Orbit of a geostationary satellite
Question is: compute the radius of a geostationary satellite's orbit in units of the Earth's radius.
My answer is:
Earth's radius R = 6378.1 km approx
Satellite is 35,786km above ground so radius of the orbit in terms of earth's radius is (35,786/6378.1)R + 1R = 6.61 R
Have I missed anything here or is it just that simple?
Thanks for any advice.
Yes, as simple as that ... a better question is:
Yes, as simple as that ...
the geostationary orbit pretty much depends only on the (polar) rotation rate of a (any) planet (also almost incidentally in this case, the mass M of the planet), so there is no fundamental relationship between the geostationary orbit radius and the planet's radius: for example, a less dense planet of equal mass to the Earth, but by dint of it being less dense having a larger radius, with the same rotation period, would possess exactly the same geostationary orbit radius, and so a different ratio between the two radii ...
As such this isn't really an "Advanced Applied Maths" topic ... is it?
... a better question is:
*compute the radius of a satellite's orbit in units of the Earth's radius, such that there are no time-dilation effects experienced by the satellite ;-).*
* O.K - admittedly more advanced Physics than Maths, perhaps, but in this case there is a fundamental relationship between the "zero time-dilation orbit radius" and the planet's radius - and, to me, at least, an astonishingly simple one.
I do have the answer and the working for it, in case you give up ;-)
9 weeks into an undergrad degree? That's great.
Originally Posted by jackiemoon
Hey yerself, Jackie,
9 weeks into an undergrad degree? That's great. What subject?
Whatever, it's obviously working; they've already got you proficient at dividing one number into another ...