Potential energy increase of an expanding stellar object

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The discussion centers on calculating the energy required to double the radius of a uniformly dense stellar object, expressed in terms of mass and radius. Participants emphasize the importance of demonstrating an effort to solve the problem before seeking help. A link to homework guidelines is provided, highlighting the need for adherence to forum rules. The thread is ultimately closed, indicating that no further responses will be given until the original poster follows the proper procedure. Engaging with the community requires an initial attempt at problem-solving.
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How much energy is required to double the radius of a uniformly dense stellar object? Express the answer in terms of mass and the radius of the object.
 
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Thread 'Derivation of Hamilton's Principle: Questions'

I have recently been really interested in the derivation of Hamiltons Principle. On my research I found that with the term ##m \cdot \frac{d}{dt} (\frac{dr}{dt} \cdot \delta r) = 0## (1) one may derivate ##\delta \int (T - V) dt = 0## (2). The derivation itself I understood quiet good, but what I don't understand is where the equation (1) came from, because in my research it was just given and not derived from anywhere. Does anybody know where (1) comes from or why from it the...
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