万有引力定律测试题

万有引力定律测试题 ,、在研究宇宙发展演变的理论中，有一种学说叫“宇宙膨胀说”这种学说认为 引力常量G在缓慢的减小，据这一理论，在很久很久以前太阳系中地球的公 转情况与现在相比 A、公转半径R较大 B、公转周期T较大 C、公转速率较大 D、公转角速度较小 2、2003年8月29日，火星、地球和太阳处于三 点一 线，上演“火星冲日”的天象奇观(这是 6万年 来火星距地球最近的一次，与地球之间 的距离只有5576万公里，为人类研究火星提供 了最佳时机(如图所示为美国宇航局最新公布 “火星大冲”的虚拟图(由此可知( ) 的 A、2003年8月29日，火星的线速度大于地 球的线速度 B、2003年8月29日，火星的线速度小于地球的线速度 C、2004年8月29日，火星又回到了该位置 D、2004年8月29日，火星还没有回到该位置 ,、,,,,年,月,,日“和平”号空间站完成了它的历史使命，坠落在浩瀚 的南太平洋。下面有关“和平”号空间站坠落过程的说明正确的是 ,、“和平”号空间站进入大气层前，高度降低，速度变大 ,、“和平”号空间站在整个坠落过程中的运动轨迹是曲线 ,、“和平”号空间站在整个坠落过程中的运动轨迹是直线 ,、“和平”号空间站进入较稠密大气层时，将与空气摩擦，空气阻力大大 增加 4、2005年北京时间7月4日下午1时52分，美国探测器成功撞击“坦普尔一号”彗星，投入彗星的怀抱，实现了人类历史上第一次对彗星的“大对撞”,如图所示. 假设“坦普尔一号”彗星绕太阳 运行的轨道是一个椭圆，其运动周期为5.74 年，则关于“坦普尔一号” 彗星的下列说 法正确的是( ) A、近日点处加速度大于远日点处加速度 B、绕太阳运动的角速度不变 C、近日点处线速度小于远日点处线速度 D、其椭圆轨道长半轴的立方与周期的平方之比是一个与太阳质量有关的常 数 5、如图所示，a、b、c是大气层外圆形轨道上运行的三颗人造卫星，a、b质量upgrade and expansion, whole system construction of guideline followed following principles: Advanced: full reference both at home and abroad advanced, and mature of technology, and method and means, Project design, technical product leader, mature products as possible on the main equipment selection, technical lead and aligned with national standards of general-purpose, standard equipment. Systematization: strictly follow the view of system engineering and construction, has always been to practice engineering integrity, hierarchy, and adaptability to the external environment for constructive purposes. Maximize the business integration, functional integration and avoid different products, different standards and specifications of piecing together and combination of the system. Openness and standardization: hardware device selects the domestic and foreign well-known products, system architecture and protocol standards are in accordance with the ITU-t international industry standards and ISO standards of design, core systems and devices, following international standards, harmonization of standards, ensure system scalability and continuity of the system. Practicality: ensure high availability of the system performance with high reliability and flexibility both; first to ensure stable and reliable operation of the system, and using redundancy design of key components of the key position then to simple, technologically advanced, economical and practical. Extensible and maintainable: within the expected life cycle of systems or equipment, can be upgraded and modified to meet the needs of the user actions and application requirements change. And ensures after-sales service 相同且小于c的质量，下面说法中正确的是( ) A、 b、c的线速度大小相等且大于a的线速度 B、 b、c的向心加速度相等且大于a的向心加速度 C、 b、c的周期相等且大于a的周期 D、 b、c的向心力相等且大于a的向心力 6、如图所示，图中a、b、c、d四条圆轨道的圆心均在地 球的自转轴上，均绕地球做匀速圆周运动的卫星中， 下列判断图中卫星可能的轨道正确说法是( ) A、只要轨道的圆心均在地球自转轴上都是可能的轨 道,图中轨道a、b、c 、d都是可能的轨道 B、只有轨道的圆心在地球的球心上,这些轨道才是可 能的轨道，图中轨道a、b、c均可能 C、只有轨道平面与地球赤道平面重合的卫星轨道才是可能的 轨道，图中只有a轨道是可能的 D、只有轨道圆心在球心，且不与赤道平面重合的轨道，即图 中轨道、才是可能的 bc ,、在,轨道上运动的卫星比在,轨道上运动的卫星能观察到地面上更大范 围 7、地球赤道上的物体重力加速度为g，物体在赤道上随地球自转 的向心加速度为a，要使物体(赤道上的)飘起来，测地球的 转速为原来转速的 g，ag,aggA、倍 B、倍 C、倍 D、 倍 aaaa8、下列各组数据中只需要知道一组就能计算地球质量的是(引力常量为已知) A、地球绕太阳运行的周期及日地间的距离 B、月球绕地球运行的周期及月地间的距离 C、人造地球卫星在地面附近绕行速度和运动周期 D、地球同步卫星离地面的高度 9、位于赤道面上的一颗人造卫星绕地球运行，傍晚在赤道上的某人发现卫星 位于自己的正上方，相对地面运动。