Gravitation Flashcards
Force between two masses
F = G m₁ m₂/ r²
Properties of gravitational force
- always attractive
- independent of medium
- conservative force
- works over wide range
Acceleration due to gravity
g = GM/R²
M- mass of earth
R - radius of earth
Value of G (gravitational constant)
G = 6.67 × 10-¹¹
Dimensional formula of G
M-¹ L³ T-²
Acceleration due to gravity at height h above the surface of earth
- g’ = g/(1 +h/R)²
If h «R
- g’ = g (1 - 2h/R)
Acceleration due to gravity at a depth d below the surface of the earth
g’ = g(1 - d/R)
Gravitational intensity
- Intensity at a distance ‘r’ from point mass ‘M’
I = GM/r² - Intensity at a point on the surface of earth
I = GM/R² = g
Orbital velocity of a satellite
- V = √ (GM/r)
- V = √ [GM/ (R +h) ]
- V = √ [gR² / (R +h)]
Orbital velocity when orbit is close to earth
V = √ (GM/R)
V = √gR = 7.92 km/s
Time period of a satellite
T = 2π √ (r³/GM)
Time period of geostationary satellite
24 hours
Escape velocity
- V = √ (2GM/R)
- V = √ (2gR) = 11.2km/s
Energy of satellite
- P.E: -GMm/r
- K.E: GMm/2r
- TE: -GMm/2r
Gravitational potential energy
- Gravitational potential × mass of body
- U = -GMm/r
Escape velocity of moon
2.3 km/s
Weight of a body in free fall
Zero.
Because during free fall there is no reaction force on the body…. ‘g’ is utilised for acceleration
Angular momentum
L = mvR
m: mass
v: velocity
R: radius
For closed orbits what is always conserved?
Angular momentum
Time period and semi major axis relation
T² ∝ a³
Polar satellites are used for
Environmental studies
Percentage change in energy
(∆E/ Ei ) × 100
∆E: change in energy
Ei: initial energy
Total energy and potential energy
PE = 2 × TE
Total energy and kinetic energy
TE = - KE
