GRAVITATION Flashcards
G EQUALS
6.67 * 10^ -11
g EQUALS
GM/R^2 = 9.8
RADIUS OF EARTH
6400 KM
MASS OF EARTH
5.98 *10^ 24 Kg
g AT A HEIGHT H
GM/(R+H)^2 OR g(1- 2h/R) IF H«<R
g AT A DEPTH D
g(1- D/R)
VARIATION OF g WITH LATITUDE @ WHERE ANGULAR VELOCITY IS #
g(@) =g - r#^2 COS^2@
VARIATION OF g WITH SHAPE
gP > gE
GRAVITATIONAL INTENSITY
GM/R^2 (-r^)
I AND G RELATION AT A POINT
NUMERICALLY EQUAL
INTENSITY DUE A SOLID SPHERE OUTSIDE (r>R)
GM/r^2
INTENSITY DUE TO A SOLID SPHERE AT THE SURFACE (r=R)
GM/R^2
INTENSITY DUE TO A SOLID SPHERE INSIDE (r<R)
GMr/R^3 i.e I PROP TO r
INTENSITY DUE TO A SHELL OUTISIDE (r>R)
GM/r^2
INTENSITY DUE TO A SHELL AT THE SURFACE (r=R)
GM/R^2
INTENSITY DUE TO A SHELL INSIDE (r<R)
0
SUM OF AN INFINITE GP
a/1-r
UNIT OF INTENSITY
N/Kg
UNIT OF GRAVITATIONAL POTENTIAL
J/Kg scalar
V EQUALS
-GM/r AS r INCREASE V INCREASES
POTENTIAL DUE TO A SOLID SPHERE OUTSIDE (r> R)
-GM/r
POTENTIAL DUE TO A SOLID SPHERE AT THE SURFACE(r=R)
-GM/R
POTENTIAL DUE TO A SOLID SPHERE INSIDE (r<R)
-GM/2R^3 * (3R^2- r^2)
POTENTIAL DUE TO A SOLID SPHERE AT THE CENTER (r=0)
3/2 V AT SURFACE
POTENTIAL DUE TO SHELL OUTSIDE (r>R)
-GM/r
POTENTIAL DUE TO A SHELL AT THE SURFACE(r=R)
-GM/R
POTENTIAL DUE TO A SHELL INSIDE (r<R)
-GM/R
GRAVITATIONAL POTENTIAL ENERGY U
mV
U OF A SYSTEM IS
WORK DONE TO ESTABLISH THE SYSTEM
NO OF PAIRS FOR N PARTICLE SYSTEM
N(N-1)/2
WORK DONE IN TERMS OF POTENTIAL ENERGY
Uf-UI
WORK DONE TO LIFT A BODY TO HEIGHT H FROM SURFACE
mgRH/(R+H)
TOTAL ENERGY NEGATIVE MEANS
IT IS BEING ATTRACTED
ESCAPE VELOCITY
SQRT(2GM/R) OR SQRT (2gR)
ESCAPE VELOCITY FOR EARTH
11.2 KM/S
ESCAPE VELOCITY FOR MOON
2.3 KM/S
VELOCITY OF BODY AT INFINITY IF IT IS PROJECTED WITH AN INITIAL VELOCITY V
SQRT(V^2 - Ve^2)
VELOCITY OF BODY AT INFINITY IF IT IS PROJECTED WITH AN INITIAL VELOCITY V
SQRT(V^2 - Ve^2)
ORBITAL VELOCITY
Sqrt (GM/(R+h))
FIRST COSMIC VELOCITY
Sqrt(GM/R)= 1/√2 Ve
SECOND COSMIC VELOCITY
ESCAPE VELOCITY
TIME PERIOD OF A SATELLITE
2π√(R+h)³/√GM
T⁰
2π√R/√g~85 mins
TIME PERIOD AND ORBITAL VELOCITY IS INDEPENDENT OF
MASS OF SATELLITE
KINETIC ENERGY OF SATELLITE
GMm/2(R+h)
POTENTIAL ENERGY OF SATELLITE
-GMm/(R+h)
REALTION BETWEEN TOTAL ENERGY, PE AND KE
TE =-KE=PE/2
BINDING ENERGY
KINETIC ENERGY
VELOCITY OF SATELLITE AT THE MOMENT OF ESCAPE
SQRT(2) V
TORQUE OF PLANET DUE TO GRAVITY OF SUN
o
dA/dt
L/2m constant
L WRT LINEAR VELOCITY
mvrsin@
Vmax/Vmin = rmax/rmin =
1+e/1-e
RELATIVE VELOCITY OF APPROACH OF TWO PARTICLES AT INFINITY AT REST
SQRT(2G(M1+M2)/r)
RELATION B/W I AND V
I= -dV/dr
POTENTIAL DUE TO A RING AT AN AXIAL POINT
-GM/sqrt(R^2 + X^2)
FIELD DUE TO A RING AT AN AXIAL POINT
-GMX/(R^2 + X^2)^3/2
GRAVITATIONAL FLUX
-4PI G M
ESCAPE VELOCITY FROM A BLACK HOLE
c
