Question

Определите массу Юпитера сравнением системы Юпитера со спутником с системой Земля - Луна, если первый спутник Юпитера отстоит от него на 422 000 км и имеет период обращения 1,77 сут. Данные для Луны должны быть вам известны.

Answer 1

Ответ:

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Answer 2

Determining the Mass of Jupiter

To determine the mass of Jupiter compared to the Earth-Moon system, we can use the information provided about the first moon of Jupiter and its orbital period. However, it is important to note that the given information does not include specific numerical values for the mass of the Moon or the distance between the Earth and the Moon. Therefore, we will need to rely on existing knowledge to provide an estimate.

1. Determining the Mass of Jupiter:

To estimate the mass of Jupiter, we can use Kepler's Third Law, which states that the square of the orbital period of a planet or moon is proportional to the cube of its average distance from the central body. This law allows us to compare the orbital periods and distances of different celestial bodies.

Let's assume that the given information about the first moon of Jupiter is accurate. The moon's orbital period is stated as 1.77 days, and its average distance from Jupiter is given as 422,000 km.

To compare this with the Earth-Moon system, we need to know the orbital period and average distance of the Moon from the Earth. The average distance between the Earth and the Moon is approximately 384,400 km, and the Moon's orbital period is approximately 27.3 days.

Using these values, we can set up a proportion to compare the mass of Jupiter to the Earth-Moon system:

Jupiter's mass / Moon's mass = (Jupiter's distance / Moon's distance)^(3/2) * (Moon's period / Jupiter's period)^(2)

Let's calculate this:

Jupiter's distance / Moon's distance = (422,000 km) / (384,400 km) = 1.097

Moon's period / Jupiter's period = (27.3 days) / (1.77 days) = 15.42

(Jupiter's distance / Moon's distance)^(3/2) * (Moon's period / Jupiter's period)^(2) = 1.097^(3/2) * 15.42^(2) ≈ 1.097 * 15.42^(2) ≈ 1.097 * 237.8 ≈ 260.7

Therefore, the mass of Jupiter is estimated to be approximately 260.7 times the mass of the Moon compared to the Earth-Moon system.

Please note that this is an estimate based on the given information and assumptions made about the mass of the Moon and the distance between the Earth and the Moon. The actual mass of Jupiter may vary.