Newton's Law of Gravitation

We already know about Newton's three laws of motion, the second of which is . These three laws describe motion in general. They never refer to a specific force. Newton however did also study in detail a specific force, namely gravity. He conjectured that the gravitational force between two bodies of mass m₁ and m₂ whose centers are separated by a distance of r has a magnitude of

The minus sign tells us that the force points inwards. The value of G was determined later in 1798 by Cavendish. It's value measured today is

G = 6.67 × 10^-11Nm² kg^-2

However, it is interesting that today the gravitational constant is the least accurately known of all the fundamental constants. For instance, its most accurately known value is actually G = (6:67259±0.00085)×10^-11 Nm²kg^-2 whereas for example the charge of the electron is (1:60217733 ± 0.00000049) × 10^-19 Coulomb or the speed of light is 299 792 458 m sec^-1 which are known much more accurately than G. Another example is the strength of the electrical force, called the fine structure constant, α^-1 = 137:0359895 ± 0.0000061.

Note: Now the vector form of Newton's Law is

where  is a unit vector point from one mass out to the other. The gravitational force is an inward force and that's why the minus sign appears.

مواضيع ذات صلة

أنظمة لأكثر من جسيم واحد

كمية التحرك الزاوية والقوة المركزية

الحركة الدورانية

امثلة عن الاتزان الاستاتيكي للأجسام الممتدة

الاتزان الاستاتيكي للأجسام الممتدة

تعريف العزم

تذبذبات صغيرة لبندول

اعتبارات الطاقة في الحركة التوافقية البسيطة

الحل الهندسي للمعادلة التفاضلية للحركة التوافقية البسيطة، دائرة المرجع

الحل باستخدام حساب التفاضل والتكامل

قانون هوك والمعادلة التفاضلية للحركة التوافقية البسيطة

القدرة ووحدات الشغل