Question

Масса планеты в 16 раз превышает массу спутника. Расстояние между их центрами 600000 км. На каком расстоянии от центра планеты находится космический корабль когда силы притяжения к планете и спутнику скомпенсированы.

Answer 1

В искомой точке гравитационные силы равны:
GmM₁/x² = GmM₂/(L-x)²
G - гравитационная постоянная,
m - масса космокорабля
M₁ - масса планеты
M₂ - масса спутника
L - расстояние между их центрами
x - расстояние от центра планеты до точки, в которой силы притяжения к планете равно силе притяжения к спутнику.
Решая уравнение относительно x получим:
x = L√(M₁/M₂)/(1 + √(M₁/M₂)) = L*√16/(√16 + 1) = L*4/5 = 600000*4/5 = 480 000 км

Answer 2

Calculation of the Distance from the Center of the Planet

To determine the distance from the center of the planet where the gravitational forces from the planet and the satellite are balanced, we can use the concept of gravitational force and the equation for gravitational attraction.

The gravitational force between two objects can be calculated using Newton's law of universal gravitation:

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

Where: - F is the gravitational force between the 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 - r is the distance between the centers of the two objects

In this case, we have a planet and a satellite. Let's assume the mass of the planet is M and the mass of the satellite is m. The given information states that the mass of the planet is 16 times greater than the mass of the satellite.

So we have: - Mass of the planet (M) = 16 * Mass of the satellite (m)

The distance between the centers of the two objects is given as 600,000 km.

To find the distance from the center of the planet where the gravitational forces are balanced, we need to find the value of r in the equation.

Since the gravitational forces from the planet and the satellite are balanced, the equation can be written as:

G * (M * m) / r^2 = G * (m * m) / (600,000)^2

Simplifying the equation, we can cancel out the gravitational constant (G) and the mass of the satellite (m):

M / r^2 = 1 / (600,000)^2

Now we can solve for r:

r^2 = (600,000)^2 / M

Taking the square root of both sides:

r = sqrt((600,000)^2 / M)

To calculate the value of r, we need to know the mass of the planet. Unfortunately, the search results provided do not contain the necessary information to determine the mass of the planet. Therefore, without additional information, we cannot calculate the exact distance from the center of the planet where the gravitational forces are balanced.

Please provide the mass of the planet or any additional information to proceed with the calculation.