today: newton's law of universal...
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Phys 40S_Fields_Lesson 1.notebook
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May 01, 2014
Apr 221:59 PM
Physics 40S
Fields Lesson 1
Apr 221:59 PM
Today:
issues pertaining to space exploration
Kepler's Laws
Newton's Law of Universal Gravitation
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Space Exploration Issues1. Technological advancement drive to spread genetic material. The wider the distribution of a species, the better the chance of survival.
2. Promotion of global cooperation
3. Social and economic benefits locate more resources
4. Allocation of resources shifted away from other pursuits
5. Possibility of disaster
Apr 222:01 PM
Your task:
choose one of the topics from the previous page (everyone should choose a different topic)
create oneminute presentation to be shared next class
how did you interpret your topic
pros, cons
articles, media examples
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Kepler's Laws:
First Law: Each planet moves around the Sun in an orbit that is an ellipse, with the Sun at one focus of the ellipse
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Note: An ellipse is a curve on a plane surrounding two focal points such that a straight line drawn from one of the focal points to any point on the curve and then back to the other focal point has the same length for every point on the curve.
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Second Law: The straight line joining a planet and the Sun sweeps out equal areas in space in equal intervals of time. (Each planet moves most rapidly when closest to the Sun and least rapidly when farthest from the Sun.)
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Third Law: The squares of the orbital periods of the planets around the Sun are proportional to the cubes of the orbital semimajor axes.If you know the time of a planet's orbit around the Sun, you can calculate its average distance from the Sun (or vice versa). The ratio of the cube of the radius of orbit to the square of the time is a constant, and Kepler's Third Law can be stated as:
K = R3
T2
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Kepler's Third Law applies to objects other than planets, including comets, satellites, and spacecraft
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Ex1/ Calculating the Period of a Planet of the SunA new planet has been discovered in our solar system. What would be the orbital period of this planet if the mean radius of orbit is 8.83 x 1012 m? Note: Ksun = 3.35 x 1018 m3/s2
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Ex 2/ Calculating the Radius of Orbit of a Moon of MarsA moon of Mars named Deimos orbits Mars with a period of 30 h 18 min with a mean distance from the centre of Mars of 2.30 x 104 km. Another moon of Mars called Phobos has a period of 7 h 39 min. What is the mean radius of the orbit of Phobos around Mars?
Apr 222:01 PM
Universal Gravitation
Newton and the apple
Is the force that causes the apple's fall to accelerate the same force responsible for maintaining the Moon's orbit?
The Moon moves in a circular orbit, thus, centripetal acceleration caused by the gravitational pull between the Moon and Earth
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The amount of this acceleration due to gravity was proportional to the gravitational force between earth and the moon (F = ma, so
aMOON FEARTHMOON.
Newton saw that as the distance between objects increased, the force of gravity decreased. The question was, "How is the force of gravity 'diluted' as the separation of objects decreases?"
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By using his knowledge of circular motion and Kepler's Third Law, Newton deduced that the gravitational force was inversely proportional to the square of the distance from earth to the moon:
FEARTHMOON 1
R2
where R is the radius of the Moon's orbit
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Newton's reasoning:
See handout.
May 110:23 AM
Newton's Law of Universal Gravitation says that any two bodies attract each other with forces proportional to the mass of each and inversely proportional to the square of the distance between them.
Fg = Gm1m2
R2
G = 6.67 x 1011 N m2/kg2
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The force of gravity is always attractive.
F21 represent the force of gravity of object 2 on object 1 (21).
F12 represent the force of gravity of object 1 on object 2 (12).
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Ex1/ Determining the Force of Gravitational AttractionTwo basketballs of mass 0.65 kg are placed 1.0 m apart.
The force of gravitational attraction between them is:
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Ex 2/The Effect of Changing Mass on Fg
If the mass of one of the basketballs were to suddenly double to 1.3 kg with the distance between the masses, R, was kept constant, the new force would be:
If both of the masses double:
May 11:02 PM
Ex 3/ The Effect of Changing Separation on Fg
Masses stay the same, but the distance between them doubles:
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Ex 4/ Determining the Mass of a Central BodyMasses of planets cannot be determined directly; must be determined indirectly from other measured values.
Moon orbits earth with a mean radius of orbit 3.80 x 108 m and period 2.36 x 106 seconds. What is the mass of the earth?
May 11:06 PM
To increase the separation of two masses from R1 to R2 requires work to be done to overcome the force of attraction.
As a result of this work being done, the gravitational potential energy of the system increases.
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At any separation distance R, the gravitational potential energy, PEg, between two masses m1 and m2 is given by
PEg = Gm1m2
R
May 11:15 PM
For any object moved from an initial separation distance, R1, to a final separation distance, R2, from another object, then change in gravitational potential energy, ΔPEg, between the two masses m1 and m2 is given by
ΔPEg = Gm1m2 Gm1m2
R2 R1
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Ex/ Calculating Gravitational Potential Energy: General CaseA satellite of mass 275 kg orbits the earth at an altitude of 525 km. The earth has a radius of 6.38 x 106 m and a mass of 5.98 x 1024 kg. What is the gravitational potential energy of the satellite?
May 11:24 PM
Ex/ Calculating a Change in Gravitational Potential Energy: General CaseHow much work would have been done to raise the satellite from the surface of the earth to a point 525 km above the surface of the earth where the satellite is stationary?
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Escape Velocity:
Throw an object up, it will fall back down due to gravity. Throw harder, it will go up farther, but still eventually fall back down.
How fast does an object need to be thrown so that it will never fall back down?
May 11:33 PM
Rocket must reach infinite distance where PEg = 0 before coming to rest. Minimum velocity required to achieve this is called escape velocity.
Math ....
vescape = 2GmE
RE
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May 11:41 PM
Ex/ Escape Velocity for MarsThe Mars rover Spirit is to escape from the surface of Mars out beyond the gravitational field of Mars. What is the escape velocity of Spirit from the surface of Mars?