Satellite aerials are not omni-directional
Stricto senso this is incorrect.
Eg. Iridium, Orbcomm, Globalstar, Thuraya are satellites or constellations of satellites that are accessible by portable equipment with rubberduck type of antennas.
What matters is frequency band (L, C, Ku or Ka), what it is aiming for (in terms of bandwidth/speed, which correlates to satellite power and antennas' gains) and type of orbit and height (LEO, MEO or GEO, which correlates also to latency, a critical factor for some applications).