Question

Визначте прискорення вільного падіння поблизу поверхні астероїда. Вважайте, що маса астероїда дорівнює 87‧〖10〗^18 кг, а середній діаметр становить 430 км.

Answer 1

Можно считая астероид однородным шаром оценить ускорение свободного падения по стандартной формуле

$\displaystyle g = \frac{GM}{R^2} = \frac{4 G M}{D^2}\approx0.126$

Примерно 0.126 м/с^2

Answer 2

Calculation of Free Fall Acceleration near the Surface of an Asteroid

To calculate the free fall acceleration near the surface of an asteroid, we can use Newton's law of universal gravitation. According to this law, the gravitational force between two objects is given by the equation:

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^2/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 calculate the free fall acceleration near the surface of an asteroid. The free fall acceleration is the acceleration experienced by an object in free fall due to the gravitational force. Near the surface of an asteroid, we can assume that the distance between the center of the asteroid and an object on its surface is equal to the radius of the asteroid.

Given the mass of the asteroid (87 × 10^18 kg) and the average diameter (430 km), we can calculate the radius of the asteroid as half of the diameter.

Radius of the asteroid = 430 km / 2 = 215 km = 215,000 m

Now, we can substitute the values into the equation to calculate the free fall acceleration near the surface of the asteroid.

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

F = (6.67430 × 10^-11 N m^2/kg^2) * (87 × 10^18 kg) / (215,000 m)^2

Calculating this equation will give us the free fall acceleration near the surface of the asteroid. However, since we don't have the exact value of the gravitational force, we cannot provide a precise answer without further information.

Please note that the calculation assumes a spherically symmetric asteroid and neglects other factors that may affect the acceleration, such as the irregular shape of the asteroid, its rotation, and the presence of other celestial bodies nearby.

If you have any further questions, feel free to ask!