Answer:
b. 433 N
Explanation:
From Newton's law of universal gravitation,
F = [tex]\frac{GMm}{r^{2} }[/tex] ........... 1
where: F is the force of attraction, G is Newton's universal gravitation constant, M is the mass of massive object, m is the mass of the other object and r is the radius.
Also, from Newton's second law,
F = mg ............ 2
Thus,
mg = [tex]\frac{GMm}{r^{2} }[/tex]
g = [tex]\frac{GM}{r^{2} }[/tex]................ 3
Equation 3 can be used to determine the gravitational force on Titan.
Given that: G = 6.6743 x [tex]10^{-11}[/tex] [tex]Nm^{2}kg^{-2}[/tex], M (mass of Titan) = 1.35 x 10^23 kg, and
r = [tex]\frac{diameter of Titan}{2}[/tex]
= [tex]\frac{5150}{2}[/tex]
= 2575 km
r = 2575 000 m
g = [tex]\frac{(6.6743*10^{-11}*1.35*10^{23} }{(2575 000)^{2} }[/tex]
= [tex]\frac{9.010305*10^{12} }{6.630625*10^{12} }[/tex]
= 1.3589
g = 1.36 m/[tex]s^{2}[/tex]
The acceleration due to gravity, g, on Titan's surface is 1.36 m/[tex]s^{2}[/tex].
On the earth,
weight = mass x acceleration due to gravity
3120 = m x 9.81
m = [tex]\frac{3120}{9.81}[/tex]
= 318.0428135
The mass of the probe is 318 kg.
So that its weight on the surface of Titan = m x g
= 318 x 1.36
= 432.5 N
The weight of the probe on the surface of Titan is 433 N.
