A satellite in a circular orbit 879.4 mi above the earth makes one complete orbit every 83.42min. What is its linear velocity? Use 3963 mi for the length of the radius of the earth.
the radius of your satellite's orbit is 3963+879.4 = 4842.4
C = 2pi*r = 30425 mi
velocity = 30425mi/83.42min = 364.73mi/min
To find the linear velocity of the satellite in a circular orbit, we can use the following formula:
Linear Velocity = 2π * Radius / Time period
First, we need to convert the altitude of the satellite from miles to the same unit as the radius of the Earth. Since the radius of the Earth is given in miles, we'll convert 879.4 mi to miles by adding it to the Earth's radius:
Altitude = 879.4 mi + 3963 mi = 4842.4 mi
Next, we can calculate the linear velocity using the formula:
Linear Velocity = 2π * (Radius + Altitude) / Time period
Plugging in the values, we get:
Linear Velocity = 2π * (3963 mi + 4842.4 mi) / 83.42 min
To simplify the calculation, let's convert the time period to hours:
Time period = 83.42 min / 60 min/hour = 1.39 hours
Now we can calculate the linear velocity:
Linear Velocity = 2π * (3963 mi + 4842.4 mi) / 1.39 hours
Linear Velocity ≈ 2π * 8805.4 mi / 1.39 hours
Linear Velocity ≈ 54868.18 mi/h
Therefore, the linear velocity of the satellite is approximately 54868.18 miles per hour.