergoes acceleration.
The Moon orbiting Earth A leaf falling from a tree A car slowing down with the brakes on
Match the variables and constants from the modified form of Kepler's third law to their correct units.
d - meters P - seconds G - m^3 X kg^-1 X s^-2 π - no units
___velocity is the speed an object must attain to overcome a planet's gravitational force and move into space.
escape
An astronaut floating in space throws a wrench, exerting a 20 N force. The astronaut
experiences a 20 N force in the opposite direction - (Newton's third law requires that the forces be equal and opposite)
The___force is the fundamental force that gives the Universe its structure.
gravitational (Gravity holds together astronomical bodies of all sizes, from planets to galaxies)
The tendency of a body at rest to remain at rest, or of a body moving in a straight line to remain moving in a straight line, is known as
inertia
A car turns a corner, and the Moon orbits Earth. There is more inertia overcome in changing the Moon's direction because
it is much more massive - (The more mass, the more inertia)
If a spacecraft launched from Earth doesn't have sufficient velocity, ____
it won't break free of Earth's gravity - (The spacecraft has to be going faster than the escape velocity)
The speed of an object is how fast it moves--how far it goes over a period of time. The velocity of an object is
its speed and the direction it travels
For the same radius, the larger a planet's mass, the___the escape velocity.
larger
The surface gravity of a planet with twice the mass and twice the radius of Earth will be ______ surface gravity of Earth
less than - (The radius is squared but the mass isn't)
