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Saturn’s moon Titan has a mass of 1.35 × 1023 kg. If Titan is 1.19 × 106 km from Saturn, and Saturn’s mass is 5.86 × 1026 kg, what is the gravitational force between Saturn and its moon?

2.76 × 104 N
3.29 × 107 N
3.73 × 1021 N
4.43 × 1030 N

Respuesta :

Arnold11
The gravitational force equation is Fg=(G*M*m)/r² where, G is the gravitational constant, G=6.67*10^-11 m³/kg*s², M is the mass of Saturn, M=5.86*10^26, m is the mass of Titan, m=1.35*10^23 and r is the distance, r=1.19*10^6 km=1.19*10^9 m. Now we simply input the numbers into the equation:

Fg=(6.67*10^-11)*(5.86*10^26)*(1.35*10^23)/(1.19*10^6)²
Fg=(5.277*10^39)/(1.41*10^18)=3.743*10^21 N 

The correct answer is the third one. 

The gravitational force between Saturn and its moon Titan is [tex]3.743\times 10^{21} \rm \ N[/tex].

How to calculate gravitational force?

The gravitational force is directly proportional to the product of masses and inversely proportional to the distance between them.

[tex]F_g=G\dfrac {Mm}{r^2}[/tex]

Where,

[tex]F_g[/tex] - gravitational force

[tex]G[/tex] - Universal Gravitational Constant = [tex]\bold {6.67 \times 10^{-11} N.m^2/kg^2}[/tex]

[tex]M[/tex] - mass of Saturn = [tex]5.86\times10^{26} {\rm \ kg}[/tex]

[tex]m[/tex] - mass of Titan =[tex]1.35\times10^{23} {\rm \ kg}[/tex]

[tex]r[/tex] - distance, r = [tex]1.19\times10^{6} {\rm \ km}[/tex] = [tex]1.19\times 10^9 {\rm \ m}[/tex]

Put the values in the formula,

[tex]F_g=\bold {6.67 \times 10^{-11} N.m^2/kg^2} \dfrac {5.86\times10^{26} {\rm \ kg}\times 1.35\times10^{23} {\rm \ kg}}{(1.19\times 10^9 {\rm \ m})^2}\\\\F_g= 3.743\times 10^{21} \rm \ N[/tex]

Therefore, the gravitational force between Saturn and its moon Titan is [tex]3.743\times 10^{21} \rm \ N[/tex].

Learn more about gravitational force:

https://brainly.com/question/24783651

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