Given: radius of the Earth = 6.37*10^6 m
radius of the Moon = 1.73*10^6 m
G = 6.67*10^(-11) N m2 kg(-2)
Assume Earth is 81 times heavier than Moon, and the distance between their centres is about (3.8)*10^5 km.
The maximum gravitational potential between Earth and Moon is -1.3*10^6 J kg(-1). Show that this point divides the distance between the centres of Earth and Moon roughly in the ratio 9:1.
點解唔係81:1 ? 如何計到 9:1?
請各位brothers指教！
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Physics AL Mechanics Question (緊急！）
2008-01-25 8:36 am
回答 (2)
2008-01-25 9:03 am
✔ 最佳答案
Let the distance between the point and the centre of the EARTH be d mwhen the GRAVITATIONAL POTENTIAL is MAXIMUM at the point , then the FIELD STRENGTH at that point is ZERO
Let 81m be the mass of EARTH and m be the mass of MOON
G(81m)/d^2+[-G(m)/(3.8*10^8-d)^2]=0
G(81m)/d^2=G(m)/(3.8*10^8-d)^2
81/d^2=1/(3.8*10^8-d)^2
[d/(3.8*10^8-d)]^2=81
[d/(3.8*10^8-d)]=9
d=9(3.8*10^8-d)
d=3.42*10^9-9d
10d=3.42*10^9
d=3.42*10^8 m
Therefore,
the distance between the point and the centre of the EARTH : the distance between the point and the centre of the MOON
=3.42*10^8 m :(3.8*10^8-3.42*10^8)m
=3.42*10^8 m : 0.38*10^8 m
=9:1
2008-01-27 9:33 am
x^2008-x^1004+1/x^1004
收錄日期: 2021-04-25 17:18:22
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https://hk.answers.yahoo.com/question/index?qid=20080125000051KK00089