Question

5. Определить во сколько раз ускорение свободного падения на поверхности некоторой планеты больше, чем на Земле, если масса планеты равна массе Земли, а ее радиус в два раза меньше радиуса Земли.​

Answer 1

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Answer 2

Calculation of Acceleration Due to Gravity on Another Planet

To determine the ratio of the acceleration due to gravity on another planet compared to Earth, 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 planet - R is the radius of the planet

Given that the mass of the planet is equal to the mass of Earth, and its radius is half the radius of Earth, we can substitute these values into the formula.

Let's calculate the ratio of the acceleration due to gravity on the other planet compared to Earth:

1. Mass of the planet (M) = Mass of Earth 2. Radius of the planet (R) = (1/2) * Radius of Earth

Substituting these values into the formula, we get:

g_planet = (G * M) / (R_planet^2) g_earth = (G * M_earth) / (R_earth^2)

To find the ratio, we divide the acceleration due to gravity on the other planet by the acceleration due to gravity on Earth:

Ratio = g_planet / g_earth

Let's calculate the ratio using the given values.