Derive the concept of gravity.
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Answer:
Gravity, also called gravitation, is a force that exists among all material objects in the universe. For any two objects or particles having nonzero mass, the force of gravity tends to attract them toward each other. He also demonstrated mathematically that gravitational fields cause distortion in space and time.
Answer:
A knowledge of acceleration due to gravity enables us to determine the following three quantities, namely_
(i) Mass of the earth
(i) Mass of the earth(ii) Density of the earth
(i) Mass of the earth(ii) Density of the earth(iii) Mass of the sun
Now let's come to the point of derivation_
(i) Mass of the earth:
Mass 'M' of the earth can be calculated fro the equation (9) of universal gravitational constant (G).
Such that,
M = gR^2/g
since g = 9.8 m/s^2
R= 6.38*10^6
R= 6.38*10^6G= 6.67*10 ^11
∵ Metric system
M=9.8 * 10^6/6.67 * 10^-11
=> 5.98 * 10^-11
So, the mass of the earth is 5.98*10²⁴ kg.
(ii) Density of the earth:
If ' ρ' is the mean density of the earth then,
M= V * I
= 4/3) IGRP
Substituting for M in equation (9),
I = 3g/4IGRP
=>5497kg/mA^3
So, the density of the earth is 5497 kg/m³
(iii) Mass of the sun:
If 'm' be the mass of the sun, gravitational attraction between the sun, and the earth is_
Where 'r' is the radius of orbit around the sun and M is the mass of the earth. Centripital force 'Fc' required by the earth is_
Where, 'ω' is the angular velocity of the earth.
In equlibrium,
In equlibrium,Fc= Fg
In equlibrium,Fc= FgmrIa^2= GMm/rA^2
Where 'T' is the time period of rotation of earth around the sun.
Here,
r = 150 million km
r = 150 million km = 150*10 ⁶ km
r = 150 million km = 150*10 ⁶ kmor, r = 1.5*10⁸ km
r = 150 million km = 150*10 ⁶ kmor, r = 1.5*10⁸ km = 1.5*10¹¹ km
r = 150 million km = 150*10 ⁶ kmor, r = 1.5*10⁸ km = 1.5*10¹¹ kmG = 6.67*10⁻¹¹ M.K.S. units
r = 150 million km = 150*10 ⁶ kmor, r = 1.5*10⁸ km = 1.5*10¹¹ kmG = 6.67*10⁻¹¹ M.K.S. units = 365*24*60*60s
So, the mass of the sun is 2*10³⁰ kg.