Question

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

(1)

(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.​

Answer 1

Explanation:

(a) Determine the total mass M of the planet:

F=mac

=G{Mm}/{R^2}

ac=G{M}/{R^2}

ac={v^2}/{R}

{(2pi R/T)^2}/{R}

={4pi^2R}/{T^2}

{4pi^2R}/{T^2}

=G{M}/{R^2}

M={4pi^2R^3}/{GT^2}

=1.03 × 10^{26} kg

.F=mac

(b) That is Neptune and the moon is Naiad with the semi-major axis of 48224 km.