Observing the International Space Station ISS

Compute the speed of the ISS ISS on 2009, Mar 20 at 19:57 CET, 51.62° N, 7.97° E, mag -2.3
exposure time 15 s, ASA 200
horizontal angle of the photo: 51.4°, angle of ISS: 14.8°

ISS moving from West (right) to East (left), approaching Pollux (Gemini). Sky Chart: StarryNight

ISS height
on 2009, Mar 20 (Heavens Above):  h = 354 km

Elevation above local horizon (from StarryNight
sky chart): begin a1 =57.9, end a2 = 64.6°

The velocity of the ISS may be computed: distance: s1 = h /
sin a1 = 354 km / sin 57.9° = 417.9 km
distance: s2 = h / sin a2 = 354 km / sin 64.6° = 391.6 km
a = 14.8°
during exposition: s = sqrt(s12 + s22 - 2 s1 s2 cos
a) = 107.5 km

velocity of ISS: v = s / t = 107.5 km / 15 s = 7.2 km/s
instead of v = sqrt(GM/r) = sqrt[
6.674·10-11·5.976·1024/(6.371·106+354·103)] km/s = 7.70 km/s ISS on 2009, Mar 21 at 20:24 CET, 51.62° N, 7.97° E, mag -2.3
exposure time 15 s, ASA 200
horizontal angle of the photo: 51.4°, angle of ISS: 17.0°

ISS moving from West (right) to East (left), passing the zenith.

s = h tan
a = 354 km tan 17.0° = 108 km
v = s/t = 108 km / 15 s = 7.2 km/s