On the occasion of Gagarin’s 50th anniversary and Ambedkar Jayanti take a look at my article
This corrects (the conceptual defect in) Newton’s “law” of gravitation, and explains the anomalous orbits of NASA spacecraft, and also stars in the galaxy, which that “law” cannot explain (and which have not been explained using general relativity either).
This completes the story. Newtonian physics was based on the calculus which developed in India, as the work of the low-caste 5th c. Aryabhata from Patna. It was adopted by the highest-caste Namboodri Brahmins of Kerala, from the 8th c. onwards, and developed further. In the 16th c. this work was secretly transmitted by Jesuits from Cochin to Europe for it contained accurate trigonometric values (accurate to the 9th decimal place) which Europeans badly needed for navigation—then their biggest scientific challenge.
However, the Indian way of calculating these trigonometric values by summing infinite series was beyond the comprehension of intellects like Descartes and Newton, because European ideas of mathematics were (and still are) mixed-up with religious beliefs about mathematics as eternal truth. (See my book, Cultural Foundations of Mathematics, Pearson Longman, 2007.)
Newton thought his doctrine of fluxions made calculus “rigorous” when it only made time metaphysical (see e.g. my paper, “Time: What is it That it can be Measured?” Science&Education, 15(6) (2006) pp. 537–551, or draft ).
This intrusion of religious beliefs into physics both directly and through Western mathematics was the reason Newton’s “laws” failed.