an artificial satellite is moving in a circular orbit of radius 42250 km calculate its speed if it takes 24 hours to revolve around the earth
An artificial satellite is moving in a circular orbit of radius 42250 km calculate its speed if it takes 24 hours to revolve around the earth
Answer: To calculate the speed of an artificial satellite moving in a circular orbit, we need to determine the circumference of the orbit and then divide it by the time it takes to complete one revolution.
-
Calculate the circumference of the orbit:
The formula for the circumference (C) of a circle is:C = 2\pi rwhere (r) is the radius of the orbit.
Given:
r = 42250 \text{ km}So,
C = 2\pi \times 42250 \text{ km}Calculating the circumference:
C \approx 2 \times 3.14159 \times 42250 \text{ km}C \approx 265,165 \text{ km} -
Convert the time period from hours to seconds:
Given that the satellite takes 24 hours to complete one revolution, we need to convert this time into seconds to use it in our speed calculation.1 \text{ hour} = 3600 \text{ seconds}24 \text{ hours} = 24 \times 3600 \text{ seconds}24 \text{ hours} = 86400 \text{ seconds} -
Calculate the speed of the satellite:
Speed (v) is given by the formula:v = \frac{C}{T}where (C) is the circumference and (T) is the time period.
Substituting the values:
v = \frac{265,165 \text{ km}}{86400 \text{ s}}Calculating the speed:
v \approx 3.07 \text{ km/s}
Therefore, the speed of the artificial satellite is approximately (3.07 \text{ km/s}).