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Monday, September 19, 2011

ORBITS of Satellites … Part 1

ORBITS of Satellites … Part 1 ( Essential Background Information )

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We have read that the satellites are launched using rocketsand are placed in orbit. But based onhow and where it was released inorbit the satellite takes various types of orbits.

Depending on the usage few chosen orbits types that are GeoSynchronous, Sun Synchronous, Molniya etc.
Orbits are also classified as Equatorial, Polar, Inclined, Prograde, Retrograde etc.

What are the different possible orbits and why these satellitesareplaced in that orbit is the subject matter of these few posts.

But before we go into detailes on the subject of Orbits a littlerevision of facts about the shape of our dear Earth and its position in Solar systemand in Galaxy will be helpful.
Shape of Earth and its spinning motion:

1. Shape of Earth :
EquatorialRadius = 6318.1370 Kms
PolarRadius = 6356.7513 Kms
Mass ofEarth = 5.9722X1024 Kgs

Flatteningof Earth = 1/298.257223563 ( It is the ratio of Difference in the Polar
and Equatorial radii divided by Equatorial Radius )
2. Earth spins around its PolarAxis and its rotational period is : (hold your breath !! ) 23h56m4.09s

3. Speed at which Equator rotates: ( = Circumference at Eq / rotationperiod ) =1674.366 Kms/hr

This was about how the Earthrevolves on its axis.One may go through an earlier post

Revolution of Earth around Sun. Solar and Sidereal Periods:

The Earth revolves around Sun anda small revision on that subject follows:

1 Earth’s Orbit around sun: Elliptical with about147m Kms X 151m Kms radii ( m=million )
2. Period for one revolution(ie period for exact 3600 around Sun ) = 365.2421 days
3. Earth’s speed around Sun ( =Circumference / 365.2421 ) = 29.8 Kms/sec approx

A Good animation about our galaxy is available here .

We said the day length is 23h56m4s ( not 24 hrs ) . Why?

Imagine that you are fixed on the earth and that what yousee is only through a narrow tube and you can’t see any othersurroundings. Now if you see a star whichis at infinity thru that tube today then you will see that star again exactly after24 hours by which time the earth would have rotated around its axis by 360degand so the tube would again point to that direction.

An exaggerated figure is drawn here .. the star direction are two parallel directionson two days.

Day 1 the star andsun are in the same diection so you see both the sun and star simultaneously.But on Day2 the Star appears first and the Sun appears only after some morerotation of Earth because the Earth has moved some distance away from the day 1’s position.

By definition our one day of 24 hours is based on Sun’s reappearancein the same direction ( hence the name Solar day ) and therefore the rotation of of Earth by 360deg takes less than 24 hours. This period is called as a Sidereal ( ie correspondingto Star reference ) day.

One can easily find a relation between the two periods.

When the Earth rotates around sun through 360 degrees ( That is say for example 'second day' position now and same position after one year ) , the Earth would have taken 365 .2421 Sidereal days and so the Star would have been visible 365 times. BUT in the same period the sun would would have been visible 366 times ( Because the earth would have spinned one extra rotation on its axis ).

So the Solar day = ( 365.2421/366.2421 ) * 24 Hrs = 23h56m approx.

Earth's Magnetic Field:

We have come across the concept of a Huge Virtual Magnet inside the Earth with two North and South poles as shown in the figure here:

It shows that the magnetic poles is not exactly matching with Geographic poles which are related to the axis on which the Earth spins. There is a tilt of about 10 degrees between the two axes and the South pole is located near the Geographic North Pole. Therefore there exists a varying angular difference between the Magnetic Lines of force and the Longitudinal lines. This difference is called Magnetic Deviation and this correction has to be applied if we use a magnetic compass for surveying because the magnetic compass will always be parallel to Magnetic line whereas the Longitude line will be connecting the Geographic poles.

But this simplified concepts needs to be refined. Actually the Earth;s core is not solid and so there really is no SOLID magnet. The magnetic axis is also not exactly passing through the center point of Earth because the two magnetic poles wander about rather unilaterally and not as if they are at end of a rigid rod.

This table shows how the poles have wandered in the recent past.

Graphically the same is shown below over a longer period:

Charts of secular variation

In addition to this there is also a variation in Earth's Magnetic Field from place to place due to the Variation in the density of Landmass and Earth's oblateness. A detailed representation map is available here and its thumbnail looks like this:
This needs to be understood correctly because this variation in magnetic intensity causes the Geosynchronous satellites to slowly drift to the two points over equator ( 75 deg E and 105 deg W ) if periodically not corrected intentionally through proper station keeping maneuvers . These two points are called as Stable points because the satellite placed there will not drift even in the absence of station-keeping.

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