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## Homework Statement

The Moon's distance from Earth is approximately 60 Earth radii, and it takes the Moon 27 days to orbit Earth. A satellite just above Earth's atmosphere orbits in 84 min. Show that these data are consistent with Kepler's third law [itex] T^2≈R^3 [/itex]. What radius orbit is required for a satellite to have a period of exactly 1 day? (Such an orbit is called geosynchronous).

## Homework Equations

[itex]T^2≈R^3[/itex],

## The Attempt at a Solution

I found the orbital radius in astronomical units, it's ##0.17614## AU. I think I'm confused as how to figure out the orbital radius for the satellite. I always get very large numbers, because 1 AU is equal to ~24,000 Earth radii. I don't understand how to show this relationship because I can't even understand it myself! Could someone walk me step by step? I think I am to show the orbital radius of the Moon in Earth radii, but it's ##4135.95## ER, which seems far too large.