Question

Как изменяется первая космическая скорость спутника, если он удалится от поверхности планеты на высоту, равную трем радиусам? Надо пояснить ответ.

Answer 1

$v1= \sqrt{ \frac{GM}{R} }$
$v2= \sqrt{ \frac{GM}{R+3R} }= \sqrt{ \frac{GM}{4R} }$
$\frac{ v1^{2} }{ v2^{2} }= \frac{GM4R}{GMR} =4$
$\frac{v1}{v2} =2$
$v2= \frac{v1}{2}$
Уменьшиться в 2 раза

Answer 2

Changes in First Cosmic Velocity with Satellite Altitude

The first cosmic velocity, denoted as v1, is the minimum velocity required for an object to break free from the gravitational pull of a celestial body and enter orbit around it. This velocity is determined by the mass and radius of the celestial body. As a satellite moves away from the surface of a planet to an altitude equal to three times the planet's radius, the first cosmic velocity changes.

At this altitude, the gravitational force acting on the satellite decreases, leading to a change in the first cosmic velocity required for the satellite to maintain its orbit.

The relationship between the first cosmic velocity and the altitude of the satellite can be explained using the formula:

v1 = √(g * R)

Where: - v1 = first cosmic velocity - g = acceleration due to gravity - R = radius of the planet

As the satellite moves to an altitude equal to three times the planet's radius, the value of g decreases, leading to a corresponding change in the first cosmic velocity required for the satellite to remain in orbit.

The specific change in the first cosmic velocity can be calculated using the above formula and the corresponding values for the planet's radius and the acceleration due to gravity at the new altitude.