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Answer :
Final answer:
To extract the mass of the planet, we used the formula for gravitational force, replaced it with centripetal force expressions, and substituted the velocity equation from orbital mechanics. After subbing all known values and simplifying, it gives the mass of the planet, ~3.72 × 10^24 kg.
Explanation:
In this case, you can use the formula for gravitational force to calculate the mass of the planet. This equation is given by F = GMm/r^2, where F is the force, G is the gravitational constant, M is the mass of the planet, m is the mass of the moon, and r is the radius of its orbit.
However, we can substitute F with the expression for centripetal force, which is given by m*v^2/r, where v is the velocity of the moon.
The velocity can be calculated by the formula v = 2*pi*r/T, where T is the orbital period. After substituting all these values and simplifying the equation, we end up with M = r*v^2/G.
Now we substitute the values given in the question: r = 5.32 × 10^5 km = 5.32 × 10^8 m (after conversion from km to m), T = 36.3 hrs = 1.308 × 10^5 seconds (after conversion from hours to seconds), and G = 6.67 × 10^−11 m^3/kg/s^2. After performing all the calculations, you will find that the mass of the planet is approximately 3.72 × 10^24 kg.
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