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A very dense planet has the same radius as Earth but objects on its surface weigh 9 times more than on Earth. What is the mass of this planet in Earth masses?

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Answer:

the mass of this planet is about 8.2 × 10^22 kg, or approximately 8.2 trillion trillion (8.2 × 1022) times the mass of Earth, which has a mass of approximately 5.97 × 10^24 kg.

Step-by-step explanation:

We can use the formula for the gravitation acceleration:

g = GM/r^2

where g is the acceleration due to gravity, G is the gravitational constant, M is the mass of the planet, and r is the radius of the planet.

We are told that the acceleration due to gravity on the planet is 9 times that on Earth, which means:

9 = GM/r^2

Rearranged, this gives:

M = g * r^2 / G

where g is the acceleration due to gravity on Earth, which is approximately 9.81 m/s^2. Earth's radius is approximately 6.371×10^6 meters, so:

M = (9.81 m/s^2 ) * (6.371×10^6 m)^2 / 6.67×10^(-11) m^3/kg/s^2

M = 5.97×10^24 kg, which is approximately 6.16×10^24 Earth masses. This is a very massive planet, much more so than Jupiter or Saturn. It would be the most massive object in our solar system by far, if it existed.

User Gaurang Sondagar
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