# 6.6 Satellites and kepler’s laws: an argument for simplicity

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• State Kepler’s laws of planetary motion.
• Derive the third Kepler’s law for circular orbits.
• Discuss the Ptolemaic model of the universe.

Examples of gravitational orbits abound. Hundreds of artificial satellites orbit Earth together with thousands of pieces of debris. The Moon’s orbit about Earth has intrigued humans from time immemorial. The orbits of planets, asteroids, meteors, and comets about the Sun are no less interesting. If we look further, we see almost unimaginable numbers of stars, galaxies, and other celestial objects orbiting one another and interacting through gravity.

All these motions are governed by gravitational force, and it is possible to describe them to various degrees of precision. Precise descriptions of complex systems must be made with large computers. However, we can describe an important class of orbits without the use of computers, and we shall find it instructive to study them. These orbits have the following characteristics:

1. A small mass $m$ orbits a much larger mass $M$ . This allows us to view the motion as if $M$ were stationary—in fact, as if from an inertial frame of reference placed on $M$ —without significant error. Mass $m$ is the satellite of $M$ , if the orbit is gravitationally bound.
2. The system is isolated from other masses . This allows us to neglect any small effects due to outside masses.

The conditions are satisfied, to good approximation, by Earth’s satellites (including the Moon), by objects orbiting the Sun, and by the satellites of other planets. Historically, planets were studied first, and there is a classical set of three laws, called Kepler’s laws of planetary motion, that describe the orbits of all bodies satisfying the two previous conditions (not just planets in our solar system). These descriptive laws are named for the German astronomer Johannes Kepler (1571–1630), who devised them after careful study (over some 20 years) of a large amount of meticulously recorded observations of planetary motion done by Tycho Brahe (1546–1601). Such careful collection and detailed recording of methods and data are hallmarks of good science. Data constitute the evidence from which new interpretations and meanings can be constructed.

## Kepler’s laws of planetary motion

Kepler’s First Law

The orbit of each planet about the Sun is an ellipse with the Sun at one focus.

Kepler’s Second Law

Each planet moves so that an imaginary line drawn from the Sun to the planet sweeps out equal areas in equal times (see [link] ).

example ofchange of state of the body in the effectof heat
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the force that pushes upward on us. the force that opposes gravity
clifford
upthrust of air
Newton's 3rd law. the force of the ground (earth) that pushes back on gravity, keeping us on the ground instead of sinking into it.
clifford
I really need lots of questions on frictional force
Shii
I can help answering what I can
Shii
does friction also need some force to perform?
Mohit
no friction is a force just like the gravitational force
clifford
yeah but u can't apply friction anywhere else like other forces
Mohit
I don't understand that question. friction does work alongside other forces based on the situation.
clifford
eg. when walking there are two forces acting on us gravitational and frictional force. friction helps us move forward and gravity keeps us on the ground
clifford
friction is a contact force. Two surfaces are necessary for the force to work.
clifford
hope this helped
clifford
the friction force which oppose while it contact with surrounding. there are two kind of friction. slidding and rolling friction.
Neyaz
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Ogboru
Hi
Olamide
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Fauzia
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vijay
Good
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Yuri
Straight out of google, you could do that to, I suppose.
Yuri
*too
Yuri
ok
Fauzia
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Neyaz
examples of work done by load of gravity
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Yuri
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Yuri
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Maureen
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ok thanks
Fauzia
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Fauzia
concave and convex
right
Fauzia
speed of light in space
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ok
Vikash
2.99×10^8m/s
Umair
2.8820^8m/s
Muhammed
Vikash
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vijay
3×10^8m/s
vijay
is it correct
Fauzia
I mean 3*10^8 m/s ok
vijay
299792458 meter per second
babar
3*10^8m/s
Neyaz
how many Maxwell relations in thermodynamics
vijay
how we can do prove them?
vijay
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Neyaz
please who has a detailed solution to the first two professional application questions under conservation of momentum
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Osei
I can help
Emeh
okay go on
True
I mean on pressure
Emeh
definition of Pressure
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pls explain Doppler effect
Emmex
solve this an inverted differential manometer containing oil specific gravity 0.9 and manometer reading is 400mm find the difference of pressure