Here, M_e = 6 x 10²⁴ kg. M_s = 2 x 10³⁰, r = 1.5 x 10¹¹ m
\(F=G\frac { { m }_{ e }{ m }_{ s } }{ { r }^{ 2 } } \) = \(\frac { 6.67\times { 10 }^{ -11 }\times 6\times { 10 }^{ 24 }\times 6\times { 10 }^{ 30 } }{ { \left( 1.5\times { 10 }^{ 11 } \right) }^{ 2 } } N\)
 \(\frac { 6.67\times 12\times { 10 }^{ 21 } }{ 1.5\times 1.5 } =3.56\times { 10 }^{ 22 }N\) 

Force, F =80 kg f =80 x 9.8 N
(i) When the man is lying on the ground, A = 0.6 m²
\(P=\frac { F }{ A } =\frac { 80\times 9.8 }{ 0.6 } =1.307\times { 10 }^{ 3 }N/{ m }^{ 2 }\)
(ii) When the main is standing on his feet,
\(A=2\times 80{ cm }^{ 2 }=160\times { 10 }^{ -4 }{ m }^{ 2 }\) 
\(\\ P=\frac { F }{ A } =\frac { 80\times 9.8 }{ 160\times { 10 }^{ -4 } } =4.9\times { 10 }^{ 4 }N/{ m }^{ 2 }\) 

For the moon: M_m=7.3x10²²kg, R_m=1740 km
Acceleration produced on moon,\(g=\frac { { GM }_{ m } }{ { R }^{ 2 } } \)

\(\therefore \frac { a }{ g } =\frac { { GM }_{ m }/{ R }_{ m }^{ 2 } }{ GM/{ R }^{ 2 } } =\frac { { M }_{ m } }{ M } .\frac { { R }^{ 2 } }{ { R }_{ m }^{ 2 } } \) 
\(=\frac { 7.3\times { 10 }^{ 22 }kg }{ 6\times { 10 }^{ 24 }kg } \times \frac { { (6400km) }^{ 2 } }{ { \left( 1740km \right) }^{ 2 } }\) 
\( \\ =0.16\)
\(g=9.82\quad m/{ s }^{ 2 }\) 
\(\therefore a=0.16\times g=0.16\times 9.82=1.578m/{ s }^{ 2 }\) 

Here,
\(M=1.99\times { 10 }^{ -11 }\quad kg,\quad m=1.9\times { 10 }^{ 27 }kg,\quad r=7.8\times { 10 }^{ 11 }m\) 
\(G=6.67\times { 10 }^{ -11 }\quad { Nm }/{ kg }^{ 2 }\) 
\(F=\frac { GMm }{ { r }^{ 2 } } =\frac { 6.67\times { 10 }^{ -11 }\times 1.99\times { 10 }^{ 30 }\times 1.9\times { 10 }^{ 27 } }{ { \left( 7.8\times { 10 }^{ 11 } \right) }^{ 2 } }\) 
\(=4.145\times { 10 }^{ 23 }\quad N.\) 

Importance of the universal law of gravitation. The universal law of gravitation successfully explained many phenomena occurring in nature. Some of these phenomena are as follows:
1. The force that binds us to the earth.
2. The motion of the moon around the earth.
3. The motion of planets around the sun.
4. The tides due to the moon.

Gravitation. Everybody in this universe attracts every other body with a force known as 'force of gravitation'. Gravitation is the force of attraction between any two bodies in the universe. The attraction between the sun the earth, the attraction between a table and a chair lying in a room, the attraction between the earth and a satellite revolving around it etc.; are all examples of gravitation.
Gravity. Gravity is a special case of gravitation. Gravity is the attraction between the earth and any object lying on or near its surface. A body thrown up falls bask on the surface of the earth due to earth's force of gravity.

Time ascent = Time of descent = 2/6 = 3 sec
(a) For upward motion of the ball, 
v = 0, t = 3s, g = -9.8 ms^-2
As, v = u + gt
0 = u - 9.8 x 3
or u = 9.8 x 3 = 29.
(b) The hight, s = ut + 1/2 gt²
= 29.4 x 3 - 1/9 x 9.8 x 3²
= 88.2 - 44.1 = 44.1 m.
(c) the position of the ball after 4 s is given by
s = ut + 1/2 gt²  
= 29.4 x 4 - 1/2 x 9.8 x 4² = 117.6 - 78.4 = 39.2 m 
The ball is at a height of 39.2 from the ground or 4.9 m from the top.

(a) The centripetal force required for the revolution of a planet around the sun is provided by force of gravitation between the planet and the sun. This depends on the masses of planet and the sun: and also the distance between their centres.
(b) If centripetal force suddenly becomes zero, planet will begin to move in the direction of tangent of its orbital path if no other celestial body affects it.

Force of gravitation, F = \(F'=G\frac { { m }_{ 1 }{ m }_{ 2 } }{ { r }^{ 2 } } \)
(i) When mass of one body (m1 or m2) is doubled, the force gets doubled.
\(F'=G\frac { { (2m }_{ 1 }){ m }_{ 2 } }{ { r }^{ 2 } } =2G\frac { { m }_{ 1 }{ m }_{ 2 } }{ { r }^{ 2 } } =2F\)
(ii) when the distance between the bodies is doubled, 
\(F'=G\frac { { m }_{ 1 }{ m }_{ 2 } }{ (2{ r }^{ 2 }) } =\frac { 1 }{ 4 } G\frac { { m }_{ 1 }{ m }_{ 2 } }{ { r }^{ 2 } } \frac { 1 }{ 4 } F\)i.e. the force becomes one-fourth of the original force.
(iii) When the masses of both bodies are doubled,
\(F'=G\frac { { (2m }_{ 1 }){ (2m }_{ 2 }) }{ { r }^{ 2 } } =4G\frac { { m }_{ 1 }{ m }_{ 2 } }{ { r }^{ 2 } } =4F\)
i.e., the force becomes four times the original force.
(iii) When the distance between the two bodies is tripled,
\(F'=G\frac { { m }_{ 1 }{ m }_{ 2 } }{ (3{ r }^{ 2 }) } =\frac { 1 }{ 9 } G\frac { { m }_{ 1 }{ m }_{ 2 } }{ { r }^{ 2 } } \frac { 1 }{ 9 } F\)
i.e., the force becomes one-ninth of the originals force.