llllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllxml> qjiang Normal james_paladine 2 2 2001-10-03T04:27:00Z 2001-10-03T04:27:00Z 1 89 508 tsinghua university 4 1 623 9.2812

2000网易杯全国大学生数学建模竞赛题目(大专组)

C  飞越北极

    今年6月,扬子晚报发布消息:“中美航线下月可飞越北极,北京至底特律可节省4小时”,摘要如下:

    71日起,加拿大和俄罗斯将允许民航班机飞越北极,此改变可大幅度缩短北美与亚洲间的飞行时间,旅客可直接从休斯敦,丹佛及明尼阿波利斯直飞北京等地。据加拿大空中交通管制局估计,如飞越北极,底特律至北京的飞行时间可节省4个小时。由于不需中途降落加油,实际节省的时间不止此数。

假设:飞机飞行高度约为10公里,飞行速度约为每小时980公里;从北京至底特律原来的航线飞经以下10处:

A1 (北纬31度,东经122)       A2 (北纬36度,东经140)

A3 (北纬 53度,西经165)      A4 (北纬62度,西经150);

A5 (北纬 59度,西经140)      A6 (北纬 55度,西经135)

A7 (北纬 50度,西经130)      A8 (北纬 47度,西经125)

A8 (北纬 47度,西经122)      A10 (北纬 42度,西经87)

请对“北京至底特律的飞行时间可节省4小时“从数学上作出一个合理的解释,分两种情况讨论:

(1)      设地球是半径为6371千米的球体;

(2)      设地球是一旋转椭球体,赤道半径为6378千米,子午线短半轴为6357千米。