天文物理學會講座 牛頓力學與天體運動

牛頓運動第一定律 (Newton’s first law of motion) 牛頓 (1642-1727) 除非受到不平衡力作用的影響， 所有物體都會保持靜止 或勻速直線運動。 ...基本上與伽利略的慣性定律相同，不過我進一步對力(force)下了定義。

牛頓運動第二定律 (Newton’s second law of motion) F = m a 物體加速度 a 的大小 與作用在物體上的淨力 F 成正比， 與物體本身的質量m 成反比； 而加速度 a 的方向與淨力 F 的方向相同。

牛頓運動第三定律 (Newton’s third law of motion)： 對每一個作用力，都有一個大小相等、方向相反的反作用力。 我們必須緊記： 牛頓運動第三定律應用於兩個物體之間的互相作用，並非指作用在同一個物體上的力。

Newton’s Second Law of Motion The rate of change of momentum of an object is directly proportional to the net force acted on it, and the motion occurs along the direction of the force.

Centripetal acceleration An object in uniform circular motion experiences a centripetal acceleration which is the acceleration directed towards the centre of the circle.

Centripetal acceleration Change in velocity (v) = vB – vA (represented by QR) Particle experiences change of velocity (acceleration) along direction AO (pointing to centre of circle)

Centripetal acceleration pointing to centre of circle

centripetal force (Fc) Steady speed v but changing direction of motion - force acting on it (Newton’s 1st Law) No force in direction of motion (constant speed) Force towards centre of circular path centripetal force (Fc)

Centripetal force Centripetal force experiment

Newton’s Law of Gravitation Launch object horizontally from incredibly high mountain - greater initial speed, further away it lands - if u is large enough, object will move in circular orbit around earth

Newton’s Law of Gravitation Gravitation force - all objects attract each other with the force Newton’s Law of Gravitation where G is called the universal gravitational constant and the value of G is 6.67 ×10−11 N m2 kg−2.

Orbital motion of satellite Moon – only natural satellite of earth Artificial satellites – man put them around earth

Orbital motion of satellite launching speed of satellite at its orbital height

Weightlessness Weightlessness occurs when - we are in free-falling motion - in spacecraft moving in circular orbit around earth Astronaut experiences no reaction, he feels weightless

Kepler’s Laws of Planetary Motion Three laws describing planetary motion 1. Kepler’s First Law states that each planet moves in an ellipse which has the sun at one focus. ellipses (not perfect circle)

Kepler’s Laws of Planetary Motion 2. Kepler’s Second Law states that the line joining the sun and the planet sweeps out equal area in equal time interval. http://www.arachnoid.com/gravitation/small.html planets move faster when nearer to sun

Kepler’s Laws of Planetary Motion 3. Kepler’s Third Law states that the squares of the periods of revolution of the planets (T2) are proportional to the cubes of their mean distances (r3) from the sun. http://www.arachnoid.com/gravitation/small.html

Kepler’s Laws of Planetary Motion Verification:

Kepler’s Laws of Planetary Motion