Calculate Geosynchronous Orbit Dist. to Earth's Center

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To calculate the distance from a satellite in a geosynchronous orbit to the Earth's center, the formula T=((2*Pi)*r^(3/2))/sqrt(GM) is used, where T is the orbital period. The user initially misinterprets T as equal to 2Pi, leading to incorrect calculations. The expected result for the distance is approximately 4.2 x 10^7 meters. Clarification on the units of T is sought, specifically whether they are in radians. Understanding the units derived from the formula is crucial for solving the problem correctly.
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Homework Statement


A satellite is in a circular, geosynchronous orbit (makes one revolution around Earth in 24 hours). Calculate the distance in meters from the satellite to the Earth's center. Mass of Earth = 5.97 x 1024 kg



Homework Equations


T=((2*Pi)*r^(3/2))/sqrt(GM)


The Attempt at a Solution



I thought T equals the period 2Pi. So the the 2Pi's cancel and then you just plug in the variables. Unfortunately I'm not getting the right answer which is supposed to be: 4.2*10^7.

Any help would be greatly appreciated.
 
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Check to see what units the formula will produce.
 
Would the units for T be radians?
 
Shaunzio said:
Would the units for T be radians?
You're guessing? Why don't you expand the units from the formula and actually see what it is?
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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