Calculating Height of a Twice-Daily Orbit Above Earth's Surface

[haruspex]

Wait wait, I'm a bit confused.
So M = gR²/G
R = squareroot(MG/g)

sqrt(MG/g) = cbrt(GMT²/4pi²)

You are confusing two radii. On the left is R, the radius of the Earth; on the right is r, the orbital radius of your satellite.
Use R = squareroot(MG/g) to get rid of the MG factor in your expression for r.

 

[somekid99]

You are confusing two radii. On the left is R, the radius of the Earth; on the right is r, the orbital radius of your satellite.
Use R = squareroot(MG/g) to get rid of the MG factor in your expression for r.

So if R is the radius of Earth and r is the radius of the the satellite's orbit then to find the height of the satellite:
Height = cbrt(GMT²/4pi²) - sqrt(MG/g)

Or what do you mean by get rid of the MG factor?
So I substitue MG with R?
r = cbrt((sqrt(MG/g))T²/4pi²)?

 

[Orodruin]

So if R is the radius of Earth and r is the radius of the the satellite's orbit then to find the height of the satellite:
Height = cbrt(GMT2/4pi2) - sqrt(MG/g)

You were supposed to replace GM with gR^2, not the other way around. All that happened now was that you complicated the expression. The point was to get rid of constants you did not know.

 

[somekid99]

You were supposed to replace GM with gR^2, not the other way around. All that happened now was that you complicated the expression. The point was to get rid of constants you did not know.

ohhh, I thought that was to prove what the radius of the Earth was, that's why I got confused.

r = cbrt(gR²T²/4pi²)
r = cbrt(9.8*6371000²43200²/4pi²)
r = 26591919.1 m

Then I subtract r with Earth's radius
26591919.1 m - 6371000 m = 20220919.1 m

and that's the height.

 

[Orodruin]

Apart from the fact that you again have way too many significant digits. You really do not have more than two at best. I suggest writing the answer in units of Mm (megameter) or, even in units of the Earth's radius. Giving nine significant digits you are essentially saying you know all the input variables to a precision that would be the same as knowing your height with a precision of the size of an atom. This is completely unreasonable.

 

[somekid99]

Apart from the fact that you again have way too many significant digits. You really do not have more than two at best. I suggest writing the answer in units of Mm (megameter) or, even in units of the Earth's radius. Giving nine significant digits you are essentially saying you know all the input variables to a precision that would be the same as knowing your height with a precision of the size of an atom. This is completely unreasonable.

I used meters to try to keep the units the same.
So if my smallest significant figures is 9.8, with 2 significant digits, then the final answer would be 2.6E7 m?

 

[Orodruin]

I used meters to try to keep the units the same.

I suggest you get comfortablr with prefixes. That is what they are for.

You also forgot to remove the Earth radius now.

 

[somekid99]

I suggest you get comfortablr with prefixes. That is what they are for.

You also forgot to remove the Earth radius now.

I have subtracted the radius with Earth's radius in the previous post.

Isn't mega meter the same thing as kilometer? I don't understand the difference? So your'e putting it in kilometers but you write it as mega meters?

 

[Orodruin]

Isn't mega meter the same thing as kilometer?

No, mega and kilo are different prefixes. Why would they be the same? While kilo denotes $10^3$, mega denotes $10^6$.