Question

Радиус планеты Меркурий 2,420 км, а ускарение свободного падение 3,72 м/с. Найти массу планеты Меркурий.

Answer 1

F=G*M*m/r^2
F=mg
mg=GMm/r^2
сократим m
g=GM/r^2 (G-гравитационная постоянная, равная 6,67*10^-11)
M=g*R^2/G
M=3.72*2420000^2/6.67*10^-11 = 3.27*10^23 кг

Answer 2

Finding the Mass of Planet Mercury

To find the mass of the planet Mercury, we can use the formula for acceleration due to gravity:

Acceleration due to gravity (g) = G * (mass of the planet) / (radius of the planet)^2

Where: - G is the gravitational constant - The radius of the planet is given as 2420 km - The acceleration due to gravity is given as 3.72 m/s^2

We can rearrange the formula to solve for the mass of the planet.

Calculation

Using the given values: - Radius of Mercury (r) = 2420 km = 2,420,000 m - Acceleration due to gravity (g) = 3.72 m/s^2

We can rearrange the formula to solve for the mass (m) of the planet: m = (g * r^2) / G

Result

By substituting the given values into the formula, we can calculate the mass of the planet Mercury.

m = (3.72 * (2,420,000)^2) / G

Let's calculate the mass using the gravitational constant (G) value.

Gravitational Constant (G)

The gravitational constant (G) is approximately 6.674 × 10^-11 m^3 kg^-1 s^-2.

Calculation

Substitute the value of G into the formula: m = (3.72 * (2,420,000)^2) / (6.674 × 10^-11)

By performing the calculation, we can find the mass of the planet Mercury.