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
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
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
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
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
.
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
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.
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
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
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
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
As shown in the below figure
If Gravitational field Intensity due to uniform solid sphere= I
Then Inside surface I.e for
Where
Radius of shell
Position of Pt.
Mass of Solid sphere
As shown in the below figure
If Gravitational field Intensity due to spherical shell= I
then
Outside the surface I.e
Where
Radius of shell
Position of Pt.
Mass of spherical shell