Gravitation Flashcards
Acceleration due to gravity
g= (GM)/R^2
R-radius of Earth
M-mass of Earth
Variation of ‘g’ with height
g’ = g/[(1+h/R)^2]
h
Variation of ‘g’ with depth
g’ = g*(1-h/R)
Variation of ‘g’ due to rotation of Earth
g’ = g - R(wcos@)^2
@-latitude
g at poles
g
g at equator
g - R*w^2
Orbital Speed
vo = (GM/a) ^0.5
a= R+h
Time period of satellite
T= [(4||^2a^3)/GM]^0.5
Angular momentum of satellite
(m^2GM*a)^0.5
Total energy of satellite
TE= -GMm/2a
Binding Energy
BE = GMm/2a = -TE
Escape velocity
ve >= (2gR)^ 0.5
ve >= (2GM/R) ^0.5
Relationship between escape velocity and orbital speed
ve >= (2^0.5) * vo
Escape velocity at earths surface
11.6 km/s
Gravitational field due to point mass
Eg = -GM/r^2 *er
Gravitational field at axial point of circular ring
Eg = GMx/[(a^2+x^2)^3/2]
Gravitational field at an axial point of circular disc
[2GM*(1-cos@)]/a^2
Gravitational field inside a uniform spherical shell
0
Gravitational field at a distance ‘r’ from a uniform spherical shell
GM/r^2
Gravitational field inside a uniform spherical sphere
GMx/r^3
Gravitational field at a distance ‘x’ from a uniform spherical sphere
GM/x^2
Graph for gravitational field of uniform solid sphere
/|(
/ | (
/ | (
X axis- distance r
Y axis- gravitational field
Gravitational potential of point mass
-GM/r
Gravitational potential at axial point of uniform ring
-GM/(r^2+x^2)^0.5
Gravitational potential Inside a uniform shell
-GM/r
Equipotential surface
Gravitational potential outside uniform shell at a distance R
-GM/R
Gravitational potential inside uniform solid sphere
-[GM(3r^2 - x^2)]/(2r^3)
Gravitational potential outside uniform solid sphere
-GM/r
