Celestial Navigation Kepler’s Laws of Planetary Motion

Celestial Navigation

Celestial

Various methods are available e.g. Marq St Hilaire, Longitude by Chronometer, to obtain a circle of position. 

Celestial

• Vertical sextant angles of heavenly bodies and their azimuths.

Use celestial position lines to obtain a position

Celestial position lines are actually short segments of a position circle centered on the geographical position of the body. The position circle is so large (radius is angular zenith distance) that the segment can be said to be a straight position line. The following diagrams illustrate the concept which is in the region of practical navigation and will be studied in the relevant section of this function. In chart work we are limited to assuming that the position line we obtain from calculations is a small section of arc.

These position lines obtained from sextant altitudes and subsequent calculations are treated as a terrestrial one and either crossed with a second celestial position line to obtain an observed position at the time of the initial observation, or transferred to a time when a second celestial position line is obtained, i.e. treated as a 'running fix', and a position obtained.

Kepler’s Laws of Planetary Motion

Earth
 and planets revolve around the Sun, and Moon revolves around the Earth,
 in their respective orbits due to force of gravitation. In this topic 
Kepler’s three laws of planetary motion based on his investigation, are 
explained.

Kepler's first law (law of orbits)

• In the solar system every body revolves around the central body in an elliptical orbit.
• The central body is located at one of the foci of the orbit. Hence the distance of a revolving body from the central body continuously changes during its revolution.

Kepler's second law (law of areas)

The line joining the planet to the sun (radius vector) sweeps equal area in equal intervals of time. In order to keep the area velocity constant the linear velocities of the planet keeps on changing. When the planet is close to the sun its linear velocity is more and when it is away from the sun the liner velocity is less.

Kepler's third law (law of period)

 

 --- Time period of one revolution of a body.

 --- Mean distance of that body from the central body i.e. the mean of semi-major and semi-minor axis of the orbit.

Hence larger the size of the orbit of a planet, greater will be its period of revolution.

The following media explains about the kepler's laws: