George Saoulidis 
Space Girls: Saturna 1 

When three moons are doomed to fall into the nearest gas giant, the queen of a nearby planet is asked to help them. Will she manage to make a decision in time, when the ship that will help avoid the destruction is three days away, when she can only save one moon of the three and when her decision means she has to test the princes in bed before marrying them?

This is book 1 of the Saturna series.
Warning: Contains explicit content.