Gravitational Field Flashcards
State Newton’s Law of Gravitation and the formula from this law.
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
Define gravitational field.
A gravitational field is a region of space where a mass experiences a gravitational force.
Define gravitational field strength and its formula.
Gravitational field strength at a point is the gravitational force exerted per unit mass placed at that point.
g = GM/r^2
Define gravitational potential Φ and its formula.
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
Why is gravitational potential and gravitational potential energy negative?
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.
Define gravitational potential energy and its formula.
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
Using Newton’s Law of gravitation and the definition of gravitational field strength, derive the equation g = GM/r^2
g = Gravitational Force/Mass
= F/M
= GMm/r^2 ÷ m
= GM/r^2
Define an object’s escape velocity, and using the Principle of Conservation of Energy, derive its formula as v = √2gr.
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)
What are the features of a geostationary satellite?
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)