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Flashcards in Gravitation. Deck (24):
1

What is the formula of acceleration due to gravity on the surface of the earth ?

g= GM/R^

2

What is the formula of acceleration due to gravity at a height h from the surface of the earth ?

g'= g( 1 - 2h/R) if h

3

What is the acceleration due to gravity from the surface of the earth ?

g'= g(1-d/R); if d = R, then g' = 0

4

What is the formula for effect of rotation of earth at latitude ?

g'= g-Rω²cos² δ
At equator ,
δ=0, g'=g-Rω= minimum value.
At poles,
δ= 90, cos 90=0, there g'= max value.
At pole effect of rotation of earth is zero and g is maximum.

5

What is the gravitational field strength at a point in a gravitational field ?

E= F/m= Gravitational force per unit area.

6

What is the gravitational field strength due to a point mass ?

E= GM/r^
E~1/r^

7

What is the gravitational field strengths due to a solid sphere ?

Inside points ie at centre
E= (GM/R³) r
At outside points
E₀=GM/r²
On the surface , E-r graph is continuous.

8

What is the gravitational field strength due to a spherical shell?

Inside points
E(i)=0
Outside points
E₀=GM/r²
Just outside the surface
E=GM/R^
On the surface ,E-r graph is discontinuous.

9

What is gravitational potential?

Gravitational potential at a point in a gravitational field is the negative of work done by gravitational force in moving a unit mass from infinity to that point.

10

What is the gravitational potential to point mass ?

V=-GM/r

11

What is the gravitational potential due to a solid sphere ?

Inside points:
V(i) = -GM÷R³(1.5R²−0.5r²)
On surface, V=-GM/R
At centre, V=-1.5GM/R
V-r graph is parabolic for inside points and potential at centre is 1.5times potential at surface.
Outside points:
V=-GM/r

12

What is the gravitational potential due to a spherical shell?

Inside points:
V(i)= -GM/R= constant
Outside points:
V=-GM/r

13

What is the gravitational potential on the axis of the ring ?

V=−GM÷√R²+x²

14

What is really gravitational potential energy for two point masses?

U=-Gm₁m₂÷r

15

Why is the relation between field strength E and potential V if V is a function of only one variable (say r)?

E=-dV/dr=- slope of V-r graph

16

What is the formula of escape velocity form the surface of the earth ?

V(e)= √2gR = √2GM/R~ 11.2 km/s
It does not depend upon the angle at which particle is projected from the earth.

17

Formula of orbital speed Vo?

v₀=√GM/r

18

For motion of satellites , formula of kinetic energy k?

K= GMm/2r

19

For motion of satellites, formula of potential energy U?

U=-GMm/r

20

For motion of satellites , formula for total mechanical energy ?

E=-GMm/2r

21

What is the minimum time period of any earth satellite ?

84.6 min

22

What is Kepler' first law?

Kepler's first law states that each planet moves in an elliptical orbit, with the sun at one focus of the ellipse.

23

What is Kepler's second law ?

Kepler's second law states that the radius vector , drawn from sun to planet, sweeps out equal areas in equal time interval ie areal velocity is constant. This law is derived from the law of conservation of angular momentum.
dA/dt= L/2m= constant.

24

What is Kepler's third law ?

T² is directly proportional to r³ where r is a semi major axis of elliptical path.