问题 问答题

某课外小组经长期观测,发现靠近某行星周围有众多卫星,且相对均匀地分布于行星周围,假设所有卫星绕该行星的运动都是匀速圆周运动,通过天文观测,测得离行星最近的一颗卫星的运动半径为R1,周期为T1,已知万有引力常为G.求:

(1)行星的质量;

(2)若行星的半径为R,行星的第一宇宙速度;

(3)通过天文观测,发现离行星很远处还有一颗卫星,其运动半径为R2,周期为T2,试估算靠近行星周围众多卫星的总质量.

答案

(1)根据万有引力提供向心力得:

G

Mm
R12
=m
2R1
T12

解得行星质量为:M=

2R13
GT12

(2)由G

Mm
R2
=m
v2
R

得第一宇宙速度为:v=

2πR1
T1
R1
R

(3)因为行星周围的卫星分布均匀,研究很远的卫星可把其他卫星和行星整体作为中心天体,

根据万有引力提供向心力得:G

Mm
R22
=m
2R2
T22

所以行星和其他卫星的总质量M=

2R23
GT22

所以靠近该行星周围的众多卫星的总质量为:△M=

2R23
GT22
-
2R13
GT12

答:(1)行星的质量为

2R13
GT12

(2)若行星的半径为R,行星的第一宇宙速度为

2πR1
T1
R1
R

(3)通过靠近行星周围众多卫星的总质量为

2R23
GT22
-
2R13
GT12

阅读理解

One day, I saw Harry sitting under a tree. He looked very sad. So I asked him what was wrong.

“Nothing,” He said, “I’m too short to join the school basketball team.” “And our P.E .teacher thinks I’ve little hope to be in the team in half a year,” he added.

“Why not join another team?” I asked.

“But my dream is to be an excellent basketball player in the future,” he said.

He told me his father wanted him to change his idea to join the school ping-pong team.

“Good idea.” I agreed. “You’re sure to be popular, because you have a smart head.”

The next day, he joined the school ping-pong team. He worked harder than any other boy. Soon he was very popular in the team and looked happy every day.

At the end of last month, his team took part in the city’s high school ping-pong match. He and his team beat the others and won the championship.

Sometimes your dream may not come true. Then make a small change, and it will bring you another success.

根据短文内容,选择最佳答案,并在答题卡上按要求作答。

小题1:Why did Harry look sad that day?

A.There was something wrong with his leg.

B.His P.E. teacher told him not to play basketball.

C.He was too short to join the school basketball team.

D.He wasn’t well enough for the school basketball team.小题2:Harry’s father would like him to _______.

A.join the school ping-pong team.

B.take part in another basketball club.

C.take part in the city ping-pong match.

D.beat others and win a championship.小题3:According to the passage, we know ______.

A. Harry dreamed to be a ping-pong player.

B. Harry worked harder than others in the team.

C. Harry was soon popular in their team.

D. Both B and C.

小题4:Which of the following is NOT true?

A.Ping-pong made Harry happy.

B.Ping-pong is easier than basketball.

C.Harry is a high school student.

D.Harry and his team won the match.小题5:The passage tells us that ______.

A.Harry is too short to play basketball.

B.Harry wants to be a basketball player.

C.Making a change may be good for you.

D.a big dream can bring you success.

单项选择题