# orbitual velocity

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#### asplode

##### Guest
i need to work out the orbital velocity of a satellite around an imaginary spherical planet with a diameter of 1600 km with a uniform density of 5200 kilograms per cubic metre. the only other details i have are that it is a circular orbit 630 km above the surface of the planet. i need to know its orbital velocity in metres per second. i have looked at a lot of formulae but cant understand them. Can you help please??

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#### heliox

##### Guest
This sounds awfully like school homework type questioning.......

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#### alokmohan

##### Guest
Plese check up title,is it orbitual velocity?

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#### asplode

##### Guest
sorry, title should be orbital velocity

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#### kmarinas86

##### Guest
<font color="yellow">i need to work out the orbital velocity of a satellite around an imaginary spherical planet with a diameter of 1600 km with a uniform density of 5200 kilograms per cubic metre. the only other details i have are that it is a circular orbit 630 km above the surface of the planet. i need to know its orbital velocity in metres per second. i have looked at a lot of formulae but cant understand them. Can you help please??</font><br /><br />Volume=4/3*pi*r^3<br />Voiume=4/3*pi*(1,600 km)^3<br /><br />http://www.google.com/search?q=4%2F3*pi*%281%2C600km%2F2%29%5E3*%285200+kilograms+per+cubic+meter%29<br /><br />Volume*Density=Mass=<br />(4 / 3) * pi * (((1 600 km) / 2)^3) * ((5 200 kilograms) per (cubic meter)) = 1.1152235 × 10^22 kilograms<br /><br />http://www.google.com/search?q=sqrt%28G*1.1152235*10%5E22+kilograms%2F%281600km%2F2%2B630km%29%29<br /><br />Then Orbital Velocity =<br />sqrt(GM/R) = sqrt((G * 1.1152235 * ((10^22) kilograms)) / (((1 600 km) / 2) + (630 km))) = 721.395618 m / s <br /><br />What you have is a planet that is much smaller than Earth:<br /><br />http://www.google.com/search?q=1.1152235*10%5E22+kilograms+%2F+mass+of+earth<br /><br />http://www.google.com/search?q=%28radius+of+earth+%2F+800+km%29%5E3<br /><br />Earth's volume is 506.761965 times greater.<br /><br />Show your work.

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#### asplode

##### Guest
thanks, i made the mass 11146581333316000 kg, and the volume 2143573333330 but had no idea how to do the orbital velocity formula

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#### drwayne

##### Guest
The recipe for circular motion is this:<br /><br />a = v^2 / r<br /><br />where v is the orbital velocity, r is the radius of the orbit, and a is the acceleration of the body (don't forget that an object in orbit is constantly accelerating)<br /><br />Now if I multiply both sides of this equation by m, the mass of the object (don't worry, it will go away later), I get m * a, which you should recognize as a force, i.e.<br /><br />F = ma = v^2/r<br /><br />Now, F is the force acting on the body, which you can get from the equation for the force between two masses, i.e.<br /><br />F = Gm1m2/r^2<br /><br />where m1 and m2 are the two masses.<br /><br />That should be close enough for you to finish.<br /><br />Wayne <div class="Discussion_UserSignature"> <p>"1) Give no quarter; 2) Take no prisoners; 3) Sink everything."  Admiral Jackie Fisher</p> </div>

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#### newtonian

##### Guest
asplode - Note that this is simplifying the math, whereas actual orbits are often far more complex.<br /><br />This is why man-made orbits usually either decay or escape, while our moon and earth are in stable orbits and the moon is actually slightly receeding at this time due to tidal effects.<br /><br />Of course, one must understand the relatively simple formula before attempting to formulate the actual future orbit of earth or moon. <br /><br />So, as the above poster requested, can you show your work so we can check - and simplify so we can all understand the math?<br />

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