Final answer:
To calculate the mass of the hypothetical planet, you can use the formula for gravitational force and set it equal to Earth's gravitational force. The mass of the hypothetical planet would be 2.61 times the mass of Earth.
Step-by-step explanation:
The mass of a hypothetical planet can be calculated using the formula for gravitational force:
Fgravity = G * (m1 * m2) / r^2
Where Fgravity is the gravitational force, G is the gravitational constant, m1 and m2 are the masses of the objects, and r is the distance between their centers.
In this case, we know that the radius of the hypothetical planet is the same as Earth's. As the gravitational force is the same, we can set up the equation:
G * (mass of Earth * mass of hypothetical planet) / r^2 = G * (mass of hypothetical planet * mass of hypothetical planet) / r^2
Simplifying and solving for the mass of the hypothetical planet:
mass of hypothetical planet = mass of Earth * 2.61
So the mass of the hypothetical planet would be 2.61 times the mass of Earth.