A Classical Approach of Newtonian Mechanics

11 OSCILLATORY MOTION 11.6 Uniform circular motion ± motion simultaneously along both the x- and the y -axes. Note, however, tha ...

11 OSCILLATORY MOTION 11.6 Uniform circular motion equilibrium position, the velocity of the block is 0.75 m/s. What is the peri ...

11 OSCILLATORY MOTION 11.6 Uniform circular motion m 3 Let f 1 = k 1 x 1 and f 2 = k 2 x 2 be the magnitudes of the forces exert ...

11 OSCILLATORY MOTION 11.6 Uniform circular motion k ‚ ., Worked example 11.4: Energy in simple harmonic motion Question: A bloc ...

11 OSCILLATORY MOTION 11.6 Uniform circular motion q 2 ‚ ., ., Now, ω = g/l for small amplitude oscillations of a simple pendulu ...

12 ORBITAL MOTION 12 Orbital motion 12.1 Introduction We have spent this course exploring the theory of motion first outlined by ...

12 ORBITAL MOTION 12.2 Historical background pher Eudoxas of Cnidus (409–356 BC). According to this model, the Sun, the Moon, an ...

12 ORBITAL MOTION 12.2 Historical background epicycle deferant planet Figure 100: The Ptolemaic system. centric model, since in ...

12 ORBITAL MOTION 12.2 Historical background to displace the Earth slightly from the common centre of the deferants. More- over, ...

12 ORBITAL MOTION 12.2 Historical background Figure 101: The Ptolemaic model of the Solar System. Stars (^) 29.46 y 11.86 y 1.88 ...

12 ORBITAL MOTION 12.2 Historical background Ptolemy’s model of the Solar System was rescued from the wreck of ancient European ...

12 ORBITAL MOTION 12.2 Historical background Figure 102: The Copernican model of the Solar System. 29.46 y 11.86 y Stars 1.88 y ...

12 ORBITAL MOTION 12.2 Historical background form circular motion in his model (after all, he was trying to construct a more sym ...

12 ORBITAL MOTION 12.2 Historical background Figure 103: Kepler’s second law. Planet a(AU) T(yr) a^3 /T 2 Mercury 0.387 0.241 0. ...

12 ORBITAL MOTION 12.3 Gravity orbiting the Sun, why do we not “feel” this motion? At first sight, this objec- tion appears to h ...

12 ORBITAL MOTION 12.3 Gravity 1 2 f = G m m / r 2 m 2 m 1 Figure 104: Newton’s law of gravity. the Earth is not located in a sp ...

12 ORBITAL MOTION 12.3 Gravity × × Let r 1 and r 2 be the vector positions of the two objects, respectively. The vector gravitat ...

12 ORBITAL MOTION 12.4 Gravitational potential energy (^) where ^z is a unit vector pointing straight upwards (i.e., away from t ...

12 ORBITAL MOTION 12.4 Gravitational potential energy ∞ ∫∞ ⊕ Body Sun Moon Mercury Venus Earth Mars Jupiter Saturn M/M⊕ 3.33 × 1 ...

12 ORBITAL MOTION 12.4 Gravitational potential energy R Since potential energy is undetermined to an arbitrary additive constant ...