Respuesta :
Answer
given,
W = weight of speff at surface of planet = 384 N
h= height = 1.86 x 10⁴ Km
W' = weight of speff at height h from the planet = 24.31 N
Ms = speff mass = 75 kg
M= mass of planet = ?
R = radius of planet
G = 6.67 x 10⁻¹¹ m³/kg.s²
[tex]g = \dfrac{W}{M}[/tex]
[tex]g = \dfrac{389}{75}[/tex]
g = 5.187 m/s²
we know,
[tex]g = \dfrac{GM}{r^2}[/tex]
[tex]5.19 = \dfrac{GM}{r^2}[/tex].......(1)
now,
[tex]g' = \dfrac{W}{M}[/tex]
[tex]g' = \dfrac{24.31}{75}[/tex]
g' = 0.324 m/s²
[tex]g = \dfrac{GM}{(r+h)^2}[/tex]
[tex]0.324= \dfrac{GM}{(r+h)^2}[/tex].........(2)
dividing equation (1)/(2)
[tex]\dfrac{5.19}{0.324}=(\dfrac{(r+h)}{r})^2[/tex]
[tex]4=1+\dfrac{h}{r}[/tex]
[tex]r = \dfrac{1.86\times 10^4}{3}[/tex]
r = 6.2 x 10⁶ m
mass of planet X
from equation 1
[tex]M = \dfrac{g.r^2}{G}[/tex]
[tex]M = \dfrac{5.19 \times (6.2\times 10^6)^2}{6.2 \times 10^{-11}}[/tex]
M = 3.21 x 10²⁴ kg
