Question

Радиус планеты 1000 км,g=1,1м/с^2 какая плотность планеты?

Answer 1

Исходя из формулы плотность равна $p= \frac{m}{V}$
А массу можно вывести из формулы свободного падения $g=G\frac{m}{R^2}$ -> $m=R^2\frac{g}{G}$
Объём будем находить по формуле $V=\frac{4}{3} \pi R^3$
Откуда получаем$p= \frac{R^2 \frac{g}{G} }{ \frac{4}{3} \pi R^3}$
Подставляем значения и решаем$p= \frac{10^{12} \frac{1.1}{6.67*10^-{11}} }{ \frac{4}{3} 3.14*10^{18}}=$
Но если хотите можно решить по отдельности каждую формулу
Если нужен только ответ это примерно 4кг/м³
А решить полностью можно любым калькулятором потому что главное составить формулы!!!

Answer 2

Calculation of Planet Density

To calculate the density of a planet, we need to know its mass and volume. In this case, we are given the radius of the planet as 1000 km and the acceleration due to gravity (g) as 1.1 m/s^2.

To calculate the mass of the planet, we can use the formula for gravitational acceleration:

g = G * (M/R^2)

Where: - g is the acceleration due to gravity - G is the gravitational constant (approximately 6.67 * 10^-11 N(m/kg)^2) - M is the mass of the planet - R is the radius of the planet

Rearranging the formula, we can solve for M:

M = g * R^2 / G

Substituting the given values:

M = 1.1 * (1000 * 1000)^2 / (6.67 * 10^-11)

Now that we have the mass of the planet, we can calculate its volume using the formula for the volume of a sphere:

V = (4/3) * π * R^3

Substituting the given radius:

V = (4/3) * π * (1000 * 1000)^3

Finally, we can calculate the density of the planet using the formula:

Density = Mass / Volume

Substituting the calculated values for mass and volume, we can find the density of the planet.

Let's calculate the density step by step.

Calculation Steps:

1. Calculate the mass of the planet (M) using the formula M = g * R^2 / G. 2. Calculate the volume of the planet (V) using the formula V = (4/3) * π * R^3. 3. Calculate the density of the planet using the formula Density = Mass / Volume.

Calculation:

1. Calculate the mass of the planet (M): - g = 1.1 m/s^2 - R = 1000 km = 1000 * 1000 m - G = 6.67 * 10^-11 N(m/kg)^2

M = 1.1 * (1000 * 1000)^2 / (6.67 * 10^-11)

M = 1.1 * 10^6 / (6.67 * 10^-11)

M ≈ 1.65 * 10^16 kg

2. Calculate the volume of the planet (V): - R = 1000 km = 1000 * 1000 m

V = (4/3) * π * (1000 * 1000)^3

V = (4/3) * π * 10^9

V ≈ 4.19 * 10^9 m^3

3. Calculate the density of the planet: - Density = Mass / Volume

Density = 1.65 * 10^16 kg / 4.19 * 10^9 m^3

Density ≈ 3.94 * 10^6 kg/m^3

Therefore, the density of the planet is approximately 3.94 * 10^6 kg/m^3.

Please note that the above calculations are based on the given information and assumptions.