 Inclined Orbit – Satellite Technology

While considering an orbit of non- geostationary orbit satellite, different parameters are referred at different reference frames. The orbital elements are calculated with respect to the plane of the orbit, which is fixed in space and the earth stations position is given by geographic coordinates that rotate with the earth.

Other factors of consideration are azimuth and elevation angles. Thus for calculation purpose, transformations between coordinate system is required.

The following quantities and concepts are required o Orbital elements

• Various measures of time
• Perifocal coordinate system- based on orbital plane
• Geocentric-equatorial plane coordinate system – Earth‟s equatorial plane
• Topocentric – horizon coordinate system- observer‟s horizon plane.

Calendars

Calendars are created with respect to the position of sun. As Earth‟s motion around the sun is not uniform, its called “mean sun”. Calendar days are “mean solar days”. Tropical year has 365.2422 days. It is generally taken as 365 (commonly known as civil year). The extra 0.2422 is significant and for example after 100 years, there will be drift of 24 days between calendar year and tropical year. Hence the concept of Leap year came into existence. By the year 1582, a discrepancy was once again observed.

The discrepancy existed between the civil and the tropical years. To synchronize them, days between 5th October – 14th October 1582 were abolished. Additional constraints were added that on years ending with two zeros to be considered as leap years. The resulting calendar is called as the Gregorian Calender; named after Pope Gregory XIII.

Example:

Calculate the average length of the civil year in Gregorian calendar Solution:

Nominal number of days in 400 years = 400 x 365

Number of leap years in 400

years = 400 / 4

This must be reduced by 3 days; Hence, 14600 + 100 – 3 = 146097

Therefore, yearly average = 14697 / 400 = 356.2425

Universal Time

Universal time coordinate (UTC) is the time used for all civic time keeping purpose. Fundamental unit of UTC is mean solar day. UTC is equivalent to Greenwich mean time (GMT) and the Zullu time (Z).

1 Mean Solar Day s divided into 24 hours;

1 Hour into 60 minutes;

1 Minute into 60 seconds.

Thus there are 86,400 seconds in a day.

Example:

calculate time in days, hours, minutes and seconds for epoch day 324.95616765

Solution:

Mean solar day = 324th + 0.95616765

mean solar day Therefore; 24 x 0.95616765 = 22.948022 60 x 0.948022 = 56.881344 60 x 0.881344 = 52.88064

Thus; Epoch is at 22 hours 56 minutes a 52.88 seconds of the 324th day of the year.

For computations, UT requires two forms: 1. Fraction of a day 2. In Degrees