Question

The earth has a mass of, MEarth=6.4 X 1024 kg and a radius of REarth= 6.0 X 106meter and it has acceleration due to gravity, gE = 9.8 . One of Jupiter’s moon also has MJmoon = ½ * MEarth =3.2 x 1024 kg with a radius of, RJmoon = ½ * REarth =3.0 x 106 m and gJmoon value unknown. From the information, what is acceleration due to gravity of Jupiter’s moon, gjmoon, comparing to the earth’s acceleration due to gravity, gEarth?

Answer 1

gjmoon = 19.6 m/s2

Step-by-step explanation:

• Applying the Universal Law of Gravitation, the force exerted by the Earth on a mass m, can be written as follows:

`F_(gE) = m* (G*M_(E) )/(R_(E) ^(2) ) = m*g_(E)`

• In the same way, the force due to gravity of Jupiter's moon, can be written as follows:

`F_(gjmoon) = m* (G*M_(Jmoon) )/(R_(Jmoon) ^(2) ) = m*g_(jmoon) (1)`

• Now, we know the following:

`M_(Jmoon) = (M_(E) )/(2) (2)`

`R_(Jmoon) = (R_(E) )/(2) (3)`

• Replacing (2) and (3) in (1), we get:

`F_(gjmoon) = m* (G*M_(E) )/(2*(R_(E) ^(2))/(4) ) = m*g_(jmoon) (1) = m* 2* (G*M_(E) )/(R_(E) ^(2)) = 2* m*g_(E)`

⇒
`g_(jmoon) = 2* g_(E)`

gjmoon = 19.6 m/s2 (in magnitude).