# Notes on gravitational field for Cambridge A level and UTME

**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^{-2}m^{2}

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

Centripetal Acceleration

•For an orbiting satellite, the gravity provides centripetal force which keeps it in orbit

**Geostationary Orbits**

•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 r^{3} / T^{2} the radius of orbit needed for geostationary orbit can be calculated

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