Astronomy 1021 Chapter Notes - Chapter 4: Kelvin, Orbital Speed, Projectile Motion

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16 Aug 2016
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Chapter 4: Making Sense of the Universe
Speed: Rate at which object moves
Speed=distance/time (units of m/s)
Velocity: Speed and direction (ex: 10m/s, due east)
Change of position over time
Acceleration: change of velocity over time
Slowing down
Speeding up
Changing direction
Units of speed/time (meters/s)/s=(m/s2)
Ex: 0 to 100 km/h in 4 seconds
Gravity & acceleration
Negative velocity= in the wrong direction
falling objects accelerate due to gravity
Earth: g=10m/s2
Moon: g=1.7m/s2
Mass: the amount of matter in an object
Measured in grams or kg
On earth, we often think about this in terms of an object's weight
Not quite correct- mass and weight are different but related things
1kg on earth = 1kg on moon
Gravity Acceleration & Mass
Acceleration due to gravity is independent of the mass of object
Newton's second law: F=mg (force = mass x acceleration)
Inertia: resistance of any physical object to any change in its state of motion
oThis is why any ball dropped from the top of a building will fall at the same rate
Force: interaction between objects that changes speed, direction or shape
Net force: sum of all forces acting on an object
If net force is mon-zero, get change of momentum (usually an acceleration)
Force of gravity, air, water, etc
Newton and birth of astrophysics
Realized same physical laws that operate on earth also operate in heavens
Discovered laws of motion and gravity
Also experiments with light, created first reflecting telescope, calculus, etc.
Newton's laws of motion
Three laws that apply to all motion from our daily motions to movement of planets, stars, galaxies
1. An object moves at a constant velocity if there is no net force acting upon it
oSpacecraft don’t need fuel except to change speed or direction
oDon't feel net force when travelling in a plane
oIf net force on object is 0, it has constant velocity
2. Force = mass x acceleration
oDescribes what happens when net force is present: object will accelerate in the
direction of the force, the amount of the acceleration depends on object's mass and
strength of force
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oThe harder you push, the more acceleration you get
oYou have to push a big thing harder than a little thing to make the same change in
velocity
3. For any force, there is always an equal and opposite reaction force
oAction = reaction
Mass vs. Weight
Mass is the amount of matter in your body, measured in kilograms (kg)
Weight (or apparent weight) is the force that a scale measures when you stand on it, depends
both on mass and forces (including gravity) acting on your mass; downward force that acts upon an
object, measured in Newtons (N)
Weight is a force, while mass is not
Free-fall
Falling without resistance to slow you down
Floor drops at the same rate you fall, allows you to "float" freely about it
Free-fall makes you weightless
Weightlessness in space
Astronauts are weightless the entire time they orbit earth because they are at a constant state of
free-fall
The larger your horizontal speed, the farther you can go before gravity brings you back to the
ground (think of projectile motion)
If you were to run out of a tower that reaches to space station's orbit (350km) at 28000km/hr
(17000mi/hr), by the time gravity has pulled you forward as far as the length of the tower, you'd
already have moved far enough around the earth that you'd no longer be going down at all
You could continually "fall" around Earth, you'd be in orbit
Momentum
Product of mass and velocity, momentum = mass x velocity
The only way to change an object's momentum is to apply force (second law)
Total momentum of interacting objects cannot change as long as there is no external force acting
on them, total momentum is conserved
Conservative Laws in Astronomy
Conservation of momentum
total momentum of all interacting objects always stays the same; an individual object can gain or
lose momentum only when a force causes it to exchange momentum with another object
Angular momentum (circling/spinning/orbiting momentum)
Law of conservation of angular momentum
oTotal angular momentum can never change
oIndividual object can change its angular momentum only by changing some angular
momentum to or from another object
oAngular momentum = Mass x (rotation) velocity x distance
oTorque- a "twisting force", total angular momentum of interacting objects cannot change
as long as there is no external torque
Orbital Angular Momentum
oEarth's angular movement = earth's mass x orbital velocity x radius of orbit
oNo objects to give/take angular momentum from Earth as it orbits the sun so orbital
angular momentum must always stay the same, proves:
Earth needs no fuel or push of any kind to keep orbiting the sun - will keep
orbiting as long as nothing comes along to take angular momentum away
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Because earth's angular momentum at any point depends on product of speed
and orbital radius, earth's orbital speed must be faster when it is nearer to the sun and
slower when farther from the sun
Rotational Angular Momentum
oEarth isn't transferring any of the angular momentum of it rotation to another object,
keeps rotating at the same rate
oClouds must spin faster as gravity makes them shrink in size
Law of conservation of energy
mv2
Energy cannot appear out of nowhere or disappear into nothingness
Objects can gain or lose energy only by exchanging energy with other objects
Energy can be transformed or exchanged
Basic type of energy
oKinetic energy: energy of motion
Thermal energy: collective kinetic energy of the many individual particles moving
randomly within a substance like a rock or the air or the gas within a distant star
Thermal energy & temperature are not the same, average vs. total
energy
If density is higher, energy content is higher
Temperature measures average kinetic energy of particles
Uses Kelvin temperature scale
Coldest possible = absolute zero (0 K)
0 Celsius = 273.15 K, 0 K = -273.15 Celsius
oRadiative energy: energy carried by light
oPotential energy: stored energy
Gravitational potential energy: object has more gravitational potential energy
when it is higher and less when it is lower
As potential energy decreases, energy is converted to kinetic energy
Mass-energy: mass as a form of potential energy
E=mc2 (c=speed of light)
Small amount of mass can release lots of energy
Concentrated energy can spontaneously turn into matter (ex: in particle
accelerators)
oStandard unit of energy: joule (1 calorie = 4184 joules)
The Universal Law of Gravitation
Force that keeps planets in their orbits is an inverse square law, and is the same as the force
that on earth cases objects to fall down and accelerate
Gravitational force between objects depends on mass and distance
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