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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?

Respuesta :

cjrodriguez89

Answer:

gjmoon = 19.6 m/s2

Explanation:

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

       [tex]F_{gE} = m* \frac{G*M_{E} }{R_{E} ^{2} } = m*g_{E}[/tex]

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

      [tex]F_{gjmoon} = m* \frac{G*M_{Jmoon} }{R_{Jmoon} ^{2} } = m*g_{jmoon} (1)[/tex]

  • Now, we know the following:

       [tex]M_{Jmoon} = \frac{M_{E} }{2} (2)[/tex]  

      [tex]R_{Jmoon} = \frac{R_{E} }{2} (3)[/tex]

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

       [tex]F_{gjmoon} = m* \frac{G*M_{E} }{2*\frac{R_{E} ^{2}}{4} } = m*g_{jmoon} (1) = m* 2* \frac{G*M_{E} }{R_{E} ^{2}} = 2* m*g_{E}[/tex]

      ⇒  [tex]g_{jmoon} = 2* g_{E}[/tex]

       gjmoon = 19.6 m/s2 (in magnitude).