Solving the Astronauts' Orbital Speed & Period Around the Moon

In summary, the conversation discusses a problem involving the orbit of three astronauts on the surface of the moon, with one astronaut orbiting above. The question asks for the calculation of the orbital speed and period of the third astronaut's orbit using Newton's second law in circular motion. The answer is provided in the question, stating that the orbit is circular and 100km above the surface of the moon, with a radius of 1.70 x 10^6 and an acceleration due to gravity of 1.52 m/s. The equation a=v^2/r is used to find the orbital speed, and the period is given in the question.
  • #1
XodoX
203
0
Hey guys, I got the following problem.


Whenever two Apollo astronauts were on the surface of the moon, a third astronaut orbited the moon. Assume the orbit to be circular and 100km above the surface of the moon, where the acceleration due to gravity is 1.52 m/s. The radius of the moon is 1.70 x 106. Determine the astronauts orbital speed and the period of the orbit.

It seems east, btu I still have no idea how to get started on this one:frown:
 
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  • #2
What equations do you know that could give you a starting point?

The Bob
 
  • #3
None. got all m or T in it, so thatös not going to work.
 
  • #4
What is the equation Newton's second law in circular motion?

The Bob
 
  • #5
Thats a= v2/r.

You mean v= square root of a * r ? Ok, I didn't think of that then. But what about the period?
 
  • #6
Well that is answered for you in the question:
Assume the orbit to be circular [...]

This enough of a hint?

The Bob
 

1. What is the purpose of solving the astronauts' orbital speed and period around the Moon?

The purpose of solving the astronauts' orbital speed and period around the Moon is to accurately predict and plan their trajectory in order to successfully orbit and land on the Moon.

2. How is the orbital speed and period of the astronauts around the Moon calculated?

The orbital speed and period of the astronauts around the Moon is calculated using Newton's law of universal gravitation, which takes into account the mass of the Moon, the distance between the Moon and the spacecraft, and the gravitational constant.

3. Why is it important to accurately calculate the astronauts' orbital speed and period around the Moon?

Accurate calculations of the astronauts' orbital speed and period around the Moon are crucial for a successful mission. If the calculations are incorrect, the spacecraft could miss the Moon entirely or crash into its surface, jeopardizing the safety of the astronauts.

4. Can the orbital speed and period around the Moon be adjusted during the mission?

Yes, the orbital speed and period around the Moon can be adjusted during the mission. This can be done by firing the spacecraft's engines to change its velocity and trajectory. However, this requires precise calculations and careful planning to ensure a safe and successful maneuver.

5. Are there any factors that can affect the astronauts' orbital speed and period around the Moon?

Yes, there are several factors that can affect the astronauts' orbital speed and period around the Moon, such as the gravitational pull of other celestial bodies, solar radiation, and the spacecraft's own mass and velocity. These factors must be taken into account when calculating and adjusting the astronauts' trajectory.

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