2D creatures on expanding sphere thinking they live on a plane

[Behrad]

Some 2D creatures are living on a sphere that it radius in increasing over time. They think that they are living on a expanding plane. The max speed of information is speed of light. The life time of the creatures are very smaller that the radius divided by speed of light. How can they find out they are living on a sphere. I tried to use doppler effect but it couldn't

P.n. Sorry for my bad english!

 

[Behrad]

I also wrote the doppler effect equations but the effect was very small that they couldn't notice.

And my problem depends on the amount of dR/dt