GRAVITATION

Newton 's Law Gravitation

of
Acceleration due to gravity
Gravitational Field

Gravitational Potential

Gravitational Potential Energy

Law
Kepler 's

satellite

1- 2 Qts
 Newton 's Law of Gravitation
f- = Gm , ML

re
M , Mz
← r - F'is =
-
FI
-
"
G 6.67 X IO N
kg
=
-
m -

Gravitational constant

Properties of Gravitational force

•
Always attractive
•
Independent of medium between frarticles .

• It is a two
body interaction
-

ie gravitational
force between two particles is independent
other particles So
of presence on absence
of .
,

the principle
of superposition is valid .

conservative
.

force
• It is an action reaction pain .

•
Of two bodies are
uniform spheres ,
instead
separation
e '

of paint bodies : then

-

ee

be taken as distance between their

may
centres is
of uniform
because a
sphere
mass .
 Acceleration Due to
Gravity
GR
g
=

GF =

Este g
' '
value due to
of g vary
-

a) Earth
Shape of
b) Height above earth surface
c) Depth below earth surface
d) Arial rotation the earth
of .

Variation in due to Shape of Earth

g

.
R
equator > Rpole
Rp

re Ffp
=
LET gpoee >
gequator

Variation in
g with Height
Gm
g GM
-
-
'

g
=

RT @ they
h
N
if u R
g
's
g f
-

see

R
Absolute decrease
'

Dg
=

g
-

g
=
ZHI
R

% decrease 100%
DgI 2dg
= x
 Variation in g with Depth
( da )
'
'
g
-

t
g g
- -
-

d
R Tg At centre
of earth D= O
'

g
-

g
-

•
O

AGI
x 100% =

dy X 100%

Variation ing due to Rotation

Earth
of
I w

Rues'd
' '
w
y og
= -

a , °

• A =
go
my g pole g
-
-
-
w
'
Rues
'
90

gpole g =

• A = 00
-
Rcoszoo
geguatoee g
= -
w

WZR
g equator
=

g
-

g pole -

g equator = 0.034 MI5

•
Gravity (g) is independent of
size , shape ,
state
and Temperature of body .
 Gravitational Field
Gravitational Field
Intensity : I -
-

RI
m

• vector
Quantity
directed towards
•
Always the centre
of gravity of body
(Test Inert 12+12+13
M
) GI
=
r mass I = m, mz
z,
'
M W Y
(source body )
v
's

M3

A
P B zz +
Iz = O
m, n id
tgG.mg
n

Grader O
-

ma
-

d
n
-
-
Tm , d
@ -

a) = JMTD
Tm ,
+ Tmz FT Tmz
,
+

For
Different Bodies
••

that
goose §
book
a

toogood
spherical shell
uniform solid sphere uniform circular
Ring
I
-
GI At a
point
R on its axis

r
r -
- R r-
- R I = GMT

@ tr 2) 312

&↳%÷
GM/r2 GM/r2

Icentre = O
r LR GMr/R3 1=0 ( inside)
µ
 Gravitational Potential .

U
JI die I did
=
= -
.
-

dr

Scalar free
•

quantity -
work done unit mass

V = -
GM V = V, + the +
Vz +
- - -

GT Gtf Gmg
= -
-
-

MZ - - -

m, ee, na

•
M
Pees
Mii
V =

m,
r. -

G
MY i -

I
Mg
-

Bf9f.⑥ .
"

Haidian
v
,
l v
r

IR
'
point on anis o r o
-
r

u =
-GM_ art -
I
a2 + q2
R -

31M
ZR r -
- R

Mcentire
GMT Gmg GMG
-

=
V v
-

=
-
=

y > R

MIR
GNYR
V ↳
r= R v
- -
= =

AMIR V
Gama (3 fry)
-

re r v = =
-
-

solid sphere
IGF Z Vsusface
'

✓centre
of r
-
-
o =
-
=
-
 Gravitational Potential Energy
←
r
we = Gmm da
M
M
T s D

GMMR
'
w
[ In ]
-

↳ Mm =
w
-

D
This work done is stored inside

body as
gravitational potential energy .

U = -
G Mm .

scalar
quantity
•

Always negative in gravitational field because the

force is always attractive in nature .

• As ee increases ,
GPE becomes less -
ve .
ig increases
then GPE
Of O O
=
r
-
-
•
,

moved
•

Of body of mass m is
from distance us to
Nz ,
then
change in
potential energy :

(÷ rt )
Du = GMM -

U = MV (Relation
Potential
Between GPE and
)
Mcentire mvcentne Un -GMM_
eight
= =

R the
( EGF )
7+8R÷EF!Y)
auntie m
-
- -

=
Kepler 's laws
of Planetary Motion
Law ORBITS
Every planet moves around seen
of in elliptical orbit with
an

sun at
of foci one .

Law AREA Areal velocity is constant

of .

daft =Ir¥dt) Ine

-

today volt daff =

Im
Sun

momentum
L :
Angular
Law
of PERIODS
square of period of
revolution (t)
of any
-

planet around sun is

directly proportional to
semi orbit
cube
of major axis
of .

T2 2 a3

E
Perigee Sun f Apogee speeds of planet
←a →
. At
apogee =

Gnat :-#
D

At
perigee GF 1¥
.
=
SATELLITE .

Escape velocity
-

Satellite minimum
velocity with which or

y body must be
projected up so

enable
he
as to it to
just overcome
the
gravitational pull .

R
26M£
ve R
2g
=
=

Orbital velocity
velocity required to put the
satellite into its orbit
around earth .

Uo GM
gR
= =

R
"

Time Period satellite

of
Time taken
by satellite to
go once around earth .

I
circumference the orbit
of
=

orbital
velocity
h3
-

2A÷
i

T =
=
2A

GM

72 =
YAL r 3
GM

GEOSTATIONARY SATELLITE
• Satellite whose
period of revolution around
the earth should be same that earth
as
of
about its own ants -

T -
-
zyhr =
86400 s
ANGULAR MOMENTUM OF SATELLITE
( = mute .
Depends on both the mass
of
= m
Gtf xr
orbiting
well
and central
radius
body
orbit
as as
of .

( = m2 Gmr

ENERGY OF SATELLITE
Potential
Energy -1
( u) argue
-
= =

My 2

KE
kinetic
Energy
①
§ TE
ee
Ck) =
GEIR =
÷p
PE
Total
Energy Ut k
(TE) =

GMMZR
-
=

satellite
Binding Energy of
The to
energy required remove the satellite

from its orbit to

infinity .

BE = -

E =
GMMZR
PREVIOUS YRS Impe .