Calculate the acceleration due to gravity

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The discussion centers on calculating the acceleration due to gravity (g) at an altitude of 200 kilometers above Earth's surface, where many mistakenly believe gravity is absent. To find g, the relevant formulas include F = GMm/R² and F = ma, which can be combined to derive an expression for acceleration. The mass of the Earth is given as 6x10²⁴ kilograms and its radius as 6.38x10⁶ meters. Participants are encouraged to use algebra to simplify the equations, noting that the mass of the falling object cancels out. Ultimately, the goal is to express the calculated g as a percentage of the standard 9.8 m/s².
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Many people mistakenly believe that austronauts that orbit the Earth are "above gravity." Calculate the acceleration due to gravity (g) for space shuttle territory, 200 kilometeres above the Earth's surface. Earth's mass is 6x1024 kilograms and its radius is 6.38 x 106 meters (6380 kilometers). Your answer is what percentage of 9.8m/s2?

Can anyone point me in the right direct to figure this out? I am not really sure what formula to use.
 
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Which equation describes the force of gravity between any two point objects separated by some distance? The equation can also be used when the objects are both spherical, or when one of the two is very large and spherical.
 
Your physics textbook probably gives the formula for acceleration. If not, it surely gives these two formulas:

F=\frac {GMm}{R^2}

and

F=ma

Use Algegra to combine these formulas to write an expression for a.
Hint: If you do it right, your little m's will cancel (illustrating that objects of different mass fall at the same rate ignoring air resistance).
 
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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