Satellite orbital velocity
Satellite is an object which is moving around the Earth. There are two types of satellite one is natural satellite made by nature (Moon) and other is artificial satellite which is made by men.
One important point i want to make it clear here from childhood you learn that every planets move around the Sun, Moon moves around the Earth, even any picture of solar system shows all planet moves around the Sun including Earth.
But you will shock, When i will tell you this is technically wrong all planet and Moon does not moves around the Sun and Earth.
Then you will ask me if all the planet does not moves around the Sun, which is that body around it all planet moves. And your next question will be if it is wrong then why teach like this wrong concept in book ?
Well actually books and pictures shows all planets moves around the Sun is correct, so that you can easily understand the solar system behavior without knowing the technical point.
Now here you will learn around which all planet moves and even Sun moves around which,
and also why do you teaches that all planet moves around the Sun ?
Planets and Stars moves around the common centre of mass, This common centre of mass is also known as barycenter to understand barycenter you must know centre of mass you can refer my previous post center of mass concept.
Centre of mass is that point at which whole mass of the body or system lies at that point, means body is balanced, sometimes it can lies outside the body, some time between two masses and sometimes near the heavier mass depends upon the mass quantity and its shape and size, for more details refer above link.
In space every two bodies there is a common centre of mass which is known as barycenter as shown in above picture mass M1 and M2 point C is called barycenter around which mass M1 and M2 will move, Similarly this is the point around which planets and starts also move.
For example if you consider the Sun and the Earth then mass of the Sun is about 333,000 times heavier than Earth, so barycenter of Sun and the Earth lies near the Sun centre hence the Earth as well as the Sun move around this barycenter.
So you see from the Earth perspective and feel that Earth is moving around the Sun because this point is near and inside the Sun.
When you consider Jupiter planet it is very bigger than Earth, you can think Jupiter mass is 318 times heavier than mass of the Earth. Now if you will consider the Sun and the Jupiter barycenter then this barycenter will lies outside near the Sun, Hence Jupiter and Sun moves around this barycenter and you see a different elliptical path.
If you talk about the Solar system including all objects and planets masses then it has own barycenter including all masses.All objects and planets moves around this barycenter, This point is not fixed it change its location depends upon at a particular time where is this all planets in the orbit according to that barycenter location depend.
Since Mass of the Sun is very very heavy in Solar system so most of the time barycenter lies inside the Sun. Hence all planets moves around this barycenter and you feel that all planets move around the Sun .Due to barycenter Sun also moves little bit around it.
Barycenter evey year change its location. So this barycenter concept apply for all planet and natural satellite.
Take an example of Earth and Moon, You know Earth is very heavy than Moon you can think Moon mass is 1.2% of Earth mass, So barycenter of these two bodies lies inside the Earth approx 4671 km from the Earth centre.
The Moon and the Earth both move around this barycenter. Moon moves around this barycenter but you feel Moon is moving around the Earth. Now i hope you have understand the concept of barycenter,
Satellite orbital velocity
How Satellite move around the Earth, A satellite must have two things to move around the Earth first it must have kinetic energy and second centripetal force, if this is available for any object then that object can move around the Earth see the picture below.
Orbital velocity is the velocity with which satellite moves in the orbit, Due to centripetal force satellite moves in a circular path.
suppose m is mass of the satellite then centripetal force Fc = mv²/(h+Re) , now this force is balanced by gravitational force, You know gravitational force Fg = GMem/(h+Re)²
now equate this two force Fc = Fg
mv²/(h+Re) = GMem/(h+Re)² ( V = Vo = orbital velocity )
Vo² = GMe/(h+Re) or Vo = √GMe/(h+Re)
You also know that g = GMe/Re² so from here GMe = gRe² now put this value in above equation Vo = √GMe/(h+Re) = √gRe²/(h+Re) = Re√ g/(h+Re)
This is equation of orbital velocity for satellite, now suppose one more satellite is moving above this orbit, then can you tell me which satellite velocity will higher .
Well as from the orbital velocity equation you can see velocity is depending upon inversely distance from centre of Earth , Hence closer to the Earth satellite velocity will be higher and far satellite will be less velocity.
Velocity of satellite closer to the Earth
from above equation Vo = Re√ g/(h+Re) near closer to the Earth (h+Re)→Re since h is very very small compare to Re so Vo = Re√ g/(h+Re) = √gRe = √9.8x6400x1000 = √627.2×10⁵ = √62.72×10⁶ = 7.91×10³ m/s 7.91 km/s.
I will continue this post with more concepts, i hope you have enjoyed learning satellite orbital velocity, i want your feedback, comment, share and likes, thanks for sharing, learn and grow.
Dated 27th Jan 2019