The orbit of a moon about its planet is approximately circular, with a mean radius of 6.08 X 10^8m.The orbit of a moon about its planet is approximately circular, with a mean radius of 6.08 X...
The orbit of a moon about its planet is approximately circular, with a mean radius of 6.08 X 10^8m.
The orbit of a moon about its planet is approximately circular, with a mean radius of 6.08 X 10^8m. It takes 18 days for the Moon to complete one revolution about the planet. Find the mean orbital speed of the Moon. Answer in units of m/s
Find the Moon's centripetal acceleration. Answer in units of m/s^2
1 Answer
enotechris | College Teacher | (Level 2) Senior Educator
For an orbit that is close to circular, the formula for calculating the mean orbital speed is:
1.) v = 2(pi)*r / T
where v is velocity, r is the length of the radius, and T is the time of orbit. Since we're calculating in units of seconds, we must convert 18 days into the same units:
2.) (60 sec/1 min)*(60 min/1 hour)*(24 hour/1 day) = 86400 sec/day
3.) T = (86400 sec/day)* 18 days = 1.56*10^7 sec
4.) v = 2(3.1416) * (6.08*10^8 m) / (1.56*10^7 sec)
5.) v = (3.82 * 10^9 m) / (1.56*10^7 sec)
6.) v = 2.45 * 10^2 = 245 m/sec
Centripetal Acceleration is given by a = v^2 / r, so
7.) a = (245 m/sec)^2 / (6.08*10^8 m)
8.) a = (6.0025*10^4 m^2/sec^2) / (6.08*10^8 m)
9.) a = .9872*10^-4 = (9.872*10^-5 m/sec^2)