FACULTY OF SCIENCE, AUTUMN 2007
PHYS 124 LEC A1 : Particles and Waves
(Instructor: Marc de Montigny)
Walker, Physics, Chapter 12: Gravity
Astrophysical Sciences at the University of Alberta
- Section 12-1: Newton's Law of Universal Gravitation
- P. 359, Eq. 12-1 : F = Gm1m2/r²
- G = 6.67 × 10-11 N⋅m²/kg²
- This equation gives the magnitude of the force of gravity between
two point objects of mass m1 and m2, separated
by a distance r. See P. 359, Figure 12-1.
- The force is attractive.
- Example : P. 390, Problem 11,
Figure 12-14
- Section 12-2: Gravitational Attraction of Spherical Bodies
- P. 362, Section Uniform Sphere : the net force exerted by the sphere
on the mass m is the same as if all the mass of the sphere were concentrated
at its centre. See P. 365, Figure 12-5.
- P. 362, Eq. 12-4 : g = GME/RE²
(where ME = 5.97×1024 kg,
RE = 6.37×106 m)
- Example : P. 390, Problem 22
- Example : Satellite orbiting around a planet of mass M, at a distance
r (from the planet's centre). Newton's Law F = maCP
reads GMm/r² = mv²/r, so that v = (GM/r)1/2.
That is to say, the satellite's velocity does not depend on its size or mass,
but on the planet's mass and the distance from the planet.
- P. 365, Section "Weighing the Earth" :
In 1798, Henry Cavendish used this experimental
setup to determine the value of G. He is said to have weighed the
Earth because, knowing g, RE and, now, G,
the equation mg = G mME/RE² leads to
P. 366, Eq. 12-5:
ME = gRE²/G
- Section 12-3 : Kepler's Laws of Orbital Motion [OMITTED]
- Section 12-4: Gravitational Potential Energy
- P. 375, Eq. 12-8 : U = -G mME/r
- [Off the record: this results follows from F = -U' (where ' denotes the derivative). The
vector F is given by (-1) times the gradient of the potential function.]
- SI Unit : joule J
- U = 0 at r infinity.
- U is the work required to bring an object of mass m from infinity
to a distance r from a celestial body of mass M.
- P. 375, Figure 12-14
- P. 376, Eq. 12-9 : U = -G m1m2/r
- Example : P. 391, Problem 39
- Section 12-5: Energy Conservation
- P. 377, Eq. 12-10 : E = K + U = ½ mv2
- G mME/r
- Example : P. 379, Eq. 12-11, v = (2GM/R)1/2 gives
the impact velocity of a meteorite, which left from infinity at zero
velocity.
- P. 379, Figure 12-15 displays
the kinetic versus potential energies as a function of distance from
the planet's centre.
- Example : P. 381, Eq. 12-13, ve = (2GM/R)1/2 gives
the escape velocity necessary to take an object from the planet's surface and bring
it to infinity to zero velocity.
- Example : P. 391, Problem 51
- Example : P. 391, Problem 53
- Section 12-6: Tides [OMITTED]
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