To calculate the mass of planet X, we can use the formula for the acceleration due to gravity:
g = G * (M / 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.
Given:
Acceleration due to gravity on planet X (g) = 2.7 m/s^2
Radius of planet X (r) = (1/3) * Radius of Earth (R)
Let's denote the mass of planet X as "Mx."
Substituting the values into the formula, we have:
2.7 m/s^2 = G * (Mx / (r^2))
Now, let's consider the ratio of the radii:
r = (1/3) * R
Substituting this into the equation:
2.7 m/s^2 = G * (Mx / ((1/3 * R)^2))
Simplifying further:
2.7 m/s^2 = G * (Mx / (1/9 * R^2))
Multiplying both sides by (1/9 * R^2):
2.7 m/s^2 * (1/9 * R^2) = G * Mx
Rearranging the equation to solve for Mx:
Mx = (2.7 m/s^2 * (1/9 * R^2)) / G
The value of G, the gravitational constant, is approximately 6.67430 × 10^-11 m^3/(kg * s^2).
Let's assume the radius of Earth (R) is approximately 6,371 km (or 6,371,000 meters).
Now, we can substitute these values into the equation to calculate the mass of planet X (Mx):
Mx = (2.7 m/s^2 * (1/9 * (6,371,000 m)^2)) / (6.67430 × 10^-11 m^3/(kg * s^2))
Calculating this expression will give us the mass of planet X.