Physics - Topic 13 ( Gravitational Field )

(Gravitational Fields)

Gravitational Field

Is force per unit mass

Described by gravitational field lines

Higher density of lines = a region of stronger field

Point mass for a point outside a uniform sphere

The gravitational field behaves as if all the mass were concentrated at a single point at the center of the sphere

Newton’s Law of Gravitation

States that every mass attracts every other mass with a force proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

F = GMm/r2, where G is the gravitational constant

Centripetal acceleration for orbiting satellite

V2= GM/r, where V is the orbital speed and r is the radius of the orbit. 

Velocity is independent of mass and depends on the radius of the orbit.

Orbiting Period

Geostationary Orbit

Remains above a certain point on the Earth and is always there only

Time period = 24 hrs

Orbital radius is a fixed value from the center of the Earth, orbiting from West to East 

Directly above the Equator

Gravitational Field Strength

Is the gravitational pull of an object due to the mass of the object in its field

Equate W = mg to Newton’s Law of Gravitation      

mg = GMm / r2 
g = GM / r2

Gravitational Potential

At a point is work done per unit mass in bringing a unit test mass from infinity to a point

Gravitational Potential = -GM/r 

Reasons why the gravitational potential is negative

Force is always attractive

It increases from 0 to infinity

It decreases in the direction of field

Gravitational Potential Energy

Of a mass at a point in the gravitational field of another mass is work done in bringing that unit mass from infinity to that point

u= -GMm/r