PLANETARY MOTIONS

#ON THIS DAY

The planetary alignment of 2000: On May 5, 2000, the planets Mercury, Venus, Earth, Mars, Jupiter, and Saturn were more or less positioned in a line with the Sun. And, the Moon was almost lined up between the Earth and Sun.

While each planet has a minute and virtually undetectable gravitational pull on the Earth, with the planets on the opposite side of the Sun the force from each body will actually be at its absolute minimum during the alignment. And there is nothing "magic" about the planets being in a line, the effects do not somehow multiply simply due to a geometric arrangement. For example, the combined gravitational effect of all the planets together is much less than the effect of the Sun or the Moon on the Earth. Depending on how strictly you want to define "alignment", the inner six planets are aligned every fifty to a hundred years or so. While unusual, such alignments have happened in the past without any consequences. The planets are simply too far away to have an effect on anything here on Earth - except our imaginations. There was no disaster on May 5th, 2000, due to the planetary alignment.

The simple formulas from high school may help to get the relief in such situations. As per orbital mechanics, The force of gravity is inversely proportional to the square of the distance between two bodies. How close the two bodies is much more important than their masses in contributing to the tidal force. For example, the gravitational force exerted by the Sun on Earth is about 180 times than that by the Moon, but the Moon causes a greater tidal effect because of its closeness to the earth. Another way to analyze about this is to remember that the diameter of Earth is a much larger proportion of the distance to the Moon that it is to the Sun, so the differential gravitational force will be a larger proportion of the total gravitational force. To see why the Moon always faces us with the same side and why it is gradually moving away from Earth, take a look at Phil Plait's explanation.

REFERENCE: NASA

EARTH ORBIT CLASSIFICATION

           GEO: Geosynchronous Earth orbit, circular at 35,786-km altitude

         MEO: Mid-Earth orbit, circular at 2000 to 20,000-km altitude

         LEO: Low Earth orbit, generally circular at 200 to 2000-km altitude.

         HEO: Highly Elliptical orbit, such as Molniya

  

GEOSTATIONARY ORBIT-

• Very special geosynchronous orbit(unique)
• exactly circular with a radius of 42164 km in the earth’s equatorial plane with zero degrees inclination and zero eccentricity.   
• satellite in this orbit does not move with respect to earth.
• The satellite takes more fuel to reach and maintain itself in this orbit.

          

GEOSYNCHRONOUS ORBIT-

• Similar to geostationary orbit(except that its inclination can be any value between 0 and 90).
• Near zero gravity.
• Inclination other than 0 degrees requires ground station tracking antennas.
• Chosen for fuel-efficient launch and orbit maintenance.

HIGHLY ELLIPTICAL ORBIT-

• Molniya is one specific orbit with 1000km perigee and a 39400km apogee.
• Advantage of molniya is good coverage of entire northern hemisphere.
• The disadvantage of molniya is no coverage over the southern hemisphere.

LOW EARTH ORBIT-

• Circular orbit at low altitude.
• ISS and NASA’s space shuttle orbiter operate in LEO.
• Requires tracking of omnidirectional antennas.
• two-way communications introduce a time delay of only 0.02s versus 0.5s in geosynchronous orbits.

SUN-SYNCHRONOUS ORBIT-

• Maintains constant angle between sun’s direction and orbit plane.
• Always sees the sun at the same angle.

ORBIT MECHANICS:-

KEPLER’S LAWS-

• First law: Satellite orbit is an ellipse with the planet at one focal point.
• Second law: sweeps equal area in equal intervals of times.
• Third law: square of orbit period is proportional to the cube of the semi-major axis.

            i.e., To2 = 4π2a3/µ

where a is the semi-major axis of the orbit, and µ is the gravity constant of the planet. For the Earth, µ is 3.986×1014  3/s2 or 3.986× 105 km3/s2.

SATELLITE STABILISATION METHOD:

• Active method
• Passive method

GRAVITY GRADIENT METHOD-

• Passive method.
• Used in small LEO satellites.
• Requires long booms in order to have adequate moment.
• Do not work in geosynchronous orbit.

MAGNETIC DAMPING-

• Passive method
• Uses long booms with magnets that interact with the earth’s magnetic dipole field.

SPIN STABILIZATION-

THREE-AXIS STABILIZATION-

   REFERENCE: Spacecraft power systems by Mukund R. Patel