Cartesian co-ordinates to spherical

[hasty cobalt]

Hi guys, I'm having some difficulty with cartesian and spherical co-ordinates.

I am currently on a placement which involves working with satellites.

Can anyone help to explain the formulas of cartesian to spherical axis. If possible, how those spherical axis may be related to Azimuth and Elevation angle.

I'm not really sure which one would be elevation angle.

For example this diagram:

[obtuse crystal]

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[hasty cobalt]

for example, this is a diagram my teacher on the placement provided

[hasty cobalt]

would that not be the elevation angle?

In the diagram it shows that the angle Fi is the angle from the z axis to the line which connects from centre to the object

[hexed crag]

with this you get z=psinφ (phi taken internally)

and that's the form you'll be given, your phi is taken radiating out from the vertical axis

[hexed crag]

this specific diagram is a little strange

[mortal vessel]

Hm... I think it's a bit wrong. Should be this:
x = r cos(θ)sin(φ)
y = r sin(θ)sin(φ)
z = r cos(φ)

[hexed crag]

oh yeah

[mortal vessel]

Otherwise the sum of squares isn't r^2.

[shut gull]

apex predator

[hexed crag]

deriving each of those from your lower diagram isn't too hard and will help you not make the mistake that I made 💀

@hasty cobalt

[mortal vessel]

I usually remember it like this.

And the sin(φ) just comes naturally so that the sum of squares is r^2.

[wheat flume]

If you're talking about spherical coordinates where the origin is the center of the Earth, then the angle of elevation isn't directly represented at all because that's relative to a given point on the surface.

[hasty cobalt]

ahhh

[hasty cobalt]

the origin is the ground station, this is regarding satellites

[hasty cobalt]

I'm a little confused at that

I still don't understand how I'd be able to find azimuth from the sphere

[hasty cobalt]

so is that corresponding to distance, azimuth and elevation?

[hasty cobalt]

@wheat flume

I managed to figure the distance and elevation, struggling on azimuth

[hasty cobalt]

+close