How Long Does Moon E Take to Orbit Planet?

In summary, one moon has an orbital radius of r and takes 20 days to complete one orbit. The other moon has an orbital radius of 4r and completes one orbit in 80 days. Kepler's third law states that the square of the orbital period is directly proportional to the cube of the orbital radius. Therefore, moon E takes 80 days to complete one orbit because its orbital radius is 4 times that of moon D. The size of the orbit does matter in this case.
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Homework Statement



Two moons orbit a planet in nearly circular orbits. Moon D has orbital radius r, and moon E has orbital radius 4r. Moon D takes 20 days to complete one orbit. How long does it take for moon E to complete one orbit


Homework Equations



None - I think


The Attempt at a Solution



I am hoping that this problem is not complicated. Since it takes 20 days for moon D with radius r, it would take 80 days for moon E with radius 4r?

Is my reasoning correct ??
 
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  • #2
No, it isn't. What do Kepler's laws have to say about this problem?
 
  • #3
Is it just 20 days the same as moon D?

A line drawn from the sun to any planet sweeps out equal areas in equal time intervals.

Does the size - radius matter then?
 
  • #4
Ok the above doesn't make sense.

Then I don't know, really.
 
  • #5
It's not just 20 days.

Keplers second law is only valid for the same planet or moon (and it's trivial for a circular orbit)
Try the third law.
 

1. How long does it take for the Moon to orbit Earth?

The Moon takes approximately 27.3 days to orbit Earth. This is known as the sidereal month, which is the time it takes for the Moon to complete one orbit around Earth relative to the stars.

2. What is the average distance between the Moon and Earth?

The average distance between the Moon and Earth is about 238,855 miles (384,400 kilometers). However, due to the elliptical shape of the Moon's orbit, the distance can vary between 225,623 miles (363,104 kilometers) at its closest point (perigee) and 252,088 miles (405,696 kilometers) at its farthest point (apogee).

3. How does the Moon's orbit affect Earth's tides?

The Moon's orbit has a significant impact on Earth's tides. The gravitational pull of the Moon causes the water on Earth's surface to bulge out towards the Moon, creating high tides. As the Earth rotates, this bulge moves around the planet, creating low tides on the opposite side. The Sun also plays a role in tides, but the Moon's closer proximity to Earth makes its influence more significant.

4. Does the Moon's orbit change over time?

Yes, the Moon's orbit is constantly changing due to various factors such as the gravitational pull of the Sun and other planets, as well as the Moon's own internal processes. These changes are relatively small and take place over thousands of years.

5. How does the Moon's orbit affect Earth's climate?

The Moon's orbit does not directly impact Earth's climate. However, the Moon's gravitational pull helps stabilize Earth's axial tilt, which is responsible for our seasons. Without the Moon's stabilizing influence, Earth's tilt could vary more dramatically, leading to more extreme and unpredictable climate patterns.

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