find out the expression of orbital velocity and what is its depending factors.
Answers
hi mate...
Answer....
Derivation of orbital velocity
Orbital velocity is derived in the following way:
Fg=GMmr2 (gravitational force between the earth and the satellite) (eq.1)
Fc=mV2r (centripetal force acting upon the satellite) (eq.2)
Where,
M: mass of the earth
m: mass of the satellite
r: radius of uniform motion of the satellite around the earth
r=R+h
Where,
R: radius of the earth
h: height of the satellite
V: linear velocity of the satellite
Fc: centripetal force
Fg: gravitational force
Fg=Fc (from eq.1 and eq.2)
GMmr2=mV2r V=[GMr]12 (eq.3)
Therefore, this is the equation of orbital velocity.
Difference between orbital velocity and escape velocity
Escape velocity is defined as the minimum velocity required by a free object to escape from the gravitational force of a massive body.
It is calculated by the formula given below:
ve=2GMr−−−−√
Where,
G: universal gravitational constant
M: mass of the body to be escaped from
r: distance between the centre of mass of the body and the object
In order to break out from the orbit of the massive body, the object must have escape velocity square root of two times greater than the orbital velocity.
Derivation of orbital velocity
Orbital velocity is derived in the following way:
Fg=GMmr2
(gravitational force between the earth and the satellite) (eq.1)
Fc=mV2r (centripetal force acting upon the satellite) (eq.2)
Where,
M: mass of the earth
m: mass of the satellite
r: radius of uniform motion of the satellite around the earth
r=R+h
Where,
R: radius of the earth
h: height of the satellite
V: linear velocity of the satellite
Fc: centripetal force
Fg: gravitational force
Fg=Fc
(from eq.1 and eq.2)
GMmr2=mV2r
V=[GMr]12
(eq.3)
Therefore, this is the equation of
orbital velocity.
1)orbital velocity. noun. The velocity at which a body revolves about another body. The minimum velocity required to place or maintain a satellite in a given orbit.
2)The velocity of this orbit depends on the distance from the object to the center of the Earth. The velocity has to be just right, so that the distance to the center of the Earth is always the same. The orbital velocity formula contains a constant, G, which is called the "universal gravitational constant".
3)The expression for orbital velocity is √g( R+h) = √gr. Orbital velocity is the velocity needed to balance the pull of gravity on the satellite with the inertia of the motion of the satellite, the tendency of the satellite to continue. Considering the mass of satellite = m. The radius of satellite = r.
4)The orbital speed can be found using v = SQRT(G*M/R). The R value (radius of orbit) is the earth's radius plus the height above the earth - in this case, 6.59 x 106 m. Substituting and solving yields a speed of 7780 m/s.
i hope it helpfull to you..
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Orbital Velocity
~ orbital velocity is the velocity required to put the satellite into it's orbital around the earth
orbital velocity = R √g / r+ h
~ Orbital force between earth and satellite
= GMm/r²
Therefore,
= mv²/r = GMm/r²
v² = Gm/r = Gm/ R + h
v = √Gm/r = √Gm/ R + h
Now, g = - GM/ (R+h)²
GM/r+h = g (R+h) = gr
Therefore orbital velocity = √g( R+h) = √gr
Where..
M = Mass of the earth
R = Radius of the earth
m = mass of the satellite
v0 = orbital velocity
h = Height of the satellite above the earth's surface
r +h = orbital radius of the satellite.
Vo = 7.92 km/s
Factor in which Orbital velocity depends are :-
~ it depends on the mass and radius of the planet about which the satellite revolves.
~ it Decrease with the increase in the radius of the orbit and with increase in the height of the satellite.
~ it is independent of the mass of the satellite.
