Question

Отношение массы Меркурия к массе Земли равно 0,06, а отношение среднего радиуса Меркурия к среднему радиусу Земли — 0,4. Чему равна сила притяжения спускаемого на Меркурий аппарата массой 219 кг? Считать ускорение свободного падения на поверхности Земли равным 9,8 м/с2.

Answer 1

Ответ:

Сила равна 804.825 Ньютонам

Answer 2

Calculation of the gravitational force on the spacecraft on Mercury

To calculate the gravitational force on a spacecraft with a mass of 219 kg on Mercury, we need to 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 is the mass of the spacecraft (219 kg) - m2 is the mass of Mercury (which we need to calculate) - r is the distance between the center of Mercury and the spacecraft (which we need to calculate)

To find the mass of Mercury, we can use the given information about the ratio of the masses of Mercury and Earth. The ratio of the mass of Mercury to the mass of Earth is 0.06.

Let's calculate the mass of Mercury:

m2 = 0.06 * mEarth

Now, let's find the distance between the center of Mercury and the spacecraft. The ratio of the average radii of Mercury and Earth is 0.4.

r = 0.4 * rEarth

Given that the average radius of Earth is approximately 6,371 km (6,371,000 meters) we can calculate the radius of Mercury:

rMercury = 0.4 * 6,371,000 meters

Now, we have all the values needed to calculate the gravitational force on the spacecraft on Mercury.

Let's plug in the values into the formula:

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

F = (6.67430 × 10^-11 N(m/kg)^2) * (219 kg * 0.06 * mEarth) / (0.4 * rEarth)^2

Please note that we need to convert the units to be consistent. The gravitational constant is given in SI units, so we need to convert the mass of Earth and the radius of Earth to kilograms and meters, respectively.

Let's calculate the gravitational force on the spacecraft on Mercury using the given information:

F = (6.67430 × 10^-11 N(m/kg)^2) * (219 kg * 0.06 * mEarth) / (0.4 * rEarth)^2

F = (6.67430 × 10^-11 N(m/kg)^2) * (219 kg * 0.06 * 5.972 × 10^24 kg) / (0.4 * 6,371,000 meters)^2

F = (6.67430 × 10^-11 N(m/kg)^2) * (0.074 * 5.972 × 10^24 kg) / (0.4 * 6,371,000 meters)^2

F = (6.67430 × 10^-11 N(m/kg)^2) * (0.074 * 5.972 × 10^24 kg) / (0.4 * 6,371,000 meters)^2

F ≈ 1.09 N

Therefore, the gravitational force on the spacecraft with a mass of 219 kg on Mercury is approximately 1.09 N.

Please note that this calculation assumes that the spacecraft is at the surface of Mercury. The gravitational force would vary depending on the altitude above the surface.