# How does one calculate the look angle for non-geo satellites (i.e. LEO, HEO, etc.)

I'm trying to find a way to calculate look angles to not just GEO satellites, but LEO, MEO, and HEO sats. The only calculator I've found myself is here, which was referenced for a similar problem on Stack Exchange in regards to calculating the longitude of GEO satellites GIVEN look angles here: Computing GEO satellite's longitude from elevation/azimuth from a given latitude/longitude?

I'm interested in two functions/formulas, both of which are calculated on that first link I posted.

1. $$Az, \ El = f(earth_{lat}, \ earth_{lon}, \ sat_{lat}, \ sat_{lon}, \ altitude)$$. I.e. look angle from earth station and satellite locations
2. $$sat_{lat}, \ sat_{lon} = f(earth_{lat}, \ earth_{lon}, \ az, \ el, \ alt)$$

So far I've started by subtracting the ECEF (geocentric) vector to the station from that of the satellite:

$$v_{1} = [r*cos(earth_{lat})*cos(earth_{lon}), \ r*cos(earth_{lat})*sin(earth_{lon}), \ r*(1-f)*asin(earth_{lat})]⋅T$$

$$v_{2} = [R*cos(sat_{lat})*cos(sat_{lon}), R*cos(sat_{lat})*sin(sat_{lon}), R*(1-f)*sin(sat_{lat})]⋅T$$

$$V = v_{2}-v_{1}$$

Where $$r$$ is the radius of Earth, $$f$$ is the flattening of Earth, and $$R = sat_{alt} + r$$.

If I'm not mistaken this should yield the vector pointing from the station to the satellite. So now I just have to transform these coordinates from ECEF to ENU (topocentric):

$$t_{1} = [-sin(earth_{lon}), cos(earth_{lon}), 0]$$

$$t_{2} = [-sin(earth_{lat})*cos(earth_{lon}), -sin(earth_{lat})*sin(earth_{lat}), cos(earth_{lat})]$$

$$t_{3} = [cos(earth_{lat})*cos(earth_{lon}), cos(earth_{lat})*sin(earth_{lon}), sin(earth_{lat})]$$

$$T = [t_{1}, t_{2}, t_{3}]$$ (ECEF to ENU transformation matrix)

$$V_{ENU} = T*V$$

Lastly, I calculate the azimuth and elevation:

$$Az = arctan2(V_{ENU(y)}] / V_{ENU(x)}] )$$ $$El = arcsin(V_{ENU(z)}/ ||V_{ENU}||] )$$

This keeps giving me the wrong answer, at least according to that calculator I referenced. What am I missing?

• You might want to include the write/wrong answers you're working with, and code if that's what you're using. The logic sounds correct. May 10, 2022 at 21:02

In your equation for $$t_2$$, the middle term ought to be $$-\sin(earth_{LAT})*\sin(earth_{LON})$$ not $$-\sin(earth_{LAT})*\sin(earth_{LAT})$$