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The acceleration due to gravity on planet X is 2,7 m-s-2. The radius of this planet is a third (⅓) of the radius of Earth.

1. Calculate the mass of planet X.​

User Tamell
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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.
User Chris Riley
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