Gravitational Fields Flashcards

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1
Q

What is a Gravitational Field?

A

A region in which a mass, experiences an attractive non-contact force.

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2
Q

What is gravitational Potential?

A

The amount of work done per unit mass, to move an object from infinitely far away to that point (r).

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3
Q

What is Newton’s law of Gravitation?

A

The force of gravity is proportional to the product of the masses involved and inversely proportional to the square of the separation of the masses.

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4
Q

What is Gravitational Field strength defined as?

A

g = F/m, where F is the gravitational force and m is the mass of the object.

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5
Q

What equation is used to find the acceleration due to gravity?

A

g=GM/r², where G is the gravitational constant, M is the mass of a planet and r is the radius of the planet.

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6
Q

What is the equation for the force of gravity in Newton’s law of Gravitation?

A

F = GMm/r², where ‘M’ is the mass of the planet and ‘m’ is the mass of the object.

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7
Q

Derive ρ

A

ρ = M/V (V = 4/3πr³)
ρ = 3M/4πr³
M = ρ4πr³/3 (g = GM/r²)
g = Gρ4πr³/3r²
g = Gρ4πr/3

g = Kr (K is some constant)
∴ g ∝ r

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8
Q

What is the equation for gravitational potential at a distance ‘r’ from a planet or mass?

A

V = -GM/r

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9
Q

What is the equation for gravitational potential in a radial field?

A

Ep = GMm/r

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10
Q

What does the gradient for a ‘V’ (J/kg) over ‘r’ (m) graph give?

A

g, where g = -Gm/r²

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11
Q

What is an equipotential?

A

A surface of constant gravitational potential, that is perpendicular to the radial field lines.

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12
Q

What is a satellite?

A

Any smaller mass in the orbit of a bigger one.

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13
Q

What are the three laws of planetary motion?

A
  1. The orbit of every planet is an ellipse (meaning circular motion laws still apply)
  2. A planet sweeps out of the same area between equal time intervals
    3.T² ∝ r³
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14
Q

Derive orbital velocity ‘V’

A

Fc = Fg (Centripetal force = Gravitational force)
MV² /r = GMm/r²
V² = GMm/Mr
V² = Gm/r
V = √Gm/r

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