2.A spy satellite is in circular orbit around Earth. It makes one revolution in 6.02 hours.
(a) How high above Earth's surface is the satellite?
(b) What is the satellite's acceleration?
i dint know
The period of an orbitig satellite is given by T = 2(Pi)sqrt[r^3/µ] where T = the orbital period in seconds, r = the orbit radius and µ = the gravitational constant of the Earth.
Therefore, with T = 6.02(3600) = 21,672 seconds
21,672 = 2(3.14)sqrt[r^3/1.408x10^16]
from which r = 10,440 miles.
Subtracting the Earth's radius of 3963 miles results in an orbit altitude of 6477 miles.
To answer these questions, we can use the concepts of circular motion and gravitational force.
(a) To determine the height of the satellite above Earth's surface, we need to use the formula for the circumference of a circle.
Circumference of a circle = 2 * π * radius
In this case, the satellite completes one revolution in 6.02 hours, which is the time it takes for it to travel the circumference of its circular orbit. Therefore, we can equate the circumference to the distance traveled by the satellite in 6.02 hours.
Distance traveled by the satellite = Circumference of the orbit
Since the satellite is in a circular orbit around Earth, the distance traveled by it is equal to the length of the circular orbit. So we have:
Distance traveled by the satellite = 2 * π * radius
Now, rearranging the formula, we can solve for the radius:
radius = (Distance traveled by the satellite) / (2 * π)
To calculate the height above Earth's surface, we need to subtract the Earth's radius from the satellite's radius:
Height above Earth's surface = radius - Earth's radius
By substituting the values into the above equation, you can determine the height above Earth's surface.
(b) To calculate the satellite's acceleration, we need to use the equation for centripetal acceleration.
Centripetal acceleration (a) = (Velocity squared) / Radius
Since we know the time taken for one revolution, we can calculate the satellite's velocity by dividing the distance traveled by the time taken. Then we substitute the value of velocity and radius into the formula to find the acceleration.
Acceleration = (Velocity squared) / Radius
By plugging in the appropriate values, you can calculate the satellite's acceleration.