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A Avinash Dongre
A state in which we cannot feel the effect of gravity is called weightlessness.

A Avinash Dongre
Using time period of geostationary satellite as T= 24 hours or 86400 sec.     We get the height of geostationary satellite from the surface of the earth       as h = 6R = 36000 km

A Avinash Dongre
The time period of the satellite is given by  If the satellite is very close to the earth’s surface,    i.e., h<<<R     then                  or

A Avinash Dongre
As we know Escape velocity is given by    and Orbital velocity  is given by  So we get Relation of escape velocity and orbital velocity as

A Avinash Dongre
For the below figure If Eccentricity is given by  (e) =  Then the velocity of the planet at Apogee and Perigee in terms of Eccentricity is given by  The velocity of the planet at apogee =The velocity of the planet at apogee

A Avinash Dongre
If a planet orbiting around the sun, then what is the Velocity of a Planet at Apogee and Perigee ???   For the below figure If Eccentricity is given by  (e) =  Then the velocity of the planet at Apogee and Perigee in terms of Eccentricity is given by   Where  The velocity of the planet at apogee

A Avinash Dongre
For the below figure If Eccentricity is given by  (e) =  Then the velocity of the planet at Apogee and Perigee in terms of Eccentricity is given by  The velocity of the planet at apogee

A Avinash Dongre
Escape velocity is defined as the minimum velocity an object must have in order to escape from the earth's gravitational pull. For earth value of escape velocity  is given as   .

A Avinash Dongre
If For an eclipse  semi major Axis and b=semi minor Axis Then Area of the eclipse is given by

A Avinash Dongre
If the body of mass m is moved from the surface of the earth to a point at height h from the earth's surface. And if  'h' is not negligible then  Work done Against Gravity in this process is given by    Where R=radius of earth

A Avinash Dongre
Gravitational field and potential are related as Where E is Gravitational field And V is Gravitational potential And r is the position vector

A Avinash Dongre
if a body of mass m is moved from   to  Then Change of potential energy is given as   If  then the change in potential energy of the body will be negative. So potential energy of a body will decrease if we bring that body closer to the earth.

A Avinash Dongre
As shown in the below figure If Gravitational Potential due to uniform solid sphere= V Then  For Inside surface  I.e  for             Radius of shell  Position of Pt.  Mass of Solid sphere

A Avinash Dongre
As shown in the below figure If Gravitational Potential due to spherical shell= V then For Outside the surface , I.e For

A Avinash Dongre
As shown in the below figure If Gravitational Potential due to spherical shell= V then For Outside the surface , I.e For

A Avinash Dongre
As shown in the below figure Gravitational potential due to uniform circular disc at a point on its axis is given by          Where  Radius of disc x- position of point on the axis of the disc M-mass of disc

A Avinash Dongre
As shown in the below figure  Gravitational potential due to uniform circular ring at a point on its axis is given by Where  the distance from the ring  radius of Ring  Potential

A Avinash Dongre
Let m1 and m2 are separated at a distance d from each other as shown in the figure.            And P is the point where net Gravitational potential  Then P is the point of zero Gravitational potential  So the distance x from m1 is given by