considering the earth as a homogeneous sphere of radius R=6.41×10^3 and the value of g=9.8ms^-2 on the surface of the earth. find the mass of the earth.
Answers
Step-by-step explanation:
The Apple, the Moon, and the Inverse Square Law
Newton's Law of Universal Gravitation
Cavendish and the Value of G
The Value of g
In Unit 2 of The Physics Classroom, an equation was given for determining the force of gravity (Fgrav) with which an object of mass m was attracted to the earth
Fgrav = m*g
Now in this unit, a second equation has been introduced for calculating the force of gravity with which an object is attracted to the earth.
where d represents the distance from the center of the object to the center of the earth.
In the first equation above, g is referred to as the acceleration of gravity. Its value is 9.8 m/s2 on Earth. That is to say, the acceleration of gravity on the surface of the earth at sea level is 9.8 m/s2. When discussing the acceleration of gravity, it was mentioned that the value of g is dependent upon location. There are slight variations in the value of g about earth's surface. These variations result from the varying density of the geologic structures below each specific surface location. They also result from the fact that the earth is not truly spherical; the earth's surface is further from its center at the equator than it is at the poles. This would result in larger g values at the poles. As one proceeds further from earth's surface - say into a location of orbit about the earth - the value of g changes still.
The Value of g Depends on Location
To understand why the value of g is so location dependent, we will use the two equations above to derive an equation for the value of g. First, both expressions for the force of gravity are set equal to each other.
Now observe that the mass of the object - m - is present on both sides of the equal sign. Thus, m can be canceled from the equation. This leaves us with an equation for the acceleration of gravity.
The above equation demonstrates that the acceleration of gravity is dependent upon the mass of the earth (approx. 5.98x1024 kg) and the distance (d) that an object is from the center of the earth. If the value 6.38x106 m (a typical earth radius value) is used for the distance from Earth's center, then g will be calculated to be 9.8 m/s2. And of course, the value of g will change as an object is moved further from Earth's center. For instance, if an object were moved to a location that is two earth-radii from the center of the earth - that is, two times 6.38x106 m - then a significantly different value of g will be found. As shown below, at twice the distance from the center of the earth, the value of g becomes 2.45 m/s2