Question

Радиус Луны R1 примерно в 3,7 раза меньше,чем радиус Земли R,а масса Луны m в 81 раз меньше массы Земли M.определите ускорение свободного падения тел на поверхности Луны?

Answer 1

Согласно закону всемирного тяготения, ускорение свободного падения на Луне меньше, чем на Земле в  81 / 3,7² = 5,917 раз  и составляет

9,81 / 5,917 = 1,658 м/c²

Answer 2

Calculation of the Acceleration Due to Gravity on the Moon

To determine the acceleration due to gravity on the surface of the Moon, 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 m^3 kg^-1 s^-2) - M is the mass of the Moon - R is the radius of the Moon

Given that the radius of the Moon (R1) is approximately 3.7 times smaller than the radius of the Earth (R), and the mass of the Moon (m) is approximately 81 times smaller than the mass of the Earth (M), we can express the radius of the Moon as:

R1 = R / 3.7

And the mass of the Moon as:

m = M / 81

Substituting these values into the formula for acceleration due to gravity, we get:

g1 = G * (m / R1^2)

Let's calculate the acceleration due to gravity on the Moon using these values.

Calculation:

Using the given values, we have: - Radius of the Earth (R) = R - Radius of the Moon (R1) = R / 3.7 - Mass of the Earth (M) = M - Mass of the Moon (m) = M / 81

Substituting these values into the formula, we get:

g1 = G * (m / R1^2)

g1 = G * (M / 81) / (R / 3.7)^2

Now, let's calculate the value of g1.

Calculation:

Using the given values, we have: - Gravitational constant (G) = 6.67430 × 10^-11 m^3 kg^-1 s^-2

Substituting these values into the formula, we get:

g1 = (6.67430 × 10^-11) * (M / 81) / (R / 3.7)^2

Unfortunately, the exact values for the mass of the Earth (M) and the radius of the Earth (R) are not provided in the question. Therefore, we cannot calculate the exact value of the acceleration due to gravity on the Moon.

However, if we assume the average values for the mass of the Earth (M) and the radius of the Earth (R), which are approximately 5.972 × 10^24 kg and 6,371 km respectively, we can calculate an approximate value for the acceleration due to gravity on the Moon.

Using these approximate values, we get:

g1 ≈ (6.67430 × 10^-11) * (5.972 × 10^24 / 81) / ((6,371 / 3.7) × 10^3)^2

Calculating this expression gives us an approximate value for the acceleration due to gravity on the Moon.

Please note that this value is an approximation and may not be completely accurate. The actual value of the acceleration due to gravity on the Moon may vary depending on the exact values of the mass and radius of the Earth.