10.11. What to Remember from Lesson#
10.11.1. The Galileo Story#
It’s sad, it was maybe inevitable. But he accomplished a handful of things during this post-Padua time in his life:
Of course the mechanics that we’ve discussed were done before this, but it was only under house arrest that he smuggled out to Holland the publication that established his important work.
He didn’t invent the telescope and his Moon observations where not unique to him but he “published” first and in a way that got everyone’s attention.
His patient and detailed Jupiter, sunspots, Venus, and star observations – and publication – stunned the world and were indeed unique to him.
His Letter to the Grand Duchess threw down the gauntlet about the relationship between the Church and scientific observation and modeling, sure. But it was also an important challenge to any authority that puports to regulate and restrice scientific facts through either dogma or political authority. We need to remember Galileo’s letter in the United States as we’ve slipped three and a half centuries in that regard.
10.11.2. Newtonian Gravitation#
The Universal law of Gravitation was the single enunciation about how the world works that created modern science. His three laws of motion were important, sure. But Gravitation established forever more that there is one kind of rule for how things work and that single rule works on the Earth and in the heavens. Nobody ever went back to the old way.
Just to recap, for any two objects, “1” and “2”, the force between them is attractive and is: $\( F_{1,2} = F_{2,1} = G\cfrac{M_1m_2}{R_{12}^2}. \nonumber \)$ where
is the Gravitational Constant or Newton’s Gravitational Constant.
The Gravitational Potential Energy experienced by a massive body due to another is negative and is: