Unit 4: Planetary Motion

Kinetic Energy Formula

KE = 1/2(mass x velocity^2)

Potential Energy Formula

PE = mass x 9.8 m/s^2 x height

Newton’s Second Law Formula

Force = mass x acceleration

Eccentricity Formula

E = distance between foci/major axis

Momentum Formula

Momentum = mass x velocity

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p = mv

Universal Gravitation Formula

Force of Gravity = (G x m1 x m2)/d^2

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G = 6.673 x 10^-11 N m^2/kg^2

Kepler’s Laws

1. Law of Ellipses

2. Law of Equal Areas

3. Law of Harmonies

Law of Ellipses

The path of the planets about the Sun is elliptical in shape

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Center of Sun is one focus

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Eccentricity = distance between foci/width of ellipse

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Closer foci = more circular

Law of Equal Areas

Describes the speed at which any given planet will move while orbiting the sun

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A planet moves fastest when closer to the sun (perihelion) and slowest when farthest from sun (aphelion)

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Triangles are equal throughout orbit but some wider and shorter and some skinnier and taller

Law of Harmonies

Compares the orbital period and radius of orbit (distance from sun) of a planet to those of other planets.

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Comparison of planet/satellite speeds

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Period^2 = Distance from Sun^3

Newton’s Three Laws

1. Law of Inertia

2. F = ma

3. Law of action and reaction

Law of Inertia

An object at rest remains at rest and an object in motion maintains its velocity unless it experiences an unbalanced force

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Inertia: the tendency of an object at rest to remain at rest or continue moving with a constant velocity.

F = ma

Force = mass x acceleration Measured in Newtons

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Acceleration = change in velocity (speed or direction)

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Balanced: force = 0

Law of action and reaction

For every action force, there is an equal and opposite reaction force

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Forces are equal and opposite but not balanced because two different objects are involved

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Some forces are from contact and others are from action-at-a-distance interactions (like gravitational)

Law of Universal Gravitation

The force of gravitational attraction is directly dependent upon the masses of both objects and inversely proportional to the square of the distance that separates their centers.

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Mass increases = force of gravity increases

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Greater separation distance = weaker gravity

Apophis Relation to Kepler and Newton Laws

Apophis orbit is very circular

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Orbit speeds up when closer to the sun (higher gravity)

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Will remain in this motion unless acted on by unbalanced force (it was and path is changed)

Centripetal Force

Any force that pulls or pushes an object towards the center of the circle

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For objects moving a a circular motion, there is a net force acting towards the center

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An object moving in circles requires there to be an unbalanced force (like gravity)

Uniform Circular Motion

The motion of an object in a circle at a *constant speed*

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As objects move in circles, they constantly change direction, therefore *accelerating*

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Centripetal force is occurring

Potential Energy

Stored energy or energy held in readiness

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**Elastic:** energy stored in any type of stretched or compressed material

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**Gravitational:** stored energy that depends on height and mass. Affected more by height

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PE = Mass x 9.8 m/s^2 x height

Kinetic Energy

Energy that an object has because it’s in motion

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Depends on mass and velocity (affected more by velocity)

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Small increase in velocity = large increase in energy

Law of Conservation of Energy

Energy cannot be created or destroyed but can be transferred

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**Energy Conversions**: energy transfers or changes form to another type of energy

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Total energy in the system stays the same

Law of Momentum

Total momentum is maintained in a collision