Determining Exact Direction Of Qibla
One is always supposed to make the best decision they can given what information/resources they have. Determining qibla is no different. If you have a phone with a compass and you’re unsure of the qibla direction, you will naturally use it before you make salat. If you don’t have a compass and no other reasonable way to find the qibla, you’d pray in any direction knowing that God exists everywhere. This kind of issues are not addressed by religion. Since God has created humans with faculties of reason and rationality, He has left this kind of issues up to them to make the best use of their faculties and decide for themselves.
If you make it so then yes. Otherwise the concluding paragraph of my response above should suffice.
Do we have no religious guidance? I guess do the words in the ayah about qibla necessitate an exact calculation?