衛星及牛頓運動定律3D模型

Abstract

雖然大多數的高中程度以上的人，對牛頓運動定律和克卜勒行星運動定律並不陌生，但大部份的人終其一生都沒有機會看到物體在軌道上依著克卜勒定律即時運動的情形，很多人對"行星脫離速度"有著非常模糊的概念。我們收看經由人造衛星傳送的即時新聞或體育轉播，透過衛星連接國際電話，從哈伯太空望遠鏡拍攝的高品質天文照片得知宇宙的年齡為一百二十億年。(天文學家過去相信是一百五十億年) 衛星距離地表多遠？它們運行的軌道是什麼形狀？軌道的方位又為何？衛星高度和運行速度有怎樣的關係？衛星軌道是否有方法能夠精確地描述？我們又如何能知道某一時刻衛星的位置在哪□？從地面上如何追蹤衛星？這些問題若不用3D模型來解釋，將會非常難以回答。 本論文中，我們建立了一個3D模型來呈現克卜勒軌道運動，並儘可能使它用於不同的情況。本模型可以用來模擬太陽系，只要輸入某一時間的軌道資料，所有的行星就會依照牛頓定律的規範運動。最普遍的衛星軌道資料規格是一個稱為Two Line Elemets(TLE)的格式，許多的網站都可找到現役衛星的最新TLE資料，並且不斷地更新。只要將這些資料輸入我們的模型中，我們就可以顯示衛星的運動情形，算出他們的位置和速度。

Although Newton's Laws of Motion and Kepler's Laws of planet orbit are known to most high school graduates, most people, in their life time, have never seen an object in kepler's orbit in real time. Most people have very vague knowldge about the "escape speed of a planet". We watch live news or sport programs transmitted by satellites. We make inter-continental phone calls connected by satellites. We see pictures taken by Hubble Space Telescope(HST) and are lately told that thanks to the high quality pictures of HST, we now know that the age of our universe is 12 billion years.(Astronomers used to believe that it was 15 billion years old.) How high above the ground are the satellites? What shape are their orbits? How are their orbits oriented ? What are relations between height and speed ? Is there any precise description of the orbit of a satellite, and the exact position of a satellite in its orbit at a particular moment? How do we trace a satellite on the ground ? All these problems would be very difficult to answer, if not with a 3D model. In this thesis, we set up a 3D animation model to visualize the kepler orbit. We make it as general as we can. It can model the solar system. Just enter their object data at an epoch time, all planets will consequently move as Newton's Laws mandate. The most popular specification of Satellite movement is by a format called Two Line Element(TLE). Constantly updated TLE data for active satellites are available at many web sites. When these data are entered in our model, we can visualize movement of the satellites, find their locations, their speed (km per hour as well as revolutions per day).