Proportionality of gravitational fields

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To determine the altitude for a satellite orbit where Earth's gravitational field is half its surface value, the gravitational force is inversely proportional to the square of the distance from the center of the Earth (Fg ∝ 1/r^2). The correct altitude can be calculated using this relationship, leading to the conclusion that the answer is D, √2R. However, the original poster struggled to show their calculations and was encouraged to share their attempts for better assistance. The discussion emphasizes the importance of demonstrating problem-solving steps in physics to receive effective help. Clarifying the calculations is essential for understanding the solution.
Nikola
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Homework Statement


Scientist want to put a satellite into an orbit where the gravitational field of Earth is half its value at Earth's surface. The altitude of this orbit above the Earth's surface will be
A.3R B. √2R-R C. 4R D.√2R

Homework Equations


Fg∝1/r^2

The Attempt at a Solution


I know it is D. but i couldn't figure out how.
 
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Nikola said:

Homework Statement


Scientist want to put a satellite into an orbit where the gravitational field of Earth is half its value at Earth's surface. The altitude of this orbit above the Earth's surface will be
A.3R B. √2R-R C. 4R D.√2R

Homework Equations


Fg∝1/r^2

The Attempt at a Solution


I know it is D. but i couldn't figure out how.
Show us what you have tried. Maybe we can help you figure it out.
 
i tried using the equation
 
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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