An Earth satellite moves in a circular orbit 946 km above Earth's surface with a period of 103.8 min. What are (a) the speed and (b) the magnitude of the centripetal acceleration of the satellite?
I got an answer of 7388.897 m/s for part a, but I'm stuck on part b
To find the speed of the satellite, we can use the formula:
speed = (2πr) / T
where r is the radius of the orbit and T is the period of the satellite.
In this case, the radius of the orbit is given as 946 km above the Earth's surface. To convert this to meters, we multiply by 1000:
r = 946 km * 1000 = 946000 meters
Substituting the values into the formula, we get:
speed = (2π * 946000) / 103.8
Calculating this, we find the speed of the satellite is approximately 5807.271 m/s.
Now, to find the magnitude of the centripetal acceleration, we can use the formula:
centripetal acceleration = (speed^2) / radius
Substituting the values obtained earlier, we have:
centripetal acceleration = (5807.271^2) / 946000
Calculating this, we find the magnitude of the centripetal acceleration of the satellite is approximately 35.912 m/s².
To find the speed of the Earth satellite, we can use the formula:
v = 2πr / T
where v is the speed, r is the radius of the orbit, and T is the period of the satellite.
Given that the radius of the orbit is 946 km above Earth's surface, we need to convert it to meters:
r = 946 km = 946,000 m
The period of the satellite is given as 103.8 min, so we need to convert it to seconds:
T = 103.8 min = 103.8 * 60 s = 6228 s
Now, plugging in the values into the formula:
v = 2π * 946,000 m / 6228 s
v ≈ 2.863 * 10^5 m/s
So, the speed of the satellite is approximately 286,300 m/s.
Now, let's move on to finding the magnitude of the centripetal acceleration (ac).
The centripetal acceleration is given by the formula:
ac = v^2 / r
where ac is the centripetal acceleration, v is the speed, and r is the radius of the orbit.
Plugging in the values:
ac = (2.863 * 10^5 m/s)^2 / 946,000 m
ac ≈ 8.666 m/s^2
So, the magnitude of the centripetal acceleration of the satellite is approximately 8.666 m/s^2.