The expression e p = mgh applies only close to the surface of the earth. the general expression for the potential energy of a mass m at a distance r from the center of the earth (of mass m e ) is e p = − g m e m / r . write r = r e + h , where r e is the radius of the earth; show that, when h ≪ r e , this general expression reduces to the special case, and find an expression for g. you will need the expansion ( 1 + x ) − 1 = 1 − x + … .

g = G mE /Re^2

Explanation:

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First of all we need to find an equation where we can apply the series expansion of (1+x)^-1 where the variable x be a small number.

Since we are considering that  h<<Re  this implies that (h/Re)<<1 so this is the small number we are looking for.

Then in the equation for the earth's potential we can take of the earths radius as:

Now we can define x=h/Re and use the series expansion. Therefore:

Since x is a small number, x^2 will be even smaller, tehrefore we will only consider the first power of x:

and:

explanation:

earth's surface is mainly heated by the absorption of infrared radiation from the sun.

evaporation occurs because molecules in liquid water are warmed ( usually by the sun) and vibrate quicker, becoming less dense and rise.

condensation occurs because molecules in water vapor are cooled and therefore vibrate more slowly thus becoming more dense and eventually fall to earth.

lines of equal barometric pressure on a weather map are called: isobars : lines of equal temp on a weather map are called: isotherms.​

electromagnetic shielding is the practice of reducing the electromagnetic field in a space by blocking the field with barriers made of conductive or magnetic materials. shielding is typically applied to enclosures to isolate electrical devices from their surroundings, and to cables to isolate wires from the environment through which the cable runs. electromagnetic shielding that blocks radio frequency electromagnetic radiation is also known as rf shielding.

the shielding can reduce the coupling of radio waves, electromagnetic fields and electrostatic fields. a conductive enclosure used to block electrostatic fields is also known as a faraday cage. the amount of reduction depends very much upon the material used, its thickness, the size of the shielded volume and the frequency of the fields of interest and the size, shape and orientation of apertures in a shield to an incident electromagnetic

from wikipedia