Classical Physics- Newtons Gravitational Law

Newtons Gravitational Law

Newton in 1665 formulatedF α m₁m₂

∝ 1 / r²F = Gm₁m₂/ r²where G = 6.67 x 10^-11.Its unit isNm^-2and is called universal gravitational constant. The value of G was first experimentally determined by Cavendish in 1736. The value of G measured for small distances is about 1% less than the value ofGmeasured for large distances.

Gravitational field intercity gravitational force per unit mass is called gravitational field intensity. Gravitational field intensity of earth isg

E₈= F / m = GM / r²

Gravitational potential(V_g)the amount of work done to bring a unit mass form infinity to that point under the influence of gravitational field of a given massM, without changing the velocity.

V_g= GM /r

Gravitational potential energy the amount of work done to bring a mass m from infinity to that point under the influence of gravitational field of a given massMwithout changing the velocity.

U_g= - GMm / r note that W = ?U_gand U_g= mVg.

Gravitational field intensity due to a ring of radius R, mass M, at any point on the axial line at a distance x from the centre of the ring is

E_g= G M .x / (R²+ x²)^3/2

Gravitational field intercity inside the shell– 0

E_g= 2 GM / R²[1 – x / x²+ R²]²GM / R²[ 1 – cos θ]

In terms of angleθ.

Gravitational field intensity inside the shell = 0,

E surface = GM / R²

Gravitational potential due to a shell

Vin = V sur = - GM / r (x ≤ r)

V out = - GM / x (x > r)

Gravitational potential due to a solid sphere

V in = - GM / 2 R³(3 R²– r²) V out = -- GM / x (x > R)

V centre = - 3 GM / 2R

Gravitational field due to a solid sphere

E sur = GM /R², E out = GM / x²(x > R)

E in = G Mx / R³( x > R)

Variation ofgdue to heightg’ = g (1 – h /R) if h <

G’ g / (1 + h / R)²ifhis comparable toR

Variation ofgdue to depth

g’ = g (1 – x/ R)wherexis the depth.

= Oat the centre of the earth

Variation of g with rotation of earth/ latitude

G’ = g (1 – Rω²/ g cos²λ)

That isgis maximum at the poles and minimum at the equator

Orbital velocityv₀√(G )M / r

Wherev₀速度是一个地球啊r a satellite moves in its orbit andris the radius of the orbit.

Escape velocityv₀= √2GM / r

Escape velocity is the minimum velocity required to escape from the surface of the earth/planet from its gravitational field.

Time period T = 2 πr /v₀或T2 = 4π2 r3 /通用

Kinetic energy K_E= 1/2 mv₀²= GMm / 2a, P_E= - GM(m / a)

Net energy E = K_E+ P_E= - GMm/2a note v_e= √2v₀.

ExpertsMind.com-Physics Assignment Help,Newtons Gravitational Law Assignment Help, Newtons Gravitational Law Homework Help, Newtons Gravitational Law Assignment Tutors, Newtons Gravitational Law Solutions, Newtons Gravitational Law Answers, Classical Physics Assignment Tutors