第二天傍晚同一时刻又发现此卫星出 ,现在自己的正上方。已知地球自转的角速度是，地处的重力加速度为0 gR，地球半径为,则下列说法正确的是( ) 00 A、一定是同步卫星 B、可能是同步卫星 32gR00,RC、此卫星离地面的高度可能是: 024,0 upgrade and expansion, whole system construction of guideline followed following principles: Advanced: full reference both at home and abroad advanced, and mature of technology, and method and means, Project design, technical product leader, mature products as possible on the main equipment selection, technical lead and aligned with national standards of general-purpose, standard equipment. Systematization: strictly follow the view of system engineering and construction, has always been to practice engineering integrity, hierarchy, and adaptability to the external environment for constructive purposes. Maximize the business integration, functional integration and avoid different products, different standards and specifications of piecing together and combination of the system. Openness and standardization: hardware device selects the domestic and foreign well-known products, system architecture and protocol standards are in accordance with the ITU-t international industry standards and ISO standards of design, core systems and devices, following international standards, harmonization of standards, ensure system scalability and continuity of the system. Practicality: ensure high availability of the system performance with high reliability and flexibility both; first to ensure stable and reliable operation of the system, and using redundancy design of key components of the key position then to simple, technologically advanced, economical and practical. Extensible and maintainable: within the expected life cycle of systems or equipment, can be upgraded and modified to meet the needs of the user actions and application requirements change. And ensures after-sales service 32gR00D、此卫星离地的高度可能是: ,R02,0 10、同步卫星离地心距离为r，运行速度为，加速度为，地球赤道上的物va11 体随地球自转的加速度为，第一宇宙速度为，地球半径为R，则以下av22 说法正确的是( ) 122vvaarrrr,,,,1111A、 B、 C、 ,、 ,,,,,,,,aRvRvRaR,,,,2222 11、假设有一载人宇宙飞船在距地面高度为,,,,,,的赤道上空绕地球做匀 速圆周运动，地球半径约为,,,,,,，地球同步卫星距地面高度为,, ,,,,,，宇宙飞船和一地球同步卫星绕地球同向运动，每当两者相距最 近时，宇宙飞船就向同步卫星发射信号，然后再由同步卫星将信号发送到地 面接收站，某时刻两者相距最远，从此刻开始，在一昼夜的时间内，接收站 共接收到信号的次数为 ,、, ,、, ,、, ,、, 12、1998年8月20日，中国太原卫星发射中心为美国“铱”星公司成功发射了 两颗“铱”星系统的补网星. 1998年9月23日，“铱”卫星通讯系统正式 投入商业运行，标志着一场通讯技术革命开始了. 原的“铱”卫星通讯 系统是在距地球表面780 km的太空轨道上建立一个由77颗小卫星组成的星 座. 这些小卫星均匀分布在覆盖全球的7条轨道上，每条轨道上有11颗卫 星，由于这一的卫星排布像化学元素“铱”原子的核外77个电子围绕 原子核运动一样，所以称为“铱”星系统. 后来改为由66颗卫星，分布在 6条轨道上，每条轨道上11颗卫星组成，仍称它为“铱”星系统. (1)“铱”星系统的66颗卫星其运行轨道的共同特点是 A、以地轴为中心的圆形轨道 B、以地心为中心的圆形轨道 C、轨道平面必须处于赤道平面内 D、铱星运行轨道远低于同步卫星轨道 (2)上题所述的“铱”星系统的卫星运行速度约为 . A、7.9 km/s B、7.5 km/s C、3.07 km/s D、11.2 km/s 二、填空题: ,,、人造卫星在离地面的距离等于地球半径的圆轨道上运行，已知地球半径为 R，，地球表面的重力加速度为g，则卫星的绕行线速度大小为 . 