The 'broken window Fallacy' is Bastiat's observation that while the income generated for glaziers from repairing rboken windows is indeed a form of economic activity, and that this is nice enough if you're in the window business, it's economically inefficient because the economic activity merely restores the status quo instead of going to finance new production - had the window remained unbroken, the shopkeeper might have bought a book or a suit of clothes. The glazier's gain is the shopowner's loss and so there's no net improvement.
But that's a wholly inappropriate analogy for this situation of expenditure going towards Indian scientists and technicians, because they were engaged in new and productive work rather than merely receiving a subsidy. The Indian government didn't have an existing interplanetary program that was scrapped and replaced with another; it built one from scratch. In terms of Bastiat's analogy, it would be as if the shopkeeper hired the glazier to install a new window in what had previously been a blank wall.
The direct economic value of measuring whether there is methane in Mars' atmosphere is intangible - just as it would be hard to measure the impact of a newly-added window on a shopkeeper's turnover at the time of its installation. It could also be argued that NASA or some other space agency could conduct the same measurement on some future Mars project, and so the ISRO effort is probably duplicative. But even if the direct economic output of the craft itself is assumed to be zero, the development of the satellite manufacturing and launch capability, which is a net economic gain too, whereas the replacement of a broken window does not have any innovative component (since the prior existence of the window means the capability to make it already existed).
It seems to me that you and the other two posters who are arguing this position are making the implicit assumption that that NASA et al. have a comparative advantage in the development of space technology and that therefore Indian efforts are economically superfluous, in addition to your general distaste for the notion of government as client.