Changes

The satellite and everything in it are constantly falling towards the Earth but will never reach it. Since they are all falling with the same velocity, the satellite does not exert any force on the objects or people inside. The people inside, therefore feel weightless. remember we have a sense of weight because of the Normal force. Here the Normal force is zero and so we feel weightless.

The satellite and everything in it are constantly falling towards the Earth but will never reach it. Since they are all falling with the same velocity, the satellite does not exert any force on the objects or people inside. The people inside, therefore feel weightless. remember we have a sense of weight because of the Normal force. Here the Normal force is zero and so we feel weightless.

This is very similar to the sense of loss of weight in a lift that is accelerating downwards - except that here the acceleration is the acceleration due to gravity.

This is very similar to the sense of loss of weight in a lift that is accelerating downwards - except that here the acceleration is the acceleration due to gravity.<br><br>

Satellite

== Satellite ==

An Earth satellite is simply a projectile that falls around the Earth rather than into it. That means the horizontal falling distance matches the Earth''s curvature. Geometrically, the curvature of the surface is that its surface drops a vertical distance of 5 metres for every 8000 metres tangent to the surface.

An Earth satellite is simply a projectile that falls around the Earth rather than into it. That means the horizontal falling distance matches the Earth''s curvature. Geometrically, the curvature of the surface is that its surface drops a vertical distance of 5 metres for every 8000 metres tangent to the surface.

Therefore, if we throw a rock or a ball at a high enough speed (about 29000 km/s), it would follow the curvature of the Earth. But at this speed, atmospheric friction (due to air drag) would burn up everything. This is why satellites are launched at an altitude high enough for the air drag to be negligible.

Therefore, if we throw a rock or a ball at a high enough speed (about 29000 km/s), it would follow the curvature of the Earth. But at this speed, atmospheric friction (due to air drag) would burn up everything. This is why satellites are launched at an altitude high enough for the air drag to be negligible.

Satellite motion was understood by Newton who reasoned that the Moon was simply a projectile that was circling the Earth.

Satellite motion was understood by Newton who reasoned that the Moon was simply a projectile that was circling the Earth. <br><br>

Kepler's Laws

= Kepler's Laws =

Concept flow

== Concept flow ==

    The key concept to understand here is that gravitational forces play an important role in planetary motion.

*The key concept to understand here is that gravitational forces play an important role in planetary motion.

    Three laws of planetary motion that describe the motion of the planets have been postulated based on detailed astronomical observations

*Three laws of planetary motion that describe the motion of the planets have been postulated based on detailed astronomical observations

Laws of Planetary Motion

== Laws of Planetary Motion ==

We now know that satellites are continually falling towards the Earth following a curved path whose curvature is greater than that of the curvature of the Earth. The Moon is just such a satellite that moves around the Earth. In a similar way, all the planets that move around the Sun are satellites of the Sun. The motion described in such a situation is not strictly circular - it is elliptical.

We now know that satellites are continually falling towards the Earth following a curved path whose curvature is greater than that of the curvature of the Earth. The Moon is just such a satellite that moves around the Earth. In a similar way, all the planets that move around the Sun are satellites of the Sun. The motion described in such a situation is not strictly circular - it is elliptical.

Johannes Kepler, working with data painstakingly collected by Tycho Brahe without the aid of a telescope, developed three laws which described the motion of the planets across the sky.

Johannes Kepler, working with data painstakingly collected by Tycho Brahe without the aid of a telescope, developed three laws which described the motion of the planets across the sky.

1. The Law of Orbits: All planets move in elliptical orbits, with the sun at one focus.

1. The Law of Orbits: All planets move in elliptical orbits, with the sun at one focus.<br><br>

2. The Law of Areas: Each planet moves so that an imaginary line drawn from the Sun to the planet sweeps out equal areas in equal periods of time.

2. The Law of Areas: Each planet moves so that an imaginary line drawn from the Sun to the planet sweeps out equal areas in equal periods of time.<br><br>

3. The Law of Periods: The square of the period of any planet is proportional to the cube of the semimajor axis of its orbit.

3. The Law of Periods: The square of the period of any planet is proportional to the cube of the semimajor axis of its orbit.<br><br>

Kepler's laws were derived for orbits around the sun, but they apply to satellite orbits as well.

Kepler's laws were derived for orbits around the sun, but they apply to satellite orbits as well.<br><br>

The Law of Orbits

=== The Law of Orbits ===

All planets move in elliptical orbits, with the sun at one focus. An ellipse is a closed curve such that the sum of the distances from any point P on the curve to two fixed points (called the foci, F1 and F2) remains constant.

