Calculating Force of Gravity Between Earth & Mars

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To calculate the gravitational force between a newborn baby (3 kg) and Mars (6.4 x 10^23 kg) at their closest distance (5.6 x 10^10 m), the formula F = G m1m2/d^2 is used. The gravitational constant G is 6.67300 × 10^-11 m^3 kg^-1 s^-2. Substituting the values into the equation gives F = (6.67300 × 10^-11) * (6.4 x 10^23) * (3.00) / (5.6 x 10^10)^2. The calculation can be completed using a calculator to find the exact force. This method effectively demonstrates how to apply the gravitational force formula in practical scenarios.
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1. Calculate the force of gravity between a newborn baby (mass=3kg) and the planet Mars (mass=6.4 X 10^23 kg) when Mars is at its closest to Earth (distance=5.6 X 10^10 m).



2. F= G m1m2/d2



3. I got this far and I don't know how to break down the equation any further: F= G M m /R^2= 6.67300 × 10^-11 m^3 kg^-1 s^-2 *6.4 x 10^23 kg *3.00 kg/(8*10^10 m)^2
 
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I haven't checked all your numbers but it looks reasonable. Just calculate what the result is on your calculator.
 
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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