The planet Jupiter is more than 300 times as massive as Earth, so it might seem that a body on the surface of Jupiter would weigh 300 times as much as on Earth. But it so happens that a body would scarcely weigh 3 times as much on the surface of Jupiter as it would on the surface of Earth. Can you think of an explanation for why this is so?

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Paityn Arroyo · Accepted Answer

The weight on the surface of a planet is the gravitational force acting on the object placed at the surface of the planet.The formula for the gravitational force acting between two massive objects is:      F          g      r      a      v      i      t      a      t      i      o      n        =            G      M      m              r      2      Assume the mass of the body is       m    0  . The Jupiter is 300 times as massive as Earth and gravitational force acting on the Jupiter is 3 times the gravitational force acting on the earth. Mathematically,      F          J      u      i      p      t      e      r        =  3      F          E      a      r      t      h      Use the gravitational force expression and relation between the gravitation forces acting on the surface of Jupiter and Earth.            G              M                  J          u          p          i          t          e          r                            m        0                    r              J        u        p        i        t        e        r            2        =            3      G              M                  E          a          r          t          h                            m        0                    r              E        a        r        t        h            2                    M              J        u        p        i        t        e        r                    r              J        u        p        i        t        e        r            2        =            3              M                  E          a          r          t          h                            r              E        a        r        t        h            2                    300              M                  E          a          r          t          h                            r              J        u        p        i        t        e        r            2        =            2              M                  E          a          r          t          h                            r              E        a        r        t        h            2              r          J      u      p      i      t      e      r        2    =  100      r          E      a      r      t      h        2          r          J      u      p      i      t      e      r        =  10      r          E      a      r      t      h      The mass of the Jupiter is 300 times the mass of Earth but the gravitational force that is the weight of the body on the surface of Jupiter is 3 times only because the radius of the Jupiter is 10 times the radius of Earth.

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