Gravitation Flashcards

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1
Q

Gravitation

A

Force of attraction between any two bodies in the universe

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2
Q

Gravity

A

Force of attraction between the earth and any object lying on or near its surface

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3
Q

Newton’s law of gravitation

A

Every partice in the universe attracts every other particle with a force which is directly proportional to the produce of their masses and inversely proportional to the square of the distances between them
F = Gm1 m2 / r^2

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4
Q

G value

A

6.67 * 10 ^ -11 Nm^2 / kg^2

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5
Q

Gravitation in vector format

A

F = -G m1 m2 * (r cap) / r^2

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6
Q

Principle of Superposition of gravitational forces

A

Gravitational force between two masses acts independently and uninfluenced by the presence of other bodies. Hence, the resultant gravitational force acting on a particle due to a number of masses is the vector sum of the gravitational forces exerted by the individual masses on the given particle

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7
Q

Shell Theorem

A
  • If a point mass lies outside a uniform spherical shell with a spherically symmetric internal mass distribution, the shell attracts the point mass as if the entire mass of the shell were concentrated at its centre
  • If a point mass lies inside a uniform spherical shell, the gravitational force on the point mass is zero. But if a point mass lies inside a homogeneous solid sphere, the force on the point mass acts towards the centre of the sphere.
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8
Q

Mass of earth in terms of density

A

M = ro * V = ro * 4/3 pi * r^3

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9
Q

Acceleration due to g on different points on earth

A
  1. Above earth: F = GMm / r^2
  2. Below earth’s surface: F = GMm / R^3 * r
  3. At points on earth’s surface: F = GMm / R^2
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10
Q

Relation between g and G

A

g = GMm / R^2

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11
Q

Variation of g with altitude derivation

A

gh = g (1 - 2h / R)

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12
Q

Variation of g with depth

A

g = g(1 - d / R)

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13
Q

Formulas of g variation

A

With altitude:
1. g = g * R^2 / (R + h)^2
2. g = g (1 - 2h / R)
With depth:
1. g = g (1 - d / R)
With radius
1. Inversely proportional

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14
Q

Variation of g with shape of Earth

A
  • Flat at poles and bulges at equatior
  • Since g is inversely proportional to R^2
  • Re > Rp or ge < gp
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15
Q

Gravitational Field

A

Space surrounding a material body within its gravitational force of attraction can be experienced

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16
Q

Gravitational Field intensity

A

At any point in the gravitational field due to a given mass is defined as the force experienced by a unit mass placed at that point providede the presence of unit mass does not disturb the original gravitational field

17
Q

gravitational field intensity formula

A

E = F / m = GM / r^2 = g

18
Q

Gravitational Potential Energy

A

Energy associated with it due to its position in the gravitational field of another body and is measured by the amount of work done in bringing a body from infinity to a given point in the gravitational field of the other

19
Q

Gravitational potential energy derivation

A

U = -GMm / r

20
Q

Gravitational Potential

A

Potential energy associated with a unit mass due to its position in the gravitational field of another body
V = -GM / r

21
Q

Total energy of a body in a gravitational field

A

E = KE + PE = 1/2 mv^2 + (-GMm / R)

22
Q

Escape Velocity

A

Minimum velocity with which a body must be projected vertically upwards in order that it may just escape the gravitational field of the earth

22
Q

Escape velocity formulas and derivations

A

v = root (2 GM / R) = root (2gR) = root (8pi ro G R^2 / 3)

23
Q

Escape velocity at a height h

A

ve = root (2g (re)^2 / (re + h))
re = rad. of earth

24
Q

Orbital Velocity

A

Velocity required to put the satelleite into its orbit around the earth

25
Q
A
26
Q

Derivation of orbital velocity and formulas

A

v = root (GM / R + h) = root (gR^2 / R + h) = R root (g / R + h)

27
Q

Relation between orbital and escape velocity

A

ve = (root 2) (vo)

28
Q

Derive time period and all for satellite

A

T = 2pi [Root (R + h)^3 / gR^2]

29
Q

Total energy of satellite

A

E = GMm / 2r {-Gmm / r + 1/2 Gmm / r}

30
Q

Binding energy of a satellite

A

Gmm / 2r {energy required by a satellite to leave its orbit around the earth and escape to infinity}

31
Q

Kepler’s Laws of Motion

A
  1. dL / dt = 0 (L is constant)
  2. Delta A / Delta T = constant
  3. T1^2 / T2^2 = R1^3 / R2^3