i

The orbit inclination of the satellite is determined by first finding the apparent slope of the satellite streak. The apparent direction of travel of the satellite will be required in order to determine if the inclination is less than 90 degrees (prograde) or greater than 90 degrees (retrograde). Do not be alarmed if you arrive at negative numbers in this step. The sign of the numbers indicate which direction the satellite is travelling in RA and Dec.

Da = a₂ - a₁
Dd = d₂ - d₁

Da = 2°.74469
Dd = -2°.94402

We also need to determine the average declination between the two endpoints:

d_av = (d₁ + d₂) / 2

d_av = 45°.04611

The orbit's inclination is determined by using the following conditions:

If Da > 0 then i = tan^-1 [ tan²d_av + (Dd / Da)² / cos⁴(d_av) ]^1/2

If Da < 0 then i = 180° - tan^-1 [ tan²d_av + (Dd / Da)² / cos⁴(d_av) ]^1/2

i = 67°.13

An orbit's inclination is normally very stable over a long period of time (unless it is being manoeuvred) so this value can be compared with published orbit elements (where available) with epochs several days apart from the obtained image.

The determined value of the inclination demonstrates that this satellite's orbit is prograde (between 0° and 90°).

PROCEED TO STEP #6