All planets move in elliptical orbits, with the sun at one focus. An ellipse is a closed curve such that the sum of the distances from any point P on the curve to two fixed points (called the foci, F1 and F2) remains constant. <br>

Orbit eccentricity

'''Orbit eccentricity'''

The semi major axis of the ellipse is a and represents the planet's average distance from the Sun. The eccentricity, “e” is defined so that “ea” is the distance from the centre to either focus. A circle is a special case of an ellipse where the two foci coincide. The Earth and most of the other planets have nearly circular orbits. For Earth, “e” = 0.017.

The semi major axis of the ellipse is a and represents the planet's average distance from the Sun. The eccentricity, “e” is defined so that “ea” is the distance from the centre to either focus. A circle is a special case of an ellipse where the two foci coincide. The Earth and most of the other planets have nearly circular orbits. For Earth, “e” = 0.017.<br><br>

The Law of Equal Areas

=== The Law of Equal Areas ===

Kepler's second law states that each planet moves so that an imaginary line drawn from the Sun to the planet sweeps out equal areas in equal periods of time.

Kepler's second law states that each planet moves so that an imaginary line drawn from the Sun to the planet sweeps out equal areas in equal periods of time.

This can be shown to be true using the law of conservation of angular momentum.

This can be shown to be true using the law of conservation of angular momentum.

If “v” is the velocity of the planet, in time “dt” the planet moves a distance vdt and sweeps out an area equal to the area of a triangle of base “r” and altitude vdt sinα.

If “v” is the velocity of the planet, in time “dt” the planet moves a distance vdt and sweeps out an area equal to the area of a triangle of base “r” and altitude vdt sinα.

dA/ dt = (½)L/m

dA/ dt = (½)L/m

Because the angular momentum is conserved, the rate of change of area covered is constant. This means that the planets move with different velocities depending upon their position in the orbits.

Because the angular momentum is conserved, the rate of change of area covered is constant. This means that the planets move with different velocities depending upon their position in the orbits.<br><br>

The Law of Periods

=== The Law of Periods ===

The ratio of the squares of the periods of any two planets revolving about the Sun is equal to the ratio of the cubes of their semi-major axes.

The ratio of the squares of the periods of any two planets revolving about the Sun is equal to the ratio of the cubes of their semi-major axes.

T12/ r13 = 4π2 / G Ms

T12/ r13 = 4π2 / G Ms

Deriving this for another planet, we can arrive at the third law.

Deriving this for another planet, we can arrive at the third law.<br><br>

 

 

 

 

 

 

 

 

 

 

 

 

 

2. Cavendish experiment - This link gives a simple sketch of the Cavendish experiment.

#Gravity is more than a name - This link gives an overview of what gravity is.

3.http://sciencedemonstrations.fas.harvard.edu/icb/icb.do?keyword=k16940&pageid=icb.page80669&pageContentId=icb.pagecontent277503&state=maximize&view=view.do&viewParam_name=indepth.html - This website demonstrates the set-up of the Cavendish experiment.

#Cavendish experiment - This link gives a simple sketch of the Cavendish experiment.

    Animation of the Cavendish experiment

#http://sciencedemonstrations.fas.harvard.edu/icb/icb.do?keyword=k16940&pageid=icb.page80669&pageContentId=icb.pagecontent277503&state=maximize&view=view.do&viewParam_name=indepth.html - This website demonstrates the set-up of the Cavendish experiment.

    From Classical Mechanics to General Relativity - This is a good description of the geometry of Newtonian gravity and how to move from classical mechanics to relativity.

#www.hyperphysics.com - From Classical Mechanics to General Relativity - This is a good description of the geometry of Newtonian gravity and how to move from classical mechanics to relativity.

    The Value of "g" (http://www.physicsclassroom.com/Class/circles/U6L3e.cfm) - This is a good resource to study the variation of “g” at various distances above the Earth's atmosphere.

#The Value of "g" (http://www.physicsclassroom.com/Class/circles/U6L3e.cfm) - This is a good resource to study the variation of “g” at various distances above the Earth's atmosphere.

    http://science.nasa.gov/science-news/science-at-nasa/2004/06may_lunarranging/ - This link examines the Galileo experiment and discusses if there are other possible explanations.

#http://science.nasa.gov/science-news/science-at-nasa/2004/06may_lunarranging/ - This link examines the Galileo experiment and discusses if there are other possible explanations.

    http://www.physicsclassroom.com/Class/circles/U6L4b.cfm -This website describes the mathematics of orbital motion.

#http://www.physicsclassroom.com/Class/circles/U6L4b.cfm -This website describes the mathematics of orbital motion.

    http://spaceflight.nasa.gov/gallery/images/station/crew-9/html/iss008e21996.html

#http://spaceflight.nasa.gov/gallery/images/station/crew-9/html/iss008e21996.html  

Keywords

= Keywords =

    Mass, Inertial, Gravitational, Force field, Universal law of gravitation, Acceleration due to gravity, “g”, weight, weightlessness

Mass, Inertial, Gravitational, Force field, Universal law of gravitation, Acceleration due to gravity, “g”, weight, weightlessness