Question

Estimate the acceleration due to gravity at the surface of Europa (one of the moons of...

Estimate the acceleration due to gravity at the surface of Europa (one of the moons of Jupiter) given that its mass is 4.9

Homework Answers

Answer #1

Since

1. F=ma ( or W=mg) and

2. F=GmM/R2

3. ?Earth=?Europa

we have

WEarth = mgEarth
GmM/R2 =mgEarth
   GMErart/REart2 = gEarth similarly

WEuropa = mgEuropa

GMEuropat/REuropa2 = gEaropa

But

MEarth/ MEuropa= 5.97x1024 /4.9x1022 =122

VEarth =(4/3)?REarth3

VEuropa =(4/3)?REuropa3

VEarth /VEuropa= (REarth / REuropa)3= MEarth/MEuropa= 122

REarth / REuropa= 5 thatis

REarth = 5 R Europa

then

gEarth / gEuropa = [GMEarth/REarth2 ]/ [GMEuropa/REuropa2 ]

gEarth / gEuropa = [ MEarth    /MEuropa][REuropa/REarth]2  

gEarth / gEuropa =[  122 ][1/5]2   = 4.88

gEuropa =gEarth /  4.88

gEuropa = 9.8/4.88=2.0m/s2

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