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scZoUnD [109]
3 years ago
10

Whenever two Apollo astronauts were on the surface of the Moon, a third astronaut orbited the Moon. Assume the orbit to be circu

lar and 270 km above the surface of the Moon, where the acceleration due to gravity is 1.27 m/s2. The radius of the Moon is 1.70 ✕ 106 m. Determine the astronaut's orbital speed.
Physics
1 answer:
inysia [295]3 years ago
7 0

Answer:

v  =  1,582 \ \frac{m}{s}

Explanation:

We know that for circular motion the centripetal acceleration a_c is:

a_c = \frac{v^2}{r}

where v is the speed and r is the radius.

The centripetal acceleration for the astronaut must be the gravitational acceleration due to the gravity, as there are no other force. So

a_c = 1.27 \frac{m}{s^2}.

The radius of the orbit must be the radius of the Moon, plus the 270 km above the surface

r = 1.7 * 10^6 \ m + 270  \ km

r = 1.7 * 10^6 \ m + 270 * 10^3 \ m

r = 1.7 * 10^6 \ m + 0.270 * 10^6 \ m

r = 1.97 * 10^6 \ m

We can obtain the speed as:

v^2  = a_c r

v  = \sqrt{a_c r}

v  = \sqrt{1.27 \frac{m}{s^2} * 1.97 * 10^6 \ m}

v  = \sqrt{ 2.509 \ 10^6 \ \frac{m^2}{s^2}}

v  =  1.582 \ 10^3 \ \frac{m}{s}

v  =  1,582 \ \frac{m}{s}

And this is the orbital speed.

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