Working out the geostationary orbit

AI Thread Summary
To determine the height of a geostationary orbit above a planet with a diameter of 1600 km and a uniform density of 5200 kg/m³, first calculate the planet's mass using its volume and density. The volume can be found using the formula for the volume of a sphere, and then the mass is derived by multiplying the volume by the density. The radius of the geostationary orbit can be calculated using the formula involving gravitational constant, mass of the planet, and the period of the orbit. The discussion emphasizes the need for accurate calculations and clarifications on the density unit. The thread concludes with a reminder that it is a homework help forum, not a contest solution site.
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I have been given that this planet has a diameter of 1600km with a uniform density of 52000 per cubic metre. And if its moon is in a geostationary orbit around the planet and assuming that the sidereal is exactly 24 hours. How far is the geostationary orbit above the surface of the planet. And i need the answer in km.

I'm stuck in getting the mass of the planet as so far i have

radius of the geostationary orbit = cubed root of (GMpT2p over 4 pi 2)

so therefore the radius = cubed root of (6.6742 x 10-11 x (mass of the planet which i do not know how to find out x 864002 all over 4 pi 2)

some help would be much appreciated

thanks
 
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I guess you would have to calculate the volume of the planet?
I guess you would then do something with the density (for which you lack a unit)?
Somehow, magically, this leads to the mass of the planet?
 
thanks well I've posted it there now and yeah sorry it was meant to be 5200kg per cubic metre I've changed it for the new post now
 
Neopets "Lenny Conundrum" contest, Round 271 (closes 23 July)

dread said:
I have been given that this planet has a diameter of 1600km with a uniform density of 52000 per cubic metre...

The actual text of this week's Neopets "Lenny Conundrum" contest puzzle (Round 271) is as follows:

"Assume the world of Neopia is a spherical planet with a diameter of 1600 km with a uniform density of 5200 kilograms per cubic metre. If the moon of Kreludor is in a geostationary orbit around Neopia, and assuming a Neopian sidereal day is exactly 24 hours, how far is that geostationary orbit above the surface of Neopia?"

To get the prize-winning answer for the latest "Lenny Conundrum" contest, try following the instructions here:

. . . . .[/color]Lenny Conundrum Solutions Blog

Another resource might be http://www.able2know.org/forums/viewtopic.php?t=42093 .

Eliz.
 
Last edited by a moderator:
This is a homework help forum, designed to help students with their homework/classwork problems, not to answer quiz, or contest problems. Thus, I am closing this thread now.
 

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