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

Asked on by pavilion77

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enotechris | College Teacher | (Level 2) Senior Educator

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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)

Sources:

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