物理-萬有引力

(a) Use Newton's Law of Gravitation

Force on the masn, F = GMm/R^2
where G is the Universal Gravitational Constant (= 6.67 x 10^-11 Nm^2 kg^ -2)
M is the mass of the earth
m is the mass of the man
R is the earth radius

Hence, mg = GMm/R^2, where g is the acceleration due to gravity at earth surface
i.e. g = GM/R^2 ------------------- (1)

Similarly, acceleration due to gravity at moon orbit g' = GM/R'^2
where R' is the radius of the moon orbit

thus, g/g' = (R'/R)^2 -------------------------- (2)

Consider the moon revolving round the earth
m'g' = m'R'w^2
where m' is the mass of the moon,
w is the angular velocity of the moon, which is equal to 2.pi/T, T being the period of revolution
hence, g' = R'(4.pi^2/T^2)

substitute the value of g' into equation (2)
g = (R'/R)^2.[ R'(4.pi^2/T^2)] = (3.85x10^8)^3/(6.4x10^6)^2 x (4.pi^2)/(27.3 x 86400)^2 m/s^2 = 9.886 m/s^2

hence, force on the 70 kg man = mg = 70 x 9.886 N = 692 N

(b) From equation (1)
g = GM/R^2
i.e. M = gR^2/G = 9.886 x (6.4x10^6)^2/(6.67x10^-11) kg
= 6.07 x 10^24 kg

a) W=mg
W=70*9.81
=686N
b)By M=gR^2/G
M=9.81x(6.4x10^6)^2/6.67x10^-11
=6.14x10^24
The mas of the Earth is about 6.14x10^24