A satellite that is 4175 miles from the center of the earth, orbits with a period of 90 minutes. What is its centripetal acceleration?
acceleration= v^2/r=
= (2pir/period)^2/r= 2PI*(r)/period^2
no change 90 min to seconds, and 4175 miles to meters, and you have it.
F = G M m/r^2 = m Ac
so
Ac = G M/r^2
G = 6.67 * 10^-11
M = 6 * 10^24 kg
Copy this
4175 miles = meters
into a Google search box and get
r = 6.72*10^6 meters
and 90 minutes is 5,400 seconds
To calculate the centripetal acceleration of the satellite, we need to use the following formula:
Centripetal Acceleration (a) = (Velocity (v))^2 / Radius (r)
First, let's find the velocity of the satellite. We know that the period (T) of the orbit is 90 minutes, which means it takes 90 minutes for the satellite to complete one orbit around the Earth.
To calculate the velocity, we'll need to convert the period from minutes to seconds, as the standard unit of velocity is meters per second.
90 minutes = 90 * 60 seconds = 5400 seconds
Next, we'll calculate the velocity using the formula:
Velocity (v) = 2 * PI * Radius (r) / Period (T)
The radius of the satellite's orbit is given as 4175 miles, but we need to convert it to meters for consistent units.
1 mile = 1609.34 meters (approximately)
Radius (r) = 4175 miles * 1609.34 meters/mile = 6,706,205 meters
Now we can calculate the velocity:
Velocity (v) = 2 * PI * 6,706,205 meters / 5400 seconds
Next, we will substitute the calculated velocity and the given radius into the centripetal acceleration formula:
Centripetal Acceleration (a) = (Velocity (v))^2 / Radius (r)
Centripetal Acceleration (a) = ((2 * PI * 6,706,205 meters / 5400 seconds))^2 / 6,706,205 meters
Now, we can plug in the values and simplify the equation to find the centripetal acceleration.