gravitation
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1
Force of gravity
F=G(m1m2^2)
2
value of G only value (in SI unit)
6.67*10^-11(inSI unit), 6.67*10^-8 (inCGS)
3
a mass M is split into and seperate by certain distance the gravitational force is maximum when the mass of two bodies split in ratio of
M/2
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gravitational force vector form
F=G(m1m2^2) (vector(r)/magnitude of (r))
5
superposition principle
Fnet=F12+F13+...+F1n (vector addition)
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Fnet and Fnet if F1=F2
Fnet=√(F1^2+F2^2+2F1F2), 2Fcos(theta/2)
7
acceleration due to gravity at the surface of earth
g=GM/R^2,g=(4π/3)*(GRp) M=6*10^24 kg R=6.4*10^6 m g=9.81m/s^2 =32ft/s^2
8
variation in g due to height
g'=R^2/(R+h)^2 (if h<<R upto 5% of R then g'=g(1-2h/R)
9
variation in g due to depth
g'=R-d/R or g'=g(1-d/R) at centre g'=0
10
variation in g due to rotation of Earth w is omega lamda is angle
g'=g-w^2 Rcos^2(lamda)
11
intensity of gravitationl field
E= GM^2
12
gravitationl field due to hollow or spherical shell
E at centre=zero E at surface=GM/R^2 E at outside where x>R E=GM/x^2
13
gravitationl field due to solid sphere (uniform mass density)
E at surface =GM/R^2 E at outside=GM/x^2 E at inside =GMx/R^3 E is zero at infinite distance and at centre of solid sphere
14
gravitationl potential
V=W/m° =-GM
15
potential due to N point masses
V=-G(m11+m22+....mnn)
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gravitational potential due to spolid sphere
Vout=-GM , Vsurface=-GM/R , Vinside=-(GM/2R^3 )*(3R^2-r^2). Vcenter=-(3/2)GM/R or 3/2 *Vsurface
17
gravitational potential energy
U=-GMm°
18
work done from 2 to 1 is
W=-(U2-U1)
19
work done in moving object from surface of earth to height H above surface
∆U=-GMmh/(R+h)R or ∆U=mghR/(R+h) if h<<R ∆U=mgh
20
work done to move object to a height h=R ,h=2R
W=mgR/2 , W=2/3(mgR)
21
escape velocity
v=√(2GM/R) =√(2gR= √2 v° where v° is orbital velocity( for closer orbits v = 8√2 km/s), v=√(8/3(πGpR^2)
22
escape velocity from a height h
v=√(2GM/R+h) = √(2g'(R+h))
23
orbital velocity of satellite v°
v°=√(GM)=√(GM/R+h). =√(gR^2/R+h) if h<<R then v°=√(GM/R)=√gR for easy calculation √gR =8km/s
24
K.E of satellite, P.E of satellite, total mechanical energy
K.E=GMm/2r ,P.E= -GMm Total energy= -GMm/2r
25
binding energy
1/2mv°^2=GMm/2r=L^2/2mr^2
26
work done in moving object from one orbital to another
W=E2-E1= (GMm/2)*((11)-(12))
27
work done in moving object from surface to circular orbit
W=Etotal-Ei=-GMm/2(R+h) + (-GMm/R)
28
laws of area formula
∆A/∆t =L/2m =constant
29
perihelion and aphelion are which points
perihelion(shortest point ) aphelion(farthest point)
30
laws of periods equation
T^2 proportional to a^3 or T^2 proportional to r^3 or T^2=4π^2 r^3/GM (here M is mass of sun)
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