问题 问答题

继神秘的火星之后,土星也成了世界关注的焦点.经过近7年时间,2亿千米在太空中风尘仆仆的穿行后,美航天局和欧航天局合作研究出“卡西尼”号土星探测器于美国东部时间6月30日(北京时间7月1日)抵达预定轨道,开始“拜访”土星及其卫星家族.这是人类首次针对土星及其31颗已知卫星最详尽的探测.若“卡西尼”号土星探测器进入土星飞行的轨道,在离土星表面高h的圆形轨道上绕土星飞行,环绕n周飞行时间为t,求

(1)土星的质量;

(2)忽略土星自转的影响,求土星表面的重力加速度.

答案

(1)“卡西尼”号的质量为m,土星的质量为M.“卡西尼”号围绕土星的中心做匀速圆周运动,其向心力由万有引力提供.

G

Mm
(R+h)2
=m
4π2
T2
(R+h)

其中T=

t
n

所以有:M=

4π2n2(R+h)3
Gt2

(2)设土星表面处有一质量为m1的物体,则有

m1g=G

Mm1
R2

得:g=

GM
R2
=
4π2n2(R+h)3
R2t2

答:(1)星的质量M为

4π2n2(R+h)3
Gt2

(2)星表面的重力加速度g为

4π2n2(R+h)3
R2t2

填空题
单项选择题

The Lake District in north-west England is an area remarkably little affected by industrialization. The principal activity is still sheep-farming, as it has been for a thousand years, and many ancient words like "fell" for "hill" and "tam" for "lake" are still in daily use. In spite of its heavy rainfall and relative inaccessibility, its special atmosphere and spectacular natural beauty combine to make this one of England’s favourite holiday areas at all seasons of the year. But at Christmas 1968, still gripped by the fear that foot-and-mouth disease could spread to the hill flocks and sweep like wildfire right up to the Scottish border, it was quieter than ever before in this century. Luckily not a single farm had caught tile infection, the nearest case having been an isolated one at Kendal several weeks before. But every Lakeland farmer knows that one case among the unfenced hill flocks on the fells could lead to complete annihilation of hundreds of thousands of sheep and the virtual end of the district’s principal industry; you cannot replace sheep, acclimatized to their own part of the fell for generations, in the same way that you can replace cattle in a field.
Nobody could remember a Christmas like it, especially Boxing Dab, which is traditionally one of the big outdoor holidays of the Lakeland year. Normally this is a day spent following the mountain packs of hounds, fell-walking and, if the weather is propitious, skiing and skating, but this time there were none of these things. Visitors were actively discouraged, and those who did come were asked not to go on the fells, footpaths or bridleways or near farmland, while motorists were requested not to drive on minor roads and to shun the smaller valleys. The enterprising hotels which had earlier in the year decided to keep open during the winter were by the end of October having a desperate time. Hundreds of bookings had been cancelled and scores of dinner parties and young farmers’ reunions eliminated. All youth hostels were closed. At least one climbing club, unable to climb, substituted a training programme of films and simulated climbs on the more substantial municipal buildings.
The weather in the area was dry, crisp, windless and cold, in fact ideal for brisk outdoor activities. But nobody was able to enjoy it. Everything was stopped: hunting, walking, climbing, skiing, motor cycle trials, sporting events of every description. All the seasonal dances, festivals, conferences, shepherds’ meets and a hundred and one, other social occasions abandoned. The ice was bearing on some of the lakes but you could not go skating there. Meanwhile the foxes, emboldened by an unprecedented freedom from harassment, were stalking closer to the farms and the flocks of Christmas turkeys, while the hounds sulked miserably in their kennels.
Farmers are apt to criticize some sections of the outdoor fraternity for their occasional thoughtless behaviour, but the way that walkers, climbers, skiers, fishermen, hunters and the rest went out of their way to help them at this time should never be forgotten. The general public, locals and visitors alike, tried to give the fell farmers a sporting chance, and this remarkable display of public spirit was the one bright note in a very sad time.

Why were some hotels described as "enterprising"

A.(A) Because hundreds of bookings had been cancelled.

B.(B) Because they decided to keep open during the winter.

C.(C) Because they still held dinner parties and young farmers’ reunions.

D.(D) Because they substituted a training programme of films and simulated climbs.