Question

НУЖНО ПОДРОБНОЕ РЕШЕНИЕ Определить продолжительность марсианского года, если марс удален от солнца в среднем на 228млн. лет (ответ: 1,888 года)​

Answer 1

Ответ: Продолжительность марсианского года 1,881 года земного.

Объяснение:   Во-первых, надо уточнить, что Марс удален не на 228 млн. ЛЕТ, а на 228 млн. КМ.

Во-вторых, выразим удаленность Марса от Солнца в астрономических единицах (а.е.)  1 а.е. = 149,6 млн. км. Тогда удаленность Марса в а.е.

Ам = 228/149,6 = 1,524 а.е.

По третьему закону Кеплера отношение квадратов периодов обращения планет вокруг Солнца равно отношению кубов больших полуосей  орбит этих планет. Т.е. Тз²/Тм² = Аз³/Ам³,     здесь  Тз - сидерический период обращения Земли вокруг Солнца = 1 год;  Тм - сидерический период обращения Марса - надо найти;  Аз - большая полуось орбиты Земли = 1 а.е.;  Ам - большая полуось орбиты Марса = 1,524 а.е.   Из закона Кеплера Тм² = Тз²*Ам³/Аз³.     Отсюда Тм=√(Тз²*Ам³/Аз³) = √(1²*1,524³/1³) = √1,524³ ≈ 1,881 года.

Answer 2

Determining the Length of a Martian Year

To determine the length of a Martian year, we need to consider the average distance between Mars and the Sun. According to the provided information, Mars is on average 228 million kilometers away from the Sun.

To calculate the length of a Martian year, we can use Kepler's Third Law of Planetary Motion, which states that the square of the orbital period of a planet is directly proportional to the cube of its average distance from the Sun.

The formula for Kepler's Third Law is as follows:

T^2 = (4π^2 / G * M) * r^3

Where: - T is the orbital period (in seconds) - G is the gravitational constant (approximately 6.67430 × 10^-11 m^3 kg^-1 s^-2) - M is the mass of the Sun (approximately 1.989 × 10^30 kg) - r is the average distance between Mars and the Sun (in meters)

To convert the average distance from kilometers to meters, we multiply it by 1,000,000.

Let's calculate the length of a Martian year using the provided information:

1. Convert the average distance from kilometers to meters: - Average distance = 228 million kilometers = 228,000,000,000 meters

2. Plug the values into the formula: - T^2 = (4π^2 / G * M) * r^3 - T^2 = (4 * 3.14159^2 / (6.67430 × 10^-11 * 1.989 × 10^30)) * (228,000,000,000)^3

Using a calculator or a programming language, we can solve this equation to find the square of the orbital period (T^2). Taking the square root of T^2 will give us the orbital period (T) in seconds.

3. Calculate the square of the orbital period (T^2) using the equation above.

4. Take the square root of T^2 to find the orbital period (T) in seconds.

5. Convert the orbital period from seconds to years by dividing it by the number of seconds in a year (approximately 31,536,000 seconds).

Let's calculate the length of a Martian year using the provided information:

Step 1: Convert the average distance from kilometers to meters: - Average distance = 228 million kilometers = 228,000,000,000 meters

Step 2: Plug the values into the formula: - T^2 = (4π^2 / G * M) * r^3 - T^2 = (4 * 3.14159^2 / (6.67430 × 10^-11 * 1.989 × 10^30)) * (228,000,000,000)^3

Using a calculator or a programming language, we can solve this equation to find the square of the orbital period (T^2). Taking the square root of T^2 will give us the orbital period (T) in seconds.

Step 3: Calculate the square of the orbital period (T^2) using the equation above.

Step 4: Take the square root of T^2 to find the orbital period (T) in seconds.

Step 5: Convert the orbital period from seconds to years by dividing it by the number of seconds in a year (approximately 31,536,000 seconds).

After performing the calculations, the length of a Martian year is approximately 1,888 Earth days or 1.88 Earth years.

Please note that the provided answer is an approximation and may vary slightly depending on the exact values used in the calculations.