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

(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 it fast plz

Answer 1

(a)

Inorder to determine the total mass M of the planet , we will use the formula

$R^{3}$ = ($GT^{2}$/4π^2 ) M

    = (48.16)^3

    = { (6.67 * $10^{-11}$) (7.3600)^2 / 4π^2 } M

M= 1.03 *$10^{26}$ kg

(b)

The planet that we are observing is neptune , as its mass is about  1.03 *$10^{26}$ kg .

Answer 2

Answer:

a).$M=1.03*10^{26} KG$

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

Explanation:

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 .

A distance R of 48000 km from the centre of the planet.

  Unfortunately, the mass m of the moon is not known.

The total mass M of the planet IS

 FROM  Newton’s law of gravitation with G = ·$6.67*10^{-11} m^{3} /Kg.s$  

             $F=ma_{c}$   =   $a_{c} =G\frac{M}{R^{2} }$

           $F=G\frac{M*m}{R^{2} }$

      $a_{c}=\frac{V^{2} }{R}$    ($V^{2} =G*M$)

            =$\frac{(\frac{2\pi R}{T} )^{2} }{R}$

             =$\frac{\\\pi ^{2}R 4}{T^{2} }$

          $\frac{\\\pi ^{2}R 4}{T^{2} }=G\frac{M}{R^{2} }$

           $M=\frac{4\pi ^{2} R^{3} }{GT^{2} }$

            $M=1.03*10^{26} KG$

(b) Moon and planet of our solar system is the team observing  is  Neptune and the moon is observing with the semi-major axis of 48224 km.

The project code is #SPJ3