Theory:

Duttada was optimistic... he knew that the professionals with their pre-assigned programmes would be looking at faint stars and nebulous galaxies. They might miss such an insignificant thing as a comet which they were not expecting to see anyway! Indeed amateurs had often discovered new comets which the professionals had missed.

And, it looked to Duttada that tonight was going to be the big night. For against the background of the same old stars Duttada had detected a faint stranger. He re-examined the charts with him, checked his Dibya for any smudges on the optics, did some calculations on his pocket calculator in torchlight — for, though absent-minded about daily chores, he was meticulous in his observations.

Yes, there can be no mistake. What he was looking at had not been there earlier and it did look like a new comet.
Explanation:

In paragraph $$10$$, the author responds to the query about how an amateur astronomer like Duttada can compete with expert astronomers. The response to the question is as follows. Though there were some experienced scientists and astronomers in the astronomy field, they would be preoccupied with their own tasks and spend time observing and learning about vague, undefined galaxies. As a result, they don't bother to devote time to detecting such comets, and they place a lower priority on it. Indeed, amateur astronomers have repeatedly discovered new comets that professional astronomers have missed in the past. Duttada's positive outlook may be seen in this thought.

Duttada's intuition assured him that it would be a big night. There was something that his telescope pointed at, true to his intuition. He discovered something odd among the twinkling stars that night. He went through the charts again. The term 'chart' here refers to a 'star chart' or 'star map,' which is a night sky map. Astronomical objects like as stars, constellations, and galaxies are identified and located using them. Also, he double-checked everything with his telescope, Dibya. To arrive at the exact conclusion, he utilised his pocket calculator in torchlight once more.

Though Duttada failed at leading a practical life, being oblivious to everyday daily events, he was meticulous in his calculations, paying attention to even the smallest details. As a result, there was no blunder. The faint stranger he saw through his telescope was nothing but a "comet" that has been demanding his time for the last few days, during which he had sleepless nights. Finally, Duttada discovered a comet.

Meaning of difficult words:

 S.No Words Meanings 1. Optimistic Looking hopefully on things in a way that only good thing will happen 2. Nebulous Things which are not clear
Reference:
National Council of Educational Research and Training (2008). The Comet I - Jayant Narlikar (pp. 73-80). Published at the Publication Division by the Secretary, National Council of Educational Research and Training, Sri Aurobindo Marg, New Delhi.