A satellite orbits Earth once per day. From the reference frame of the Moon, which orbits Earth once about every 27 days, what is its motion?
To determine the motion of the satellite from the reference frame of the Moon, we need to consider the relative velocities and periods of both the satellite and the Moon.
First, let's calculate the satellite's orbital period from the reference frame of the Earth. Since the satellite orbits Earth once per day, its period is 1 day or 24 hours.
Now, let's look at the motion of the Moon. The Moon orbits Earth once every 27 days. In this 27-day period, the satellite completes 27 orbits around the Earth.
To calculate the motion of the satellite from the reference frame of the Moon, we need to take into account the relative velocities. The satellite's velocity is determined by its orbit around Earth, while the Moon's velocity is determined by its orbit around Earth as well.
Since the satellite orbits Earth once per day and the Moon takes 27 days to orbit Earth, the satellite appears to move much faster than the Moon from the Moon's reference frame. In other words, the relative velocity of the satellite with respect to the Moon is much greater than the Moon's orbital velocity around Earth.
Therefore, from the reference frame of the Moon, the motion of the satellite would appear to be much faster compared to the Moon's motion. The satellite would appear to traverse its orbit around Earth at a much higher speed than the Moon's orbit, completing multiple orbits during the Moon's single orbit.
In summary, from the reference frame of the Moon, the satellite would appear to move much faster than the Moon itself, completing multiple orbits around Earth during a single orbit of the Moon.