Universal gravitation 8- determine the speed of a satellite

AI Thread Summary
To determine the speed of a satellite in a stable orbit 525 km above Earth's surface, the relevant equations include Newton's Law of Gravitation and the formula for orbital speed, v=√(GMe/R). The calculations involve the radius of the Earth (Re) and the altitude (h) to find the total radius (R), which is 6,905,000 m. After substituting the values into the orbital speed equation, the calculated speed is approximately 7600.32 m/s. Suggestions for improvement include deriving the speed equation from fundamental principles rather than memorizing it.
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Homework Statement



Determine the speed of a satellite moving in a stable orbit about the Earth if the satellite is 525 km above the Earth's surface.

Homework Equations


I have made a list of equations that are relevant for this entire module on universal gravitation. So although there are many of them does not mean that they all apply in this circumstance. The ones relevant to this question will be placed in bold.

Kepler's 3rd law: (Ta/Tb)2=(Ra/Rb)3

motion of planets must conform to circular motion equation: Fc=4∏2mR/T2

From Kepler's 3rd law: R3/T2=K or T2=R3/K

Gravitational force of attraction between the sun and its orbiting planets: F=(4∏2Ks)*m/R2=Gmsm/R2

Gravitational force of attraction between the Earth and its orbiting satelittes: F=(4∏2Ke)m/R2=Gmem/R2

Newton's Universal Law of Gravitation: F=Gm1m2/d2

value of universal gravitation constant is: G=6.67x10-11N*m2/kg2

weight of object on or near Earth: weight=Fg=mog, where g=9.8 N/kg
Fg=Gmome/Re2

g=Gme/(Re)2

determine the mass of the Earth: me=g(Re)2/G

speed of satellite as it orbits the Earth: v=√GMe/R, where R=Re+h

period of the Earth-orbiting satellite: T=2∏√R3/GMe

Field strength in units N/kg: g=F/m

Determine mass of planet when given orbital period and mean orbital radius: Mp=4∏2Rp3/GTp2


The Attempt at a Solution



v=?
Re=6.38x106m
h=525km=525000m
G=6.67x10-11N*m2/kg2
me=5.98x1024kg

R=Re+h=6905000m

With all this information, I used to plug into the equation highlighted above to solve for v=7600.32m/s

If someone could please have a look at my work and let me know if I made any mistakes, if so point them out to me! it would be greatly appreciated! Thank you so much in advance:)
 
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Correct again!
IMHO I still suggest to start from basic equations like F=ma, F = GMm/R^{2} and centripetal acc = mv^{2}/R to derive the required equation for the speed v rather from attempting to remember the formula for v.
Also I would have written v=√GMe/R, as v=√(GMe/R,).
 
Thank you!
 

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