A hypothetical planet has a mass 1.49 times that of Earth, but the same radius.
What is g near its surface?
To calculate the acceleration due to gravity (g) near the surface of a planet, we can use the formula:
g = G * (M / r^2)
Where:
- g is the acceleration due to gravity
- G is the gravitational constant (approximately 6.67430 × 10^-11 m³/(kg·s²))
- M is the mass of the planet
- r is the radius of the planet
In this case, the radius of the hypothetical planet is the same as Earth, so we can use Earth's radius, which is approximately 6,371 kilometers (6.371 × 10^6 meters).
The mass of the hypothetical planet is given as 1.49 times that of Earth's mass. However, we do not have the exact mass value for Earth for comparison. The mass of Earth is approximately 5.972 × 10^24 kilograms.
Let's calculate g using these values:
g = (6.67430 × 10^-11 m³/(kg·s²)) * ((1.49 * 5.972 × 10^24 kg) / (6.371 × 10^6 meters)^2)
Simplifying this calculation gives us:
g ≈ 3.43 m/s²
Therefore, the acceleration due to gravity near the surface of the hypothetical planet is approximately 3.43 m/s².