Why are the orbital periods of the moons of the larger planets r so short as compared to Earths moon?

off the top of my head it would probably be because due to the larger planets stronger gravity, they would have to travel faster to remain in orbit. Any slower and they would crash into the planet any faster they would just leave.

My assumption would be the greater gravity of the larger planets exerting a greater force upon the moons and therefore increasing the speed at which they orbit, if this is the case, despite the greater time to taken to orbit a larger body, the increased speed is presumably fast enough such that the orbital period of the moons of larger planets than Earth is faster than that of Earth's moon.

Planets with stronger gravity require higher speeds to stay in orbit around them as a higher centrifugal force is necessary to compensate for the gravitational pull.

Because the moons of the larger planets need to orbit much faster than our moon because of the much higher gravity of the larger planet.
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The moon is huge compared to Earth. Large planets with tiny satellites will have them zipping around a lot faster. For an easy understanding, you may want to compare the moon with Io, which is about the same size, and density, and about the same distance from Jupiter as the moon is from Earth.

I guess cause thier closer.

Our moon orbits the Earth in 29 days.

Some of the moons of Jupiter have longer orbital periods than our own moon:
- Themisto 129 days
- Leda 241 days
- Helike 602 days, etc.

Some of the moons of Saturn have long orbital periods as well:
- Iapetus 69 days
- Phoebe 545 days

So your question is not really completely valid.

In general, though, the larger moons of the jovian planets are also closer to their primaries and so have shorter orbital periods - the closer a moon is (and the more massive the planet is), the faster it has to move to stay in orbit.

If you check you will see that five planets have a moon at about the 210,000 to 240,000 mile range:  Earth, Jupiter, Saturn, Uranus and Neptune.  However, their periods are quite different.  If you rank them from fastest (Io around Jupiter, 1.87 days) to slowest (our Moon around Earth, 27.32 days) you find that you have also ranked the planets in descending order of mass.  The reason is quite simple, the speed of an object in orbit depends on two things:  distance from its primary (which in this case we are pretty much holding constant), and the mass of the primary.
This follows from Newton's Universal Law of Gravitation:  F=G(m1+m2)/r2, where G is a constant, m1 is the mass of the primary, m2 the mass of the satellite, and r2 is the square of the distance of the satellite from the primary.