Question

Звезда Арктур имеет массу, в 1,5 раза больше, чем у Солнца, светимость - в 210 раз больше, чем у Солнца, и температуру 4300 К. Чему равна ее средняя плотность? Запишите, пожалуйста, не только ответ, а и решение

Answer 1

Дано:

M = 1,5M⊙

L = 210L⊙

T = 4300 К

T⊙ = 6000 К

M⊙ = 2×10³⁰ кг

R⊙ = 700000 км = 700×10⁶ м

---------------------------------------------------

Найти:

ρ - ?

Решение:

1) Для начала мы найдем радиус звезды Арктура используя отношение светимости звезды Солнца:

L/L⊙ = (R/R⊙)²×(T/T⊙)⁴ - Отношение светимости звезды Солнца

(R/R⊙)² = L/L⊙×(T⊙/T)⁴ ⇒ R/R⊙ = √L/L⊙×(T⊙/T)⁴ ⇒  R/R⊙ = √L/L⊙ × (T⊙/T)² ⇒ R = R⊙ × √L/L⊙ × (T⊙/T)² - Нахождение радиуса звезды.

R = R⊙ × √210L⊙/L⊙ × (6000 К/4300 К)² = R⊙ × √210 × 36000000 К²/18490000 К² ≈ R⊙ × 14,49 × 1,95 ≈ 28,2555R⊙ ≈ 28,26R⊙ ≈ 28,26 × 700×10⁶ м = 19782×10⁶ м

2) Далее мы находим объем звезды Арктура:

V = 4/3 πR³ - объем звезды Арктура

V = 4/3 × 3,14×(19782×10⁶ м)³ = 4/3 × 3,14 × 7741241079768×10¹⁸ м³ = 4/3 × 24307496990471,52×10¹⁸ м³ = 32409995987295,36×10¹⁸ м³ ≈ 3,24×10³¹ м³

3) Теперь мы находим среднюю плотность звезды Арктура:

ρ = M/V = 1,5M⊙/V = 1,5×2×10³⁰ кг/3,24×10³¹ м³ = 3×10³⁰ кг/3,24×10³¹ м³ ≈ 0,926×10⁻¹ кг/м³ ≈ 0,0926 кг/м³ ≈ 0,1 кг/м³

Ответ: ρ = 0,1 кг/м³

Answer 2

Calculation of Average Density of Arcturus

To calculate the average density of Arcturus, we need to know its mass and volume. Given that the mass of Arcturus is 1.5 times greater than the mass of the Sun, and the Sun's mass is approximately 1.989 × 10^30 kilograms we can calculate the mass of Arcturus as follows:

Mass of Arcturus = 1.5 × Mass of the Sun

Let's calculate the mass of Arcturus:

Mass of Arcturus = 1.5 × 1.989 × 10^30 kilograms

Now, to calculate the volume of Arcturus, we need to use its luminosity and temperature. However, the information provided about the luminosity of Arcturus being 210 times greater than the Sun's luminosity and its temperature being 4300 K is not sufficient to directly calculate its volume.

To calculate the volume of a star, we usually need additional information such as its radius or its luminosity and effective temperature. Without this additional information, it is not possible to accurately calculate the volume and, consequently, the average density of Arcturus.

Therefore, without the necessary information, we cannot determine the average density of Arcturus.