Exercise
https://texercises.com/exercise/astronomie-gravitationsfeld-8/
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The following quantities appear in the problem: Masse \(m\) / Volumen \(V\) / Ortsfaktor \(g\) / Radius \(r\) / Dichte \(\varrho\) /
The following formulas must be used to solve the exercise: \(\varrho = \dfrac{m}{V} \quad \) \(g = \dfrac{GM}{r^2} \quad \) \(V = \dfrac{4}{3}\pi r^3 \quad \)
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Exercise:
Der Radius einer homogenen Kugel werde bei konstanter Dichte verdoppelt. Was passiert mit der Gravitationsfeldstärke der Kugel an der Oberfläche?

Solution:
% . März Lie. * g fracGMr^ fracGrho tfracpi r^r^ propto r rightarrow fracg_g_fracr_r_ uuline * newpage
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Exercise:
Der Radius einer homogenen Kugel werde bei konstanter Dichte verdoppelt. Was passiert mit der Gravitationsfeldstärke der Kugel an der Oberfläche?

Solution:
% . März Lie. * g fracGMr^ fracGrho tfracpi r^r^ propto r rightarrow fracg_g_fracr_r_ uuline * newpage
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