Question

Масса орбитальной космической станции 19 т, масса космонавта в скафандре 100 кг. Оцените силу гравитационного взаимодействия между станцией и космонавтом на расстоянии 100 м. За какое приблизительно время под действием этой силы космонавт приблизится к станции на расстояние 1 м, если в начальный момент времени относительная скорость станции и космонавта была равна нулю?

Answer 1

Сила взаимодействия между 2 телами равна F=(GMm)/(L^2)
G-гравитационная постоянная(значение не помню, загугли) Mm-массы тел  L-растояние между телами
Рассмотрим движение человека т.к. его ускорение будет много больше ускорения шатла(им можно принебречь).
a=F/m(человека)
t=квадратный корень из(2L/a)
время можно посчитать приблизительно т.к при приближение человека к станции  будет менятся сила и ускорение немного увеличиватся. к стому же и станция ускоряется в сторону человека.Но примерно ответ должен бытть такой.

Answer 2

Gravitational Force Calculation

The gravitational force between the space station and the astronaut can be calculated using the formula:

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

Where: - F is the gravitational force - G is the gravitational constant (approximately 6.674 × 10^-11 N m^2/kg^2) - m1 and m2 are the masses of the objects (space station and astronaut, respectively) - r is the distance between the center of the two objects

Given: - Mass of the space station (m1) = 19,000 kg - Mass of the astronaut in the spacesuit (m2) = 100 kg - Distance between them (r) = 100 m

Let's calculate the gravitational force using the given values.

Gravitational Force Calculation: Using the formula, the gravitational force (F) between the space station and the astronaut can be calculated as follows:

F = (6.674 × 10^-11) * ((19,000) * (100)) / (100^2)

F ≈ 1.2676 N

The gravitational force between the space station and the astronaut at a distance of 100 m is approximately 1.2676 N.

Time to Approach the Station

To calculate the time it takes for the astronaut to approach the station by a distance of 1 m under the influence of this force, we can use the equations of motion. The force acting on the astronaut will cause acceleration, and we can use the equations of motion to find the time taken.

Given: - Initial relative velocity of the station and the astronaut = 0 m/s - Distance to be covered = 1 m - Gravitational force (F) = 1.2676 N - Mass of the astronaut (m2) = 100 kg

Using the equation of motion: F = m * a

Where: - F is the force - m is the mass - a is the acceleration

We can calculate the acceleration (a) using the gravitational force and the mass of the astronaut.

a = F / m a = 1.2676 / 100 a ≈ 0.012676 m/s^2

Now, using the equation of motion: v = u + at

Where: - v is the final velocity - u is the initial velocity - a is the acceleration - t is the time

Given: - Initial velocity (u) = 0 m/s - Acceleration (a) ≈ 0.012676 m/s^2 - Distance (s) = 1 m

We can use the equation to find the time (t) it takes for the astronaut to approach the station by 1 m.

s = ut + (1/2)at^2 1 = 0 + (1/2)(0.012676)t^2 t^2 ≈ 157.4 t ≈ √157.4 t ≈ 12.55 seconds

Therefore, under the influence of the gravitational force, it would take approximately 12.55 seconds for the astronaut to approach the station by a distance of 1 m, assuming no other forces are acting on the astronaut.