Understanding the Meaning of 'p' in Equation: p^2 = (4pi^2)(a^3)/G(m1+m2)

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In the equation p^2 = (4pi^2)(a^3)/G(m1+m2), 'p' represents the orbital period of a satellite, not a distance. The discussion clarifies that 'a' is the semi-major axis of the orbit, which is the average distance from the center of one object to the center of another. For a satellite above Earth, 'a' would include the Earth's radius plus the altitude of the satellite. Therefore, 'p' is not simply the altitude but rather the total distance from the center of the Earth to the satellite. Understanding this distinction is crucial for correctly applying Kepler's laws of planetary motion.
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hi, there's something that i don't understand in the following equation:

p^2 = (4pi^2)(a^3)/G(m1+m2)

is the p a distance measured from the center of the first object to the center of the second object? or is it just the distance between them, for example a satelitte dish is 300km above the Earth's surface, so would p be 300km or 300km+radius of earth?
 
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