Gravitational Field Flashcards

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1
Q

State Newton’s Law of Gravitation and the formula from this law.

A

Newton’s Law of Gravitation states that the gravitational force between two point masses is proportional to product of their masses and inversely proportional to square of separation/distance between them.
F = GMm/r^2

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2
Q

Define gravitational field.

A

A gravitational field is a region of space where a mass experiences a gravitational force.

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3
Q

Define gravitational field strength and its formula.

A

Gravitational field strength at a point is the gravitational force exerted per unit mass placed at that point.
g = GM/r^2

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4
Q

Define gravitational potential Φ and its formula.

A

Gravitational potential at a point in a gravitational field is defined as the work done per unit mass by an external agent in bringing a small test mass from infinity to the point without any change in kinetic energy.
Φ = -GM/r

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5
Q

Why is gravitational potential and gravitational potential energy negative?

A

Direction is taken from the direction of gravitational force exerted. Thus, work done to bring a small test mass to infinity is in the opposite direction to the gravitational force, and thus it is negative.

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6
Q

Define gravitational potential energy and its formula.

A

Gravitational potential at a point in a gravitational field is defined as the work done by an external agent in bringing a small test mass from infinity to the point without any change in kinetic energy.
U = -GMm/r

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7
Q

Using Newton’s Law of gravitation and the definition of gravitational field strength, derive the equation g = GM/r^2

A

g = Gravitational Force/Mass
= F/M
= GMm/r^2 ÷ m
= GM/r^2

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8
Q

Define an object’s escape velocity, and using the Principle of Conservation of Energy, derive its formula as v = √2gr.

A

The escape velocity of a body is the minimum velocity required such that said body is able to travel to infinity away from a planetary mass.
Ki + Ui = Kf + Uf
½mv^2 + (-GMm/r) = 0 (taking final point as infinity)
v = √2GM/r = √2gr (g = GM/r^2)

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9
Q

What are the features of a geostationary satellite?

A

A geostationary satellite is in geostationary orbit and maintains the same position relative to a point on a planet’s surface.

• Orbital period is same as the planet’s rotation period
(24 hours for Earth)
• Plane of orbit is the same as the planet’s equator
• Direction of orbit is same as the planet’s direction
of rotation (eastward for Earth)

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