Question

In January 2005, the Huygens probe landed on Saturn's moon titan, the only satellite in the solar system with a dense atmosphere. Titan`s diameter is 5150 km, and its mass is 1.35 x 10^23 kg. the probe weighed 3120 n on the earth. what did it weigh on the surface of titan?

a. 298 n
b. 433 n
c. 108
d. 367 n

Answer 1

b. 433 N

Step-by-step explanation:

From Newton's law of universal gravitation,

F =
`(GMm)/(r^(2) )` ........... 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 =
`(GMm)/(r^(2) )`

g =
`(GM)/(r^(2) )`................ 3

Equation 3 can be used to determine the gravitational force on Titan.

Given that: G = 6.6743 x
`10^(-11)`
`Nm^(2)kg^(-2)`, M (mass of Titan) = 1.35 x 10^23 kg, and

r =
`(diameter of Titan)/(2)`

=
`(5150)/(2)`

= 2575 km

r = 2575 000 m

g =
`((6.6743*10^(-11)*1.35*10^(23) )/((2575 000)^(2) )`

=
`(9.010305*10^(12) )/(6.630625*10^(12) )`

= 1.3589

g = 1.36 m/
`s^(2)`

The acceleration due to gravity, g, on Titan's surface is 1.36 m/
`s^(2)`.

On the earth,

weight = mass x acceleration due to gravity

3120 = m x 9.81

m =
`(3120)/(9.81)`

= 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.