21,、一物体在地球表面重16N，它在以5m,s的加速度加速上升的火箭中视重 为9N，则此火箭离地球表面的距离为地球半径的 倍. 1,、“大爆炸学说”认为:宇宙是很久以前发生的一次大爆炸使聚集于某处的物 质分离开来而形成的. 直到现在，这大爆炸的碎片——宇宙中的各星系仍在 以不同的相对速率相互远离. 观察表明:离我们越远的星系远离我们飞去的upgrade and expansion, whole system construction of guideline followed following principles: Advanced: full reference both at home and abroad advanced, and mature of technology, and method and means, Project design, technical product leader, mature products as possible on the main equipment selection, technical lead and aligned with national standards of general-purpose, standard equipment. Systematization: strictly follow the view of system engineering and construction, has always been to practice engineering integrity, hierarchy, and adaptability to the external environment for constructive purposes. Maximize the business integration, functional integration and avoid different products, different standards and specifications of piecing together and combination of the system. Openness and standardization: hardware device selects the domestic and foreign well-known products, system architecture and protocol standards are in accordance with the ITU-t international industry standards and ISO standards of design, core systems and devices, following international standards, harmonization of standards, ensure system scalability and continuity of the system. Practicality: ensure high availability of the system performance with high reliability and flexibility both; first to ensure stable and reliable operation of the system, and using redundancy design of key components of the key position then to simple, technologically advanced, economical and practical. Extensible and maintainable: within the expected life cycle of systems or equipment, can be upgraded and modified to meet the needs of the user actions and application requirements change. And ensures after-sales service 9速度越大. 例如，牧夫座内一星云离我们银河系的距离为s,2.74×10光 7年，它正以3.93×10m/s的速度飞离银河系. 若大爆炸后形成的星系是以不同的从大爆炸前物质聚合处沿各个方向匀速演化飞离，假设大爆炸后银河系与牧夫座的那个星云分别以速率和沿相反方向飞离大爆炸前物质聚vv12 合处，则计算宇宙的年龄的表达式为T= ，由此算出的宇宙年龄为 年. ,,、某人站在一个星球上以速度v竖直上抛一物体，经t秒后物体落回手中，1 已知此星球的半径为R，现将该物体沿星球表面平抛出去，要使其不再落回此星球，则抛出的速度至少为______。 ,,、飞船沿半径为R的圆周绕地球运动，其周期为T. 如果飞船要返回地面，可在轨道上某点A处将速率降低到适当数值，从而使飞船沿着以地心为焦点的椭圆轨道运动，椭圆和地球表面在B点相切，如图所示. 如果地球半径为R，飞船由A点到B点所需要的时间为_______。飞船在0 圆轨道上运动时机械能___恒;在圆轨道上运动时和在 R 椭圆轨道上运动时机械能___同。 R0 AB ,,、1976年10月，剑桥大学研究生贝尔偶然发现一个奇 怪的发射电源，它每隔1.337s发出一个脉冲信号. 贝 尔和她的导师曾认为他们和外星文明接上了头. 后来 大家认识到事情没有这么浪漫，这类天体被定名为“脉 冲星”. “脉冲星”的特点是脉冲周期短，且周期高度稳定. 这意味着脉冲星一定进行着准确的周期运动，自转就是一种很准确的周期运动. (1) 已知蟹状星云的中心星PS0531是一颗脉冲星，其周期为0.331s,PS0531 是万有引力，估计PS0531的脉冲现象来自自转. 设阻止该星离心瓦解的力 的最小密度约为______。 (2) 如果PS0531的质量等于太阳质量，该星的可能半径最大是______(太阳30质量是M=10kg,计算结果均取2位有效数字) ,,、如图，在天文学上把两个相距较近，由于彼此的引力作用而沿轨道互相 环绕的恒星系统称为“双星”，例如，天上明亮的天狼星就是双星系统的一 颗子星，另一颗子星是已不发光的白矮星，它们的环绕周期为50.1年，现 α星和β星组成的双星系统其“晃动”(实际上是环绕转动，不过人们往往 只能看到它们在晃动)周期为T，α星的晃动范围为D，β星的晃动范围 为Dα星的质量为_______，β星的质量为_______。 β ,,、侦查卫星在通过地球两极上空的圆轨道上运行时，它的轨道距离地面高 度为h，要使卫星在一天的时间内将地面上赤道各处的日照条件下全部拍 摄下来，卫星在赤道上空时，卫星的摄像机至少应拍摄地面上赤道圆周的 弧长是_________。(设地球半径为R，地面处的重力加速度为g，地球自转 周期为T)。 ,,、若要使地球的半面始终朝着太阳，另一半始终背着太阳，地球自转的周 期等于______________ ,,、向空间发展最具可能的是在太阳系内地球附近建立“太空城”。如图是upgrade and expansion, whole system construction of guideline followed following principles: Advanced: full reference both at home and abroad advanced, and mature of technology, and method and means, Project design, technical product leader, mature products as possible on the main equipment selection, technical lead and aligned with national standards of general-purpose, standard equipment. Systematization: strictly follow the view of system engineering and construction, has always been to practice engineering integrity, hierarchy, and adaptability to the external environment for constructive purposes. Maximize the business integration, functional integration and avoid different products, different standards and specifications of piecing together and combination of the system. Openness and standardization: hardware device selects the domestic and foreign well-known products, system architecture and protocol standards are in accordance with the ITU-t international industry standards and ISO standards of design, core systems and devices, following international standards, harmonization of standards, ensure system scalability and continuity of the system. Practicality: ensure high availability of the system performance with high reliability and flexibility both; first to ensure stable and reliable operation of the system, and using redundancy design of key components of the key position then to simple, technologically advanced, economical and practical. Extensible and maintainable: within the expected life cycle of systems or equipment, can be upgraded and modified to meet the needs of the user actions and application requirements change. And ensures after-sales service 设想中的一个太空城， 长,,,,,，直径,,,,， 上下分层，窗口和人造陆地交 错分布，陆地上土壤厚1.5m 窗外有巨大铝制反射镜可调节 阳光射入。太空城内空气、水、 食品和土壤最初可从地球、月 球运送，以后则在太空城内形成与地球相同的生态环境。为使太空城的居 民能如同在地球上一样具有重力，以适应人类在地球上的行为习惯，太空 城在电力驱动下绕自己的中心轴以一定角速度转动，其自转速度为 n________ min 若太空城中的居民同样享受阳光、日出而耕日落而息„„和现在没什么两 样!请画出该太空城与太阳、地球的位置关系并做简要说明。 ,,、,,,,年科学家佐利设计了一个测量地球质量的方法:首先，在长臂 天平的两盘放入质量同为,的砝码，天平处于平衡状态;然后，在左盘正 下方放入一质量为,的大球，且球心与砝码有一很小的距离,;接着又在 ,m右盘中加质量为的砝码，使天平又恢复平衡状态。试导出地球质量M0 的估算式_____ (地球半径为,) ,,、一艘宇宙飞船飞近某一新发现的行星，并进入靠近该行星表面的圆形轨 道绕行数圈后，着陆在行星上，宇宙飞船上备有下列仪器: ,、精确秒表一只 ,、已知标准质量为,的物体一个 ,、弹簧测力计一个 ,、天平一架(附砝码) 已知宇航员在绕行和着陆后各作了一次测量，根据测量数据可求出该行星 的半径,和行星质量,。(已知万有引力常量为,) (,)第一次测量所选用的器材是:_____(用序号表示);测量的物理量是 ____。 (,)第一次测量所选用的器材是:_____(用序号表示);测量的物理量是 ____。 (,)用该数据推导出半径,,_____ ，,,_____ 。 ,,、宇宙中存在一些离其它恒星较远的由质量相等的三颗星 ,,,组成的三星系统，通常可忽略其它星体对它们的 引力作用稳定的三星系统构成形式有四种设想:第一种 是三颗星位于等边三角形的三个顶点上，并沿外接于等 边三角形的圆形轨道运动;第二种是三颗星位于等腰直 角三角形的三个顶点上，并以三边中线的交点为圆心的 圆形轨道运动;第三种是三颗星位于等腰直角三角形的 三个顶点上，并以斜边中点为圆心做圆周运动;第四种 是三颗星位于同一直线上，两颗星围绕中央星在同一圆 形轨道上运行。则稳定的三星系统构成形式应为_____。 ,,、“神舟五号”是首先进入近地点为200km，远地点为343km的椭圆轨道， 而后并轨进入离地高度为h=343km的圆形轨道(做圆周运动。令地球半 24,1122，10径R=6400km，地球质量为M=6.00kg, 。