A Classical Approach of Newtonian Mechanics

12 ORBITAL MOTION 12.5 Satellite orbits ., ‚ ., 2 × (6.67 3 × 10 ) × (5.9 7 × 10 ) The escape velocity for the Earth is vesc = ( ...

12 ORBITAL MOTION 12.6 Planetary orbits ω^2 velocity of the Earth’s rotation is 2 π ω = 24 × 60 × 60 It follows from Eq. (12.19) ...

12 ORBITAL MOTION 12.6 Planetary orbits e Planet r  e r Sun Figure 105: A planetary orbit. These expressions are more compli ...

12 ORBITAL MOTION 12.6 Planetary orbits P Figure 106: The origin of Kepler’s second law. Equation (12.28) reduces to or d (r^2 θ ...

12 ORBITAL MOTION 12.6 Planetary orbits represents the position of the Sun. The lines SP and SPJ are both approximately of lengt ...

12 ORBITAL MOTION 12.6 Planetary orbits This equation possesses the fairly obvious general solution u = A cos(θ − θ 0 where A an ...

12 ORBITAL MOTION 12.6 Planetary orbits q Planet e Mercury 0.206 Venus 0.007 Earth 0.017 Mars 0.093 Jupiter 0.048 Saturn 0.056 T ...

12 ORBITAL MOTION 12.6 Planetary orbits Ⓢ × Figure 107: Anatomy of a planetary orbit. It follows, from Eqs. (12.47), (12.49), an ...

12 ORBITAL MOTION 12.6 Planetary orbits ! × × × 2 = 1.107 10 m. Worked example 12.2: Acceleration of a rocket Question: A rocket ...

12 ORBITAL MOTION 12.6 Planetary orbits × × The satellite’s orbital period is simply 2 π r T = v 2 × π × (1.107 × 107 ) (^) 6000 ...

12 ORBITAL MOTION 12.6 Planetary orbits × × × × × × × = −7.495 10 J. Answer: Let ω be the planet’s orbital angular velocity. The ...

13 WAVE MOTION 13 Wave motion 13.1 Introduction Waves are small amplitude perturbations which propagate through continuous media ...

13 WAVE MOTION 13.2 Waves on a stretched string tan (13.2) ' tan (13.3) Figure 108: Forces acting on a segment of a stretched st ...

13 WAVE MOTION 13.2 Waves on a stretched string Here, ∂^2 y(x, t)/∂x^2 is the second derivative of y(x, t) with respect to x, ke ...

13 WAVE MOTION 13.2 Waves on a stretched string Equation (13.7) describes a pattern of motion which is periodic in both space an ...

13 WAVE MOTION 13.2 Waves on a stretched string μ Figure 109: A sinusoidal wave propagating down the x-axis. The solid, dotted, ...

13 WAVE MOTION 13.3 General waves → λ is arbitrary. However, once the wavelength is specified, the wave frequency f is fixed via ...

13 WAVE MOTION 13.4 Wave-pulses v x −> Figure 110: A wave-pulse propagating down the x-axis. The solid, dotted, and dashed cu ...

13 WAVE MOTION 13.4 Wave-pulses π where F(p) is an arbitrary function. The above solution is interpreted as a pulse of arbitrary ...

13 WAVE MOTION 13.4 Wave-pulses Figure 111 : A propagating wave-pulse, F(x − v t), and its associated Fourier spectrum, ̄F(k). ...