Answer to Question #164542 in Astronomy | Astrophysics for Syed Abdullah Gilani

Question #164542

A research team has discovered that a moon is circling a planet of our solar system: The moon orbits the planet once every 7 hours on a nearly circular orbit in a distance R of 48000 km from the centre of the planet. Unfortunately, the mass m of the moon is not known. Use Newton’s law of gravitation with G = 6.67 · 10−11 m3 /(kg·s 2 ) to approach the following questions: F = G · mM R2 (a) Based on the observations, determine the total mass M of the planet. (b) Which moon and planet of our solar system is the team observing? (Use literature.)


1
Expert's answer
2021-02-17T14:42:48-0500

(a) We can find the mass of the planet from the Newton's form of Kepler's third law:


"\\dfrac{T^2}{R^3}=\\dfrac{4\\pi^2}{GM},""M=\\dfrac{4\\pi^2R^3}{GT^2},""M=\\dfrac{4\\pi^2\\cdot(4.8\\cdot10^7\\ m)^3}{6.67\\cdot10^{-11}\\ \\dfrac{Nm^2}{kg^2}\\cdot(7\\ h\\cdot\\dfrac{3600\\ s}{1\\ h})^2}=1.03\\cdot10^{26}\\ kg."

(b) The research team observed the planet Neptune ("M=1.02\\cdot10^{26}\\ kg") and its satellite Naiad (semi-major axis 48224 km, orbital period 7 hours).


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