G,6.67，10N,mkgupgrade and expansion, whole system construction of guideline followed following principles: Advanced: full reference both at home and abroad advanced, and mature of technology, and method and means, Project design, technical product leader, mature products as possible on the main equipment selection, technical lead and aligned with national standards of general-purpose, standard equipment. Systematization: strictly follow the view of system engineering and construction, has always been to practice engineering integrity, hierarchy, and adaptability to the external environment for constructive purposes. Maximize the business integration, functional integration and avoid different products, different standards and specifications of piecing together and combination of the system. Openness and standardization: hardware device selects the domestic and foreign well-known products, system architecture and protocol standards are in accordance with the ITU-t international industry standards and ISO standards of design, core systems and devices, following international standards, harmonization of standards, ensure system scalability and continuity of the system. Practicality: ensure high availability of the system performance with high reliability and flexibility both; first to ensure stable and reliable operation of the system, and using redundancy design of key components of the key position then to simple, technologically advanced, economical and practical. Extensible and maintainable: within the expected life cycle of systems or equipment, can be upgraded and modified to meet the needs of the user actions and application requirements change. And ensures after-sales service 求 (,)在圆轨道上运动时，在飞船内一定不起作用的仪器是: A、水银温度计 B、弹簧秤 C、天平 D、水银气压计 (,)如图是它在椭圆轨道和圆轨道上的运动情况。则: A、在椭圆轨道上运动时， B、 V,Va,aABAB C、在轨道?上和轨道?上运动经 过A点时具有的向心加速度相等。 D、要使他由?轨道转到?轨道上运 动须在A处，使其速度增大。 (,)在圆轨道上运动时 A、其轨道中心一定与地心重合 B、其轨道可以与地球表面上某一经度线所决定的圆是共面同心圆 C、宇航员处于完全失重状态 D、宇航员走出飞船后就会落回地面(不计阻力) E、飞船要与环绕地球转的空间站对接，可从低轨道上加速 ,、飞船与环绕地球转的空间站对接的最后阶段应保证二者的速度、轨道高 度、周期、角速度相同。 (,)返回舱在大气层中降落时，由于空气阻力的作用，有一段时间匀速下落， 设返回舱受的阻力f与其速度v的平方成正比，与其迎风面的面积s成正 比，比例系数为k，返回舱的质量为m，则飞船的终极速度为多少,(g 为已知) 2GMV,,,、已知物体从地球上的逃逸速度(第二宇宙速度)，其中G，2R M，R分别为引力常量，地球的质量和半径，已知 ,11228mGNmkgc,6.67，10,,,2.9979，10求: s (1)逃逸速度大于真空中光速c的天体叫做黑洞，设某黑洞的质量等于太阳 30的质量，求它的最大半径。 1.98，10kg kg27,10(2)在目前天文观测范围内，物质的平均密度为，如果认为我们3m 的宇宙是这样的一个均匀大球体，其密度使得他的逃逸速度大于光在真空 中的速度c，因此任何物体都不脱离宇宙，问宇宙的半径至少多大, ,,、一行星探测器从所探测的行星表面垂直升空，探测器的质量是,,,,, ,，发动机推力为恒力，升空途中发动机突然关闭。如图所示为探测器速 度随时间的变化图像，其中,点对应的时刻,,,,，此行星半径为,,,,,,,,667,×,,,,，引力恒量,,×,,,,?,,。求 (,)探测器在该行星表面达到的最大高度 (,)该行星表面的重力加速度 (,)发动机的推力 , (,)距此行星,,,×,,,,处的重力加速度。 