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Chapter 4

Department

Astronomy & AstrophysicsCourse Code

AST201H1Professor

Stefan MochnackiChapter

4This

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4.1 describing motion

speed: how far it will go in a certain amount of time

velocity: describes both its speed and direction

acceleration: changes in velocity whether speed or direction

acceleration works both speeding up or slowing down

one of most important acceleration: gravity

galileo: throw weights from leaning tower of pisa – learned that gravity accelerates

all objects in same amount regardless of mass

the difference in acceleration is caused by air resistance

acceleration of falling object – acceleration of gravity

on earth 9.8 meters every second (around 10m)

momentum = mass X velocity

only way to change an object’s momentum is to apply force to it

when net force = 0, you can be moving in a circle or curved road

angular momentum is turning momentum

when earth rotations, rotational angular momentum

when earth orbits sun, orbital angular momentum

torque -type of force that can change an object’s angular momentum

torque depends on how much force applied but also where

mass – amount of matter in your body (same everywhere)

weight – force that a scale measures when you stand on it (depends on mass and

forces (gravity) acting on it)

elevator: when stationary or moving at constant velocity, your weight is the same

when accelerating upwards, floor exerts more force so your weight measured is

heavier

when accelerating downwards, floor exerts weaker force so your weight is much

lighter

if elevator breaks (free fall) with no resistance, you would have zero weight (floor

exerts no force on you) weightlessness

weightlessness in space – not because theres no gravity – but they are at free fall all

the time

orbital altitude of 28,000 km/hr – if you jump that fast you would be orbiting around

earth instead of falling

4.2 newton’s law of motion

newton destroyed Aristotle’s physics and brought earth and the heavens into one

universe

his insights became the birth of astrophysics

newton published laws of motion and gravity which govern everything from daily

movements to movements of stars throughout the universe

an object moves at constant velocity if there is no net force acting upon it

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essentially restates Galileo’s discovery that objects remain in motion until a force

acts to stop it

objects at rest stay at rest and objects in motion remain in motion with no change in

either their speed or direction

force = mass X acceleration

force = rate of change in momentum

standard unit of force is kg-m per second squared, aka newton

weight = mass X acceleration of gravity

for any force, there is always an equal and opposite reaction force

standing on the ground – weight exerts downward force and floor is exerting

upward force (hence why you are not falling)

objects always attract each other through gravity

you always exerts gravitational force on earth & earth reacts

4.3 Conservation laws in astronomy

conservation of momentum: the total momentum of interacting objects cannot

change as long as no external force is acting on them

total momentum is conserved

object can only lose or gain momentum if some other object’s momentum changes by

a precisely opposite amount

eg. Pool, the momentum of one ball is transferred to the other ball but the net

momentum is the same

conservation of angular momentum: as long as there is no external torque, the total

angular momentum of a set of interacting objects cannot change

an individual object can change its angular momentum only by transferring some

angular momentum to or from another object

angular momentum = m X v X r

orbital angular momentum: m = mass of earth, v = speed (velocity) around the orbit,

r = radius of orbit

because nothing is taking or giving to the earth’s angular momentum, rotation stays

the same

tell us that: earth needs no fuel to keep orbiting

also: earth’s angular momentum at any point in its orbit depends on product of

speed and orbital radius (distance from sun), earth is faster near the sun and slower

away from sun

rotational angular momentum: same thing, it keeps rotating at the same rate until

some outside force changes it

in fact, earth is gradually transferring some of its rotational angular momentum to

the moon, and result: its own rotation is slowing down

skaters: arms out – slower (bigger radius), arms in – faster (smaller radius)

conservation of energy: energy can neither be destroyed or created

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