问题 问答题

经过天文望远镜的长期观测,人们在宇宙中已经发现了许多双星系统,通过对它们的研究,使我们对宇宙中的物质的存在形式和分布情况有了较深刻的认识.双星系统是由两个星体组成,其中每个星体的线度都远小于两个星体之间的距离.一般双星系统距离其他星体很远,可以当作孤立系统处理.现根据对某一双星系统的光学测量确定,该双星系统中每个星体的质量都是M,两者间距L,它们正围绕着两者连线的中点作圆周运动.

(1)试计算该双星系统的周期T;

(2)若实验上观测到的运动周期为T’,为了解释两者的不同,目前有一种流行的理论认为,在宇宙中可能存在一种望远镜观测不到的暗物质.作为一种简化模型,我们我们假定在以两个星体连线为直径的球体内均匀分布着密度为ρ的暗物质,而不考虑其它暗物质的影响,并假设暗物质与星体间的相互作用同样遵守万有引力定律.试根据这一模型计算双星系统的运动周期T’.

答案

(1)以双星系统中任一星球为研究对象,根据万有引力提供向心力,

由牛顿第二定律得

G
M2
L2
=Mr1ω2=Mr2ω2
r1=r2=
L
2
T=2π
L3
2GM

(2)设暗物质的总质量为m,由暗物质对双星的作用与双星之间的万有引力的合力提供双星的向心力,

由牛顿第二定律得

m=
π
6
L3ρ
G
M2
L2
+G
Mm
(
L
2
)
2
=M
L
2
(
T′
)
2

解得:

 
T′=πL
6L
3GM+2πρGL3

答:(1)该双星系统的运动周期T=

 
T=2π
L3
2GM

    (2)根据暗物质模型计算出该双星系统的运动周期T′=

 
πL
6L
3GM+2πρGL3

阅读理解

阅读理解。

     I had a summer camp with my classmates last year.

     Early in the morning. We gathered at the bus station. After saying goodbye to our parents, we got on

the buses. It took us more than two hours to arrive at the campground.

     We got off the buses cheerfully. Laughing and shouting. We jumped and ran all over the place. It was

the first time for us to be away from the parents. Some of us started to feel homesick(想家). However,

when the night party and dances began, the homesickness was gone.

     The next day, everybody rushed to the boating class, hoping to be at the head of the others. At first,

my friends and I worked hard, but the boat wouldn't listen to us and kept going round and round. Then

the teacher taught us how to work together. After many tries, we did much better.

     Swimming class was my favourite. It was about the hottest time of a day and the best time to stay in

the cool water. The swimming teacher was a funny man, and during the class he often made us laugh

happily.

     During the week I learned a lot of new things and made many new friends. I also learned how to take

care of myself.

1. They got to the campground __________.

A. on foot

B. by bike

C. by bus

D. by plane

2. The campground was __________ from their homes.

A. quite near

B. not far

C. very long

D. quite far

3. Why swimming class was the writer's favourite?

A. Because it was good to stay in the cool water when the weather was hot.

B. Because the writer felt quite relaxed during the class.

C. Because the swimming teacher was interesting.

D. Because of all the above

4. Which statement is NOT true?

A. The children were happy to be away from Dad and Mum.

B. Their homesickness lasted for long.

C. It was teamwork to boat.

D. They camped for a week.

5. Which is the best title for the passage?

A. I Learnt a lot.

B. Boating and Swimming.

C. On the Campground

D. My First Summer Camp

单项选择题