If you watch the asteroids mine, eventually a sat will show and you can tap on it. If you go away, the sats still show up anyway, seems to be about 1 per asteroid. Once you reach the end of the map, it loops back around to the beginning again.
I think mine is 132 today. It varies each day. I like the time-for-sats model better than the previous maybe-sats-in-a-box model.