Centripetal acceleration

A formula for the NET gravitational acceleration of masses rotating with the earth surface is given by:

net gravitational acceleration = gravitational acceleration exerted by the earth on the mass - centripetal acceleration.

Can someone explain the reasoning of this equation please:) thanks :)

As quoted: "For a satellite in orbit around a planet, the centripetal force is supplied by gravity"

Change your sentence as

The centripetal force IS the gravitational force.

The object is pulled toward the center of earth by this gravitational force.

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The important point to note is that the direction of the speed of the satellite.

1.
If the satellite has no speed, then it will fall down toward the earth (due to the pull of the gravity.
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2. If it has a speed and directed toward the center of earth (i.e along the radius) again it will fall toward the center of earth (due to the pull of the gravity).

2. If it has a speed and directed up (i.e. along the radius) away from the center

and its speed is less than the escape speed for that height ) after going up certain height it will fall toward the center of earth ( due to the pull of the gravity).

3.
If it has speed and directed perpendicular to the direction of the radius of earth at that point , then it cannot go up and it cannot come down toward the center , It has to follow a circular path around the earth , ( however ) this is because earth is pulling it toward it .

Any force which is perpendicular to the speed is called centripetal force or normal force .

Here the normal force is the gravitational force.

Note that there are no two forces.

The only force is the gravitational force which is otherwise called centripetal force .

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The answer to your other part: