Question

СРОЧНО! ФИЗИКА Определите высоту над Землёй, где сила тяготения уменьшилась в 3 раза? Радиус Земли принять 6400км.Помогите пожалуйста​.

Answer 1

G*m*M/(R+h)^2 = 0,8*G*m*M/R^2,

R - радиус Земли

h - высота на Землей

G - гравитационная постоянная

m и M - массы тела и Земли.

Преобразуем и получим:

(1 + h/R) = 1,25^0,5. h = 755 км.

Answer 2

Calculation of the Height above the Earth where the Gravitational Force is Reduced by 3 Times

To determine the height above the Earth where the gravitational force is reduced by 3 times, we can use the formula for gravitational force:

F = G * (m1 * m2) / r^2

Where: - F is the gravitational force between two objects, - G is the gravitational constant (approximately 6.67430 × 10^-11 N(m/kg)^2), - m1 and m2 are the masses of the two objects, and - r is the distance between the centers of the two objects.

In this case, we want to find the height above the Earth where the gravitational force is reduced by 3 times. Let's assume that the initial distance from the center of the Earth is r1, and the reduced distance is r2.

We can set up the equation as follows:

F1 = G * (m1 * m2) / r1^2

F2 = G * (m1 * m2) / r2^2

Since we want to find the height where the gravitational force is reduced by 3 times, we can write:

F2 = 1/3 * F1

Substituting the equations for F1 and F2, we get:

G * (m1 * m2) / r2^2 = 1/3 * G * (m1 * m2) / r1^2

Simplifying the equation, we can cancel out the masses (m1 and m2):

(1 / r2^2) = (1/3) * (1 / r1^2)

Now, we can substitute the given radius of the Earth (r1 = 6400 km) and solve for r2:

(1 / r2^2) = (1/3) * (1 / (6400 km)^2)

Converting the radius of the Earth to meters (1 km = 1000 m), we have:

(1 / r2^2) = (1/3) * (1 / (6400 km * 1000 m/km)^2)

Simplifying further:

(1 / r2^2) = (1/3) * (1 / (6400 * 1000)^2 m^2)

Now, we can solve for r2 by taking the square root of both sides:

r2 = sqrt((3 * (6400 * 1000)^2 m^2))

Evaluating this expression, we can find the height above the Earth where the gravitational force is reduced by 3 times.

Let's calculate it:

r2 = sqrt((3 * (6400 * 1000)^2 m^2))

r2 = sqrt((3 * (6400 * 1000)^2))

r2 = sqrt((3 * 40960000000))

r2 ≈ 2.828 * 10^6 meters

Therefore, the height above the Earth where the gravitational force is reduced by 3 times is approximately 2.828 * 10^6 meters.

Please note that this calculation assumes a simplified model of the Earth as a uniform sphere and does not take into account other factors that may affect the gravitational force at different heights.