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