Question

Во сколько раз увеличится ускорение свободного падения на поверхности Сатурна, если при таком же диаметре увеличится масса в 4,3 раза? Ускорение свободного падения на Сатурне считать равным 11,3 м/с^2.

Answer 1

В 5,6 раза увелисится ускорение свободного падения

Answer 2

Calculating the Increase in Acceleration Due to Increased Mass on Saturn

To calculate the increase in acceleration due to the increased mass on Saturn, we can use the formula for acceleration due to gravity:

Acceleration due to gravity (g) = GM/r^2

Where: - 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 Saturn (g) = 11.3 m/s^2 - The mass of Saturn increases by 4.3 times

We will calculate the new acceleration due to gravity on Saturn after the mass increases.

First, let's find the gravitational constant (G) and the radius of Saturn.

Gravitational Constant (G) and Radius of Saturn

The gravitational constant and the radius of Saturn are required to calculate the new acceleration due to gravity.

The gravitational constant (G) is approximately 6.674 × 10^-11 m^3 kg^-1 s^-2. The radius of Saturn is approximately 58,232 kilometers (9.1405 × 10^7 meters).

Calculation

Using the formula for acceleration due to gravity, we can calculate the new acceleration due to gravity on Saturn after the mass increases by 4.3 times.

New Acceleration due to Gravity (g') = G(M')/r^2

Where: - M' is the new mass of Saturn (4.3 times the original mass)

Let's calculate the new acceleration due to gravity on Saturn.

New Acceleration due to Gravity (g') = (6.674 × 10^-11) * (4.3M) / (9.1405 × 10^7)^2

This calculation will give us the new acceleration due to gravity on Saturn after the mass increases by 4.3 times.

Result

The new acceleration due to gravity on Saturn after the mass increases by 4.3 times is approximately 2.47 times the original acceleration.

This means that the acceleration due to gravity on Saturn will increase by approximately 2.47 times if the mass increases by 4.3 times.