Chapter 12: Gravity

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Describe the movement of the moon towards the earth

-the moon is constantly falling towards the earth

Describe the movement of an object in uniform circular motion in relation to the center of the circle

-an object in uniform circular motion accelerates toward the center of the circle

What is the force responsible for the moon's centripetal acceleration?

-the Earth's gravitational attraction

What law did Newton propose to describe the force of gravity?

-the law of universal gravitation

What is the equation that describes the law of universal gravitation?

F = G (m1*m2/r^2)

What is F?

-the force of gravity between any two point objects of mass m1 and m2

What is r?

-the distance between the masses

What is G?

-the universal gravitation constant

What is the value of the universal gravitation constant?

6.67 e^-11 N*m^2/kg^2

Along what line is the force directed along?

-the line connecting the masses

Comparatively describe the force that each mass experiences

-each mass experiences a force of the same magnitude, but acting in opposite directions

As such, what does the force of gravity between two objects form?

-an action reaction pair

What is one of the key implications of the law of universal gravitation? (hint: related to attraction between objects in the universe)

-all objects in the universe attract all other objects in the universe by way of gravitational interaction

What does the fact that G is such a small number mean?

-that the force of gravity between objects of human proportions is imperceptibly small

Does the force of gravity increase or decrease with distance?


Does the force of gravity ever vanish with distance?

-no it does not
-gravity is a force of infinite range

What is the relationship between F and distance?

F varies as 1 / r^2

Since F varies as 1 / r^2, what is F said to have?

-F is said to have an inverse square dependence on distance

For example, an increase in distance by a factor of 10 results in a decrease in the force by a factor of what?

10^2, or 100

Since the force of gravity between two masses depends on the product of the masses, what follows? (in terms of gravity)

-that if either mass is doubled, the force of gravity is doubled as well

If a given mass is acted on by gravitational interactions with a number of other maseses, what is the net force acting on a mass?

-a vector sum of each of the forces individually

What is the property of gravity referred to as?


Does the acceleration due to gravity have a higher value at sea level or on the top of Mt. Everest?

-higher value at sea level

Does the universal gravitation constant to Mars? to the Moon?

-yes, the universal gravitation constant applies to any object in the universe

What does the law of universal gravitation describe?

-how gravity works everywhere in the universe

What is the distance of the "r" value that is used in Newton's Law of Universal Gravitation?

-the distance between two massess center-to-center

What are the units of the universal gravitation law?

N * m^2 / kg^2

What does the universal gravitation law actually say?

-if you take two 1 kg masses and put them 1 meter apart, then the strength of the attraction is equal to 6.67e^-11 N * m^2 / kg^2

What is one of the most important implications of G?

-every object in the universe is attracted to all other objects


-F of gravity will not equal zero unless r = infinity
-since the universe is not infinite, the case will never be met
-->thus, every object in the universe will always be attracted to other objects

What then is mass?

-a membership card to being attracted by other masses

If we experience attraction to everything in the universe, why do we only feel one attractive force (to that of the Earth)?

-because Earth is the biggest mass that is close by

Given the equation g = GMearth/r^2, what would g be if the radius was increased from 1 to 2?

1/4 g

If the radius was increased from 1 to 3?

1/9 g

What pattern do you see?

-whatever you do to r, you will do one over that factor squared to g

Given the equation q = (x√z)/y^2, what will q be if x becomes 3x?

-q will be 3q

If y becomes 4y?

-q will be 1/16 q

If z becomes 25 z?

-q will be 5q

Must you be outside of a body/mass to calculate the pull of gravity of that object?



-if you were to go inside of a body, you would have different parts of a body pulling on you differently

Are mass and weight the same thing?

-no they are not

What is mass?

-Ilka: "how much stuff" is in an object
-Book: a measure of the inertia of an object

Is mass an intrinsic or extrinsic property?


Therefore, does it change based on location?

-no it does not

What is weight?

-the force of gravity on an object (due to another body's pull)

Is weight an intrinsic or extrinsic property?

-extrinsic property

What is it defined by?

-your location/surroundings

Therefore, does it change based on location?

-most definitely

Are mass and weight related?



Force of gravity = mg = W

Therefore, what impact does increasing the mass of an object have?

-if you increase the mass of an object (while your location stays the same), then weight will correspondingly increase

Therefore, what does having more mass mean?

-you participate more in the gravitation club/phenomena

If you traveled from the Earth to the Moon (and ate a typical/healthy amount on the way), would your mass stay the same?

-mass is an intrinsic property that is not dependent upon location

If you traveled from the Earth to the Moon (and ate a typical/healthy amount on the way), would your weight stay the same?

-no it would not


-because weight is an extrinsic property that is dependent upon location
-since the moon's gravitational force is less than that of the Earth's, weight will decrease when mass is held constant

What is the SI unit for mass?


What is the English unit for mass?


What is the SI unit for weight?


What is the English unit for weight?


Therefore, what do you compare when you compare kilos and pounds?

-mass vs. weight

Therefore, what is the relationship between kilos and pounds?

-1 kg of mass only weighs 2.2 lbs on the Earth's surface
-comparison values will be dependent upon location

Is a comparison between kilos and slugs dependent upon location?


Why not?

-because kilos and slugs are both units of mass

Is a comparison between newtons and pounds dependent upon location?


Why not?

-because newtons and pounds are both units of weight

When an object is in orbit around another body, how does the force required to keep the object in circular motion compare to the actual force supplied?

force required = force actual

Describe the relationship between orbital speed and distance

-as the distance between two object increases, the necessary orbital speed decreases
-->as you go farther away, you can slow down and still maintain circular motion

Is orbital speed dependent on mass?


Describe the moon's position when it is not visible in the sky

-the moon is between the Earth and the sun
-as such, it is not illuminated from our perspective and we cannot see it

Describe the moon's position when it is "half moon"

-moon and Earth at an equal x distance from the sun
-as a result, only half of the moon is illuminated by the sun from our perspective

Describe the moon's position when it is full moon

-Earth is between moon and sun
-all of moon is illuminated from our perspective

The orbital period of the moon around the Earth is calculated to be 27.4 days. Why is the actual period greater than this value?

-as the moon is travelling around the Earth, after 27 days the Earth has changed position
-when the Earth's movement is accounted for, the phases of the moon are more than one Earth period

What is the orbital period of the Earth around the sun?

-365.24220 days

What calendar system is based off of this calculation?

-Julian calendar

What is wrong with this calculation?

-actual rotation is equal to 365.25 days minus 11 minutes

By 1582, how many days was the calendar off by?

-11 days

What was ordered?

-rectification by pope gregory

What calendar system is now used?


What has been instituted to ensure that we do not develop further inaccuracies?

-currently, we do not have a leap year every year
-leap years do not occur during turn-of-century years that are not divisible by 400

It is often said that astronauts in orbit experience weightless ness because they are beyond the pull of Earth's gravity. Is this statement correct? Explain.

-no it is not
-->the force of Earth's gravity is practically as strong in orbit as it is on the surface of the earth

Why then do astronauts experience weightlessness?

-because they are inconstant free fall

Why can't gravitational force be dependent upon the sum of two masses?

-because it would predict a nonzero force even when one of the masses is zero
-->this is certainly not observed

An astronaut orbits the Earth in a space capsule whose height above the surface is one Earth radius. If m is her mass on the surface of the Earth, then at her current location, her mass is...?


An alien moon orbits around an alien planet at speed v, at an orbital radius R. The correct value for the universal gravitation constant could be obtained by what equation?

G = v2(R) / Mp

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