Final answer:
To measure the mass of a planet with the same radius as Earth, we can use the concept of gravitational acceleration and the relationship between mass, radius, and acceleration. Based on the given information, the mass of the planet is 1.794 × 10^25 kg.
Step-by-step explanation:
To measure the mass of a planet with the same radius as Earth, you can use the concept of gravitational acceleration and the relationship between mass, radius, and acceleration. From the given information, we know that the object dropped from an altitude of one radius above the surface reaches a speed that is 3 times greater than what it would be on Earth. We can use the formula for gravitational acceleration, which is given by:
g = GM/r^2
where g is the acceleration due to gravity, G is the gravitational constant (approximately 6.674 × 10^-11 N m^2/kg^2), M is the mass of the planet, and r is the radius of the planet. Since the radius of the planet is the same as Earth's radius, the gravitational acceleration on the planet will be three times larger than on Earth. So we can set up the following equation:
- g_planet = 3g_earth
- GM_planet/r^2 = 3GM_earth/r^2
- M_planet = 3M_earth
Substituting the given mass of Earth (M_earth = 5.98 × 10^24 kg), we can solve for the mass of the planet:
M_planet = 3(5.98 × 10^24 kg)
M_planet = 1.794 × 10^25 kg