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# Newtons Gravitational Law Assignment Help

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Classical Physics - Newtons Gravitational Law

**Newtons Gravitational Law**

Newton in 1665 formulated **F α m**_{1} m_{2}

**∝ 1 / r**^{2} F = Gm_{1}m_{2} / r^{2} where G = 6.67 x 10^{-11}. Its unit is **Nm**^{-2} and 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 of **G** measured for large distances.

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

**E**_{8} = F / m = GM / r^{2}

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 mass **M**, 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 mass **M** without changing the velocity.

**U**_{g} = - GMm / r note that W = ?U_{g }and 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 / (R^{2} + x^{2})^{3/2}

Gravitational field intercity inside the shell **– 0**

**E**_{g} = 2 GM / R^{2} [1 – x / x^{2 }+ R^{2}]^{2} GM / R^{2 }[ 1 – cos θ]

**In terms of angleθ.**

Gravitational field intensity inside the shell = 0,

**E surface = GM / R**^{2}

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 R**^{3} (3 R^{2} – r^{2}) V out = -- GM / x (x > R)

**V centre = - 3 GM / 2R**

Gravitational field due to a solid sphere

**E sur = GM /R**^{2}, E out = GM / x^{2 } (x > R)

E in = G Mx / R^{3 } ( x > R)

Variation of **g **due to height **g’ = g (1 – h /R) if h <<R **

**G’ g / (1 + h / R)**^{2} if **h** is comparable to **R**

Variation of **g** due to depth

**g’ = g (1 – x/ R) **where** x** is the depth.

**= O **at the centre of the earth

Variation of g with rotation of earth/ latitude

**G’ = g (1 – Rω**^{2} / g cos^{2} λ)

That is **g** is maximum at the poles and minimum at the equator

Orbital velocity** ****v**_{0}** √(G )M / r**

Where **v**_{0} is speed with which a planet or a satellite moves in its orbit and **r **is the radius of the orbit.

Escape velocity **v**_{0} **= √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 / ****v**_{0}** or T2 = 4π2 r3 / GM**

Kinetic energy K_{E} = 1/2 m**v**_{0}^{2}** = GMm / 2a, P**_{E }= - GM(m / a)

Net energy E = K_{E} + P_{E} = - GMm/2a note v_{e} = √2 **v**_{0}.

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

**Newtons Gravitational Law**

**F α m**

_{1}m_{2}

**∝ 1 / r**Its unit is

^{2}F = Gm_{1}m_{2}/ r^{2}where G = 6.67 x 10^{-11}.**Nm**and 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 of

^{-2}**G**measured for large distances.

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

**g**

**E**

_{8}= F / m = GM / r^{2}

Gravitational potential

**(V**the amount of work done to bring a unit mass form infinity to that point under the influence of gravitational field of a given mass

_{g})**M**, without changing the velocity.

**V**

_{g}= GM /rGravitational 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 mass

**M**without changing the velocity.

**U**

_{g}= - GMm / r note that W = ?U_{g }and 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 / (R^{2}+ x^{2})^{3/2}

Gravitational field intercity inside the shell

**– 0**

**E**

_{g}= 2 GM / R^{2}[1 – x / x^{2 }+ R^{2}]^{2}GM / R^{2 }[ 1 – cos θ]**In terms of angleθ.**

Gravitational field intensity inside the shell = 0,

**E surface = GM / R**

^{2}

Gravitational potential due to a shell

**Vin = V sur = - GM / r (x ≤ r)**

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

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

Gravitational potential due to a solid sphere

**V in = - GM / 2 R**

^{3}(3 R^{2}– r^{2}) V out = -- GM / x (x > R)**V centre = - 3 GM / 2R**

Gravitational field due to a solid sphere

**E sur = GM /R**

E in = G Mx / R

^{2}, E out = GM / x^{2 }(x > R)E in = G Mx / R

^{3 }( x > R)Variation of

**g**due to height

**g’ = g (1 – h /R) if h <<R**

**G’ g / (1 + h / R)**

^{2}if

**h**is comparable to

**R**

Variation of

**g**due to depth

**g’ = g (1 – x/ R)**where

**x**is the depth.

**= O**at the centre of the earth

Variation of g with rotation of earth/ latitude

**G’ = g (1 – Rω**

^{2}/ g cos^{2}λ)That is

**g**is maximum at the poles and minimum at the equator

Orbital velocity

**v**

_{0}

**√(G )M / r**

Where

**v**

_{0}is speed with which a planet or a satellite moves in its orbit and

**r**is the radius of the orbit.

Escape velocity

**v**

_{0}

**= √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 /**

**v**

_{0}

**or T2 = 4π2 r3 / GM**

Kinetic energy K

Kinetic energy K

_{E}= 1/2 m**v**

_{0}

^{2}

**= GMm / 2a, P**

Net energy E = K

_{E }= - GM(m / a)Net energy E = K

_{E}+ P_{E}= - GMm/2a note v_{e}= √2**v**

_{0}.

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