Answer: 58,045,522,878.8 meters
Explanation:
Ok, the data we have is
Period = T = 88 days
Radial acceleration = ar = 3.96x10^-2 m/s^2
And we know that the equation for the radial acceleration is:
ar = v^2/r = r*w^2
Where v is the velocity. r is the radius and w is the angular velocity.
And we know that:
w = 2*pi*f
where f is the frequency, and:
T = 1/f.
Then we can write:
w = 2*pi/T
and our equation becomes:
ar = r*(2*pi/T)^2
Now we solve this for r.
First we need to use the same units in both equations, so we want to write T in seconds.
T = 88 days,
A day has 24 hours, and one hour has 3600 seconds:
T = 88*24*3600 s =7,603,200s
Then:
3.96x10^-2 m/s^2 = r*(2*3.14/7,603,200s)^2
r = (3.96x10^-2 m/s^2) /(2*3.14/7,603,200s)^2 = 58,045,522,878.8 meters
