Is this correct ????? (1 Viewer)

[Lazy Lankan]

* Define the term orbital velocity and the quantitative and qualitative relationship between orbital velocity, the gravitational constant, mass of the central body, mass of the satellite and the radius of the orbit using Kepler's Law of Periods

To achieve and maintain a stable orbit around a planet, a satellite must have a certain velocity. In general, we define the term orbital velocity to be the velocity required by a satellite to enter and maintain a particular orbit around a celestial object. If we assume the orbit of the satellite around the celestial object is circular, we can use Kepler's Third Law (The Law of Periods) to obtain an equation for the orbital velocity of the satellite. Starting with the Law of Periods equation:

(r^3/T^2 = GM/4pi^2)

Where:
T = period of satellite around the central body r = distance from centre of the central body to the satellite M = mass of central body and G = gravitational constant

Substituting T = (2pi.r / v) for T, we obtain:

V = square root of (GM/r)

where v = orbital velocity of the satellite.

 

[George W. Bush]

Alternatively potential energy = kinetic energy. It's a lot easier to solve that way

 

[Heinz]

Originally posted by George W. Bush
Alternatively potential energy = kinetic energy. It's a lot easier to solve that way

Thats for escape velocity. Theres a slight difference in the two formulas. (theres a 2 in the formula for escape velocity)

 

[Dash]

Just wanted to point out...
There is another method of obtaining the orbital velocity formula...
Equate the centripetal and gravitational forces acting on the orbiting body:

(GMm)/(r^2) = (mv^2/r)

Multiply through by r and cancel out the m's.
Then make v the subject, and you get:

v = sqrt(GM/r)

Also, refer to the following links for more info about the dot point:
http://www.boredofstudies.org/community/showthread.php?s=&threadid=14033
http://www.boredofstudies.org/community/showthread.php?s=&threadid=11513