Answer:
(a) Speed v=1505.3 m/s
(b) Time Period=9001.56s
Explanation:
Radius of moon r=1.70×10⁶m
Acceleration due to gravity g=1.06m/s²
height h=458km=458000
For Part (a)The astronaut’s orbital speed.
By using the centripetal equation:
[tex]F=\frac{mv^2}{R+h}=mg\\ v^2=g(R+h)\\v=\sqrt{g(R+h)}[/tex]
Substitute the given values
So
[tex]v=\sqrt{1.05m/s^2(1.70*10^6m+458*10^3m)}\\ v=1505.3m/s[/tex]
For Part(b) The period of the orbit.
Total distance=Circumference
[tex]=2\pi (R+h)\\=2\pi (1.70*10^6m+458000m)\\=13.55*10^6m[/tex]
Speed v=1505.3m/s
Time Period=Distance/Velocity
[tex]=\frac{13.55*10^6m}{1505.3m/s}\\ =9001.56s[/tex]
Time Period=9001.56s
