Question

Супутник рухається круговою орбітою на висоті 630 км. Період обертання супутника навколо Землі 97,5 хвилин. Радіус Землі прийняти 6400 км. Визначте швидкість і частоту обертання супутника. ​

Answer 1

Ответ: 1,7 *10⁻⁴ с⁻¹ или Гц; 7505м/с

Объяснение:

Дано:

h=630 км=630000 м

Т=97,5 мин=5850 с

R₃=6400 км=6400000 м

Найти: V, ν

Решение:

Радиус окружности орбиты

R=R₃+h=7030000 (м)

V= 2πR/T = 2πRν

ν = 1/T

ν = 1/5850 с = 1,7 *10⁻⁴ с⁻¹ или Гц

V = 2*3,14*(6,3*10⁵ м + 64*10⁵ м) * 1,7 10⁻⁴ с⁻¹ ≈ 7505 м/с

Answer 2

Calculation of Satellite's Speed:

To determine the speed of the satellite, we can use the formula for the circumference of a circle:

Circumference = 2 * π * radius

Given that the radius of the Earth is 6400 km, we can calculate the circumference of the satellite's orbit:

Circumference = 2 * π * 6400 km

Let's calculate the circumference:

Circumference = 2 * 3.14159 * 6400 km = 40,212.8 km

Since the satellite completes one orbit in 97.5 minutes, we can calculate its speed by dividing the circumference by the time taken:

Speed = Circumference / Time

Let's calculate the speed:

Speed = 40,212.8 km / 97.5 minutes

To convert the speed to km/h, we need to multiply it by 60 (to convert minutes to hours):

Speed = (40,212.8 km / 97.5 minutes) * 60 = 24,800 km/h

Therefore, the speed of the satellite is approximately 24,800 km/h.

Calculation of Satellite's Frequency of Rotation:

The frequency of rotation of the satellite can be calculated using the formula:

Frequency = 1 / Time

Given that the time period of rotation is 97.5 minutes, we can calculate the frequency:

Frequency = 1 / 97.5 minutes

To convert the frequency to rotations per hour, we need to multiply it by 60 (to convert minutes to hours):

Frequency = (1 / 97.5 minutes) * 60 = 0.6154 rotations per hour

Therefore, the frequency of rotation of the satellite is approximately 0.6154 rotations per hour.

Please note that these calculations assume a circular orbit and do not take into account factors such as atmospheric drag or variations in the Earth's gravitational field.