What is the Correct Radius and Mass of Earth for Satellite Orbit Calculations?

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For satellite orbit calculations at 450,000 meters above Earth's surface, the correct radius (r) is the sum of Earth's radius (6,371,000 meters) and the altitude, totaling 6,821,000 meters. The mass of Earth needed for calculations can be found online, as it is not commonly memorized. The discussion emphasizes the importance of using accurate values for both radius and mass in orbital mechanics. Proper calculations are crucial for successful satellite deployment. Accurate data ensures reliable satellite operations in orbit.
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Homework Statement
I have a satellite with a mass of 30.0 kg that I wish to put into a circular orbit 450,000 m above the surface of the earth.
15. How much will the potential energy of the satellite – earth system increase by?
16. What must the kinetic energy of the satellite be when it is in orbit?
17. What will the magnitude of the gravitational force on the satellite be when it is in orbit?
18. What will the period of the satellite's orbit be? If the orbit is above the earth's equator, how long will it take for me to see the satellite again in the same spot in the sky?
Relevant Equations
U(g)=-(GM(p)m(s))/r^2
I just have a question on the problem itself. If I am putting the satellite into orbit 450,000 m above the surface, then would r=6,371,000 m(earth's radius)+450,000 m? And what mass of Earth should I be using, in kg of course.
 
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TjGrinnell said:
I just have a question on the problem itself. If I am putting the satellite into orbit 450,000 m above the surface, then would r=6,371,000 m(earth's radius)+450,000 m?
Yes.
TjGrinnell said:
And what mass of Earth should I be using, in kg of course.
Look it up on the web, I have not memorized it.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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