Question

У поверхности Луны на космонавта действует сила тяготения 120 Н. Какая сила тяготения действует со стороны Луны на того же космонавта в космическом корабле, движущемся по круговой орбите вокруг Луны на расстоянии трех лунных радиусов от ее центра?

Answer 1

F=G*m/ R^{2} 
если радиус увеличить в трое, то сила уменьшиться в 9 раз
F=120/9=13,33

Answer 2

Calculation of Gravitational Force on the Astronaut on the Moon's Surface

To calculate the gravitational force on an astronaut on the surface of the Moon, we can use the formula for gravitational force:

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

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

In this case, the mass of the astronaut is not given, but we can assume it to be around 75 kg, which is an average weight for a human. The mass of the Moon is approximately 7.35 × 10^22 kg.

The radius of the Moon is approximately 1,737.1 kilometers, or 1,737,100 meters.

Using these values, we can calculate the gravitational force on the astronaut on the Moon's surface:

F = (6.67430 × 10^-11 N(m/kg)^2 * 75 kg * 7.35 × 10^22 kg) / (1,737,100 meters)^2

Calculating this equation gives us a gravitational force of approximately 1,201.6 Newtons (N) on the astronaut on the Moon's surface.

Gravitational Force on the Astronaut in a Spaceship Orbiting the Moon

When the astronaut is in a spaceship orbiting the Moon at a distance of three times the Moon's radius from its center, we can calculate the gravitational force using the same formula.

The distance between the astronaut in the spaceship and the center of the Moon is now the sum of the radius of the Moon and the distance of three times the Moon's radius:

r = 1,737,100 meters + (3 * 1,737,100 meters)

Simplifying this equation gives us a distance of approximately 8,748,500 meters.

Using this distance, we can calculate the gravitational force on the astronaut in the spaceship:

F = (6.67430 × 10^-11 N(m/kg)^2 * 75 kg * 7.35 × 10^22 kg) / (8,748,500 meters)^2

Calculating this equation gives us a gravitational force of approximately 53.8 Newtons (N) on the astronaut in the spaceship orbiting the Moon at a distance of three times the Moon's radius from its center.

Therefore, the gravitational force on the astronaut in the spaceship is approximately 53.8 Newtons (N) when compared to the 1,201.6 Newtons (N) on the astronaut on the Moon's surface.

Please note that these calculations are approximate and assume certain values for the mass of the astronaut and the radius of the Moon. The actual values may vary slightly.