# 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

-decrease

### 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

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

-superposition

### 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

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

### Why?

-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

1/4 g

1/9 g

### What pattern do you see?

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

-q will be 3q

### If y becomes 4y?

-q will be 1/16 q

-q will be 5q

-yes

### Why?

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

-no they are not

### What is mass?

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

-intrinsic

-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

-most definitely

-yes

### How?

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?

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

-no it would not

### Why?

-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

-kg

-slugs

-newtons

-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

-no

### Why not?

-because kilos and slugs are both units of mass

-no

### 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

-no

### 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

-365.24220 days

-Julian calendar

### What is wrong with this calculation?

-actual rotation is equal to 365.25 days minus 11 minutes

-11 days

### What was ordered?

-rectification by pope gregory

-Gregorian

### 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

-m

G = v2(R) / Mp

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