How could people see from far away the speed of a thing

Astonomers use the doppler effect to calculate speed.

https://www.google.com.au/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#q=using%20the%20doppler%20effect%20astronomers%20can%20determine

I haven't looked at these but this might be a starting point for you.