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Why gravitational constant $G$ does not have the factor of $4π$?

You can define it as so. I'll name $4\pi G$ as $\mathcal{G}$. In electrostatics: $$F=\frac{1}{4\pi \epsilon_0} \frac{Qq}{r^2}$$ and so Gauss's law is: $$\nabla \cdot \vec{E}=\frac{\rho}{\epsilon_0}$$ ...
• 1,053
1 vote
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Is it possible to make a satellite orbit Earth, the same way Earth orbits Sun? ( Same orbital path pattern)

Orbits are described by their eccentricity, period, and semi-major axis. If you mean can all three be the same then no, it is not possible. The sun and the earth have different standard gravitational ...
• 69k
1 vote
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When is replacing two bodies with a single one at the centre of mass valid?

Method 2 is certainly incorrect, because the elliptical path with $M$ at the centre is not a solution of the equations of motion for a particle in an orbit. It is true that the motion of the centre of ...
• 990

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