Notes on gravitational field for Cambridge A level and UTME
According to Newton, all masses create a gravitational field in the space round them. The field give rise to a force on any object having mass placed in this field. The moon orbits the earth because it experiences a gravitational force due to the earth’s gravitational field. If an object is placed in a gravitational field, a force will act on the object because of its mass.
What is meant gravitational field?
A region where a mass/body experiences a force of attraction due its mass.
The Earth has a radial field of gravity, which means that the gravitational field is circular and acts from the center point.
The Earths radial gravitational field is represented by the lines
- The arrows on the field lines show the direction of the gravitational force on a mass placed in the field
- The spacing of the field lines indicates the strenght of the gravitational field-the farther apart they are, the weaker the field
Gravitational field strenght
Gravitational field strenght at a point is the gravitational force exerted per unit mass on a small object placed at that point.
g = f/m
g = gravitation field strength
m = test mass
units = N kg-1 = ms-2
Newton’s law of universal gravitation: it states that any two point masses attract each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of their separation
G is the gravitational constant 6.67 x 10-7 Nkg-2m2
since f= GMm/r2
g =f/m = GMm/mr2 = GM/r2 (This equation does not depend upon the mass of the small object )
g is the gravitational field strenght
Gravitational potential energy: at a point is the work done in bringing a mass from infinity to a point
gravitational potential is always negative: because of the force of attraction that exist between two masses
- Zero of potential energy is at infinity
- Potential energy taken as a negative value
- The work done in moving a mass between two points in a gravitational field is independent of the path taken
•For an orbiting satellite, the gravity provides centripetal force which keeps it in orbit
•Geostationary satellite is one which is always above a certain point on the Earth
•For a geostationary orbit: T = 24 hrs. and orbital radius is
a fixed value from the center of the Earth
By using r3 / T2 the radius of orbit needed for geostationary orbit can be calculated
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