Many planets have satellites revolving around them. While rotating around the planet, maximum extent for any satellite to go closer to it, is always limited. The minimum distance beyond which a satellite can not come closer to the planet is called ‘Roche limit’ named after “Edward Roche”, the scientist who discovered it. Whenever any satellite crosses this limit, the forces acting on it due to high & low tide will break it into pieces.
Satellite rotates around the planet in spherical orbit, it has a very low mass compared to the planet and its density is same as the planet, The Roche limit for a satellite is 2.46 times the radius of the planet. Thus for a satellite to balance with its own gravitation, it will have to rotate away from the planet at a distance more than 2.46 times its diameter. If it crosses this limit than due to gravitation pull of the planet, the low tide-high tide force developed on the surface of the planet will make it egg shaped. It will move further closer to the planet. Thus the elliptical shape of the satellite will go on increasing and at a particular moment will break into pieces.
The question, Why there are rings around Saturn ? can also be solved by using the concept of Roche limit. Very long ago, some satellite on Saturn must have crossed the Roche limit and due to the high tide-low tide forcees, it must have broken into pieces which are now seen as ring by us. As 4 major rings of Saturn are inside its Roche limit. The same is true with Earth and moon. the Roche limit for moon is 16,000 km. Moon should not cross this or else it will also break into pieces.
बुधवार, १० जानेवारी, २००७
What is the importance of rotation of Galilean satellites of Jupitor?
Many satellites are found rotating around Jupiter in a ring, of which Io, Europa, Ganymede and Calisto are four important satellites. In 1610 Galileo was the first scientist to discover them hence is called Galilean satellites. Of the various satellites in solar system Ganymede is the largest among all. Planet Mercury is also small as compared to it.
The importance of Galilean satellites is in its period of rotation. Especially the rotation of Io, Europa and Ganymede is very much systematic. Io is very close to Jupiter for one rotation it takes 1.769 days. Europa completes one rotation around Jupiter in 3.551 days and Ganymede completes one rotation in 7.155 days and comes back to its original position. It is noticed from the rotation period of all these 3 satellites, that, when Io completes two rotations, Europa completes one rotation. And when Europa completes two rotations Ganymede completes one rotation. Thus the three satellites are rotating with respect to each other in synchronous rotation.
Laplace a famous scientist has expressed a simple equation for Galilean scientist which is given as,
Period of rotation of Io - Period of rotation of Europa + Period of rotation of Ganymede = 0
Due to this synchronous rotation, Io, Europa and Ganymede never come on the same side of Jupiter. When Europa and Ganymede are on the same side of Jupiter then Io is on their opposite side. When Io is at the extreme point in its orbit of rotation, Europa is at the lowest point and they meet. When Europa is at its maximum point in its orbit, it meets with Ganymede at that point wherever it is in its orbit
The importance of Galilean satellites is in its period of rotation. Especially the rotation of Io, Europa and Ganymede is very much systematic. Io is very close to Jupiter for one rotation it takes 1.769 days. Europa completes one rotation around Jupiter in 3.551 days and Ganymede completes one rotation in 7.155 days and comes back to its original position. It is noticed from the rotation period of all these 3 satellites, that, when Io completes two rotations, Europa completes one rotation. And when Europa completes two rotations Ganymede completes one rotation. Thus the three satellites are rotating with respect to each other in synchronous rotation.
Laplace a famous scientist has expressed a simple equation for Galilean scientist which is given as,
Period of rotation of Io - Period of rotation of Europa + Period of rotation of Ganymede = 0
Due to this synchronous rotation, Io, Europa and Ganymede never come on the same side of Jupiter. When Europa and Ganymede are on the same side of Jupiter then Io is on their opposite side. When Io is at the extreme point in its orbit of rotation, Europa is at the lowest point and they meet. When Europa is at its maximum point in its orbit, it meets with Ganymede at that point wherever it is in its orbit
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