Respuesta :
Answer:
W = 28226.88 N
Explanation:
Given,
Mass of the satellite, m = 5832 Kg
Height of the orbiting satellite from the surface, h = 4.13 x 10⁵ m
The time period of the orbit, T = 1.9 h
= 6840 s
The radius of the planet, R = 4.38 x 10⁶ m
The time period of the satellite is given by the formula
[tex]T = 2\pi \sqrt{\frac{(R+h)^{3} }{R^{2} g} }[/tex] second
Squaring the terms and solving it for 'g'
g = 4 π² [tex]\frac{(R+h)^{3} }{R^{2}T^{2} }[/tex] m/s²
Substituting the values in the above equation
g = 4 π² [tex]\frac{(4.38X10^6+4.13X10^5)^{3} }{(4.38X10^6)^{2}X6840^{2}}[/tex]
g = 4.84 m/s²
Therefore, the weight
w = m x g newton
= 5832 Kg x 4.84 m/s²
= 28226.88 N
Hence, the weight of the satellite at the surface, W = 28226.88 N
