Question

1. Whenever two Apollo astronauts were on the surface of the Moon, a third astronaut orbited the Moon. Assume the orbit to be circular and 100 km above the surface of the Moon, where the acceleration due to gravity is 1.52 m/s2. The radius of the Moon is 1.70 × 106 m. Determine

   (a) the astronaut’s orbital speed, and

2. (b) the period of the orbit.

3. A space station, in the form of a wheel 120 m in diameter, rotates to provide an “artificial gravity” of 3.00 m/s2 for persons who walk around on the inner wall of the outer rim. Find the rate of rotation of the wheel (in revolutions per minute) that will produce this effect.

Answer 1

Ans:-

Given data: r1= 100km, g= 1.52m/s^2, r0 = 1.7*10^6m

A] using the basic formula for circular motion

ac= V^2/r

v= sqrt (ac*r)

v = sqrt (g(r1 + r0)

v= sqrt (1.52 (100*10^3 + 1.7*10^6)

v= 1.65km/s

b] the astronaut travels the circumference at a constant speed so

∆x = v∆t

T = 2πr/v = 2πr/ sqrt(ac*r)

T = 2π sqrt (r/ac)

T = 2π sqrt [(100*10^3 + 1.7*10^6)/1.52]

T= 6.84ks

T= 1.90hrs

2. d= 120m, a= 3m/s^2

r= 60m,

Now calculated velocity

a= v^2/r

v^2 = a*r =3*60= 180

v= 13.42m/s

T= 2π r/V

= 2*3.14*60m/13.42m/s

T = 28.08s = 0.468min

1/0.468 = 2.14rev/min