upgrade and expansion, whole system construction of guideline followed following principles: Advanced: full reference both at home and abroad advanced, and mature of technology, and method and means, Project design, technical product leader, mature products as possible on the main equipment selection, technical lead and aligned with national standards of general-purpose, standard equipment. Systematization: strictly follow the view of system engineering and construction, has always been to practice engineering integrity, hierarchy, and adaptability to the external environment for constructive purposes. Maximize the business integration, functional integration and avoid different products, different standards and specifications of piecing together and combination of the system. Openness and standardization: hardware device selects the domestic and foreign well-known products, system architecture and protocol standards are in accordance with the ITU-t international industry standards and ISO standards of design, core systems and devices, following international standards, harmonization of standards, ensure system scalability and continuity of the system. Practicality: ensure high availability of the system performance with high reliability and flexibility both; first to ensure stable and reliable operation of the system, and using redundancy design of key components of the key position then to simple, technologically advanced, economical and practical. Extensible and maintainable: within the expected life cycle of systems or equipment, can be upgraded and modified to meet the needs of the user actions and application requirements change. And ensures after-sales service upgrade and expansion, whole system construction of guideline followed following principles: Advanced: full reference both at home and abroad advanced, and mature of technology, and method and means, Project design, technical product leader, mature products as possible on the main equipment selection, technical lead and aligned with national standards of general-purpose, standard equipment. Systematization: strictly follow the view of system engineering and construction, has always been to practice engineering integrity, hierarchy, and adaptability to the external environment for constructive purposes. Maximize the business integration, functional integration and avoid different products, different standards and specifications of piecing together and combination of the system. Openness and standardization: hardware device selects the domestic and foreign well-known products, system architecture and protocol standards are in accordance with the ITU-t international industry standards and ISO standards of design, core systems and devices, following international standards, harmonization of standards, ensure system scalability and continuity of the system. Practicality: ensure high availability of the system performance with high reliability and flexibility both; first to ensure stable and reliable operation of the system, and using redundancy design of key components of the key position then to simple, technologically advanced, economical and practical. Extensible and maintainable: within the expected life cycle of systems or equipment, can be upgraded and modified to meet the needs of the user actions and application requirements change. And ensures after-sales service