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Satellite Elliptical Orbit Problem

Geosynchronous satellites do not provide good coverage for higher latitudes, such as in the country of Norway. Communication satellites in inclined elliptical orbits are an attractive alternative. For this problem you will work out a hypothetical elliptical orbit satellite for Norway. Use the given specifications below to base your calculations on.

Orbital Period = 24hrs
Sub-Satellite Point = 60deg N, 10deg E, Oslo at 2100 UT daily
Apogee = Occurs at 2100 UT everyday when the satellite is directly above the sub-satellite point
Height of Perigee = 500km above the surface of the earth

1) Determine the Semimajor Axis:

a = (T2μ / 4 π2)1/3

a = (86,400s)2(3.98613E5km3 / s2) / 4 π2)1/3

a = 42,242km


2) Find the Time Perigee Occurs:

Sense the orbital period T = 24hrs, the time of perigee is defined by T/2, or 12hrs after apogee. So perigee occurs at 0900 UT.


3) Find the Eccentricity:

The radius of perigee = rp = a ( 1 - e ), where e = eccentricity

The height of perigee = hp = rp - re = a ( 1 - e ) - re = 500

Now, solving for e,

e = 1 - (re + 500) / a = 1 - 6870 / 42,242 = 0.837


4) Find the distance from the surface of the Earth at Apogee:

The radius of apogee = ra = a ( 1 + e )

The height of apogee = ha = ra - re

ha = a ( 1 + e ) - 6370 = 42.242 ( 1 + 0.837 ) - 6370 = 71,244km


5) Determine the Orbital Inclination (i) that would provide the longest daily period of visibility at Oslo:

The longest period of visibility would occur when Oslo is in the orbital plane at apogee. This requires an inclination equal to the latitude of Oslo, which is 60 degrees.


Satellite key words: look angle, shallow, negative angle, geosynchronous, low earth orbital, LEO, GEO, latitude, longitude, SATCOM, elliptical orbits, subsatellite point, orbital period, UT, apogee, perigee, spacecraft, velocity, eccentricity, visible.


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