class26

# class26 - 1 Gravitation Newton’s law of universal...

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Unformatted text preview: 1 Gravitation Newton’s law of universal gravitation F =- G mM r 2 ˆ r (1) where G = 6 . 6726 ± . 0008 × 10- 11 Nm 2 kg 2 . This equation applies strictly only to point particles. If one or both of the particles is replaced by a body with a certain extension, we must make an additional hypothesis before we can calculate the force: that the force-field is a linear field: i.e. the total force is the vector sum of all individual forces. Then the sum becomes an integral F =- Gm Z V ρ ( r )ˆ r r 2 dv (2) where ρ is the mass density and dv is the volume element at the position defined by the vector r . The gravitational field vector is the vector representing the force per unit mass exerted on a particle: g ≡ F m =- G M r 2 ˆ r (3) or g =- G Z V ρ ( r )ˆ r r 2 dv (4) which has units force per unit mass (= acceleration). Near the earth surface, this is the usual g = | g | = 9 . 80m / s 2 ....
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class26 - 1 Gravitation Newton’s law of universal...

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