The sufferings of investigation made Galileo recant the truth he knew.
The heritage being alluded is the discovered knowledge and the efforts of wise men of the past to make life on earth better.
‘The betrayal of our trust implies’ that we enjoy the heritage of knowledge and works of our forefathers without doing anything new.
We need to question the old truths and work for the new ones in order to make the human life on earth even more better.
Inquisition – interrogation
The Planet – Earth
Falter – waver, stumble
Cynicism – pessimism
Those who are yet to be – future generations