物理引力問題 快快快快 20分

You could find this using Newton's Law of Gravitation

Acceleration due to gravity g is given by,
g = GM/R^2
where G is the Universal Gravitational Constant
M is the mass of the object (moon or earth)
R is its radius

Consider the earth, g(earth) = GM/R^2
where M and R are the mass and radius of the earth respectively

Consider the moon, g(moon) = Gm/r^2
where m and r are the mass and radius of the moon respectively

Hence, g(earth)/g(moon) = (GM/R^2)/(Gm/r^2) = (M/m).(r/R)^2
But it is given that g(moon)/g(earth) = 1/6
and m/M = 1/81
thus, 6 = (81).(r/R)^2
i.e. r/R = square-root[6/81] = 0.272

月球上的重力加速度是地球的1/6 而月球的質量約為地球的1/81
月球和地球的半徑比例大約是? 大約是1/3.8

2010-11-21 23:43:14 補充：
http://www.freemars.org/jeff/planets/Luna/Luna.htm

2010-11-23 00:40:32 補充：
地球赤道半徑6370公里
而月球的半徑1738公里


6378公里 / 1738公里 = 大約是3.69

2010-11-23 00:42:36 補充：
半徑比例是1/3.69