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I’m creating an earth-like moon that orbits a gas giant planet the size of Jupiter. The planet orbits its star at the same distance mars orbits the sun and it takes the moon 295 days to orbit its planet and 24 hours to rotate on its own axis.

How long would an eclipse last on the moon?

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  • $\begingroup$ 1. Watch for tidal locking. Moons that have been around for longer than a few million years are almost guaranteed to become tidally locked. 2. Have you tried calculating the time it takes to cross through the planet's shadow at the moon's orbital velocity? $\endgroup$
    – controlgroup
    Commented Oct 25 at 18:31
  • $\begingroup$ To be clear in order to calculate orbits, the host planet is the size and mass of Jupiter? $\endgroup$
    – jdunlop
    Commented Oct 25 at 18:49
  • $\begingroup$ it would last 4.64 units if you assume same gravity $\endgroup$
    – Kilisi
    Commented Oct 25 at 18:52

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  1. I will assume that the gas giant is about the same size and mass as Jupiter.

  2. The orbital period of the satellite is given as 295 days. I will assume that this is the sidereal orbital period and the days are ordinary days 86,400 seconds long.

  3. Our dear Callisto has a sidereal orbital period around our real Jupiter of about 16.7 days.

  4. Kepler's third law of planetary motion assures us that the squares of the orbital periods are in the same proportion as the cubes of the semi-major axes of the orbits.

  5. We can then compute that the semi-major axis of the orbit of the fictional satellite is

    $$\sqrt[3]{\left(\frac{295}{16.7}\right)^2} \approx 6.8$$

    times as large as the semi-major axis of the orbit of Callisto, or about 12,900,000 km.

  6. Assuming that the star is of about the same size as out own Sun (not specified in the question) and given that the gas giant orbits the star at the same distance as Mars orbits our Sun, the gas giant's shadow will extend to a distance of about 22,000,000 km.

  7. Jupiter has a diameter of about 133,700 km. At a distance of 12,900,000 km the shadow will have a diameter of 78,700 km, subtending an angle of about 0.006 radians or 0.34 degrees.

  8. The satellite travels 360° on its orbit in 295 days, or about 1.2 degrees per day. (I'm too lazy to compute the synodic period.) It will cross the shadow of the planet in about 0.28 days or 6.8 hours.

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  • $\begingroup$ Assuming the host planet's orbit about the sun and the moon's orbit about the host are coplanar, a 13 million km semi-major axis means that the sun->moon distance varies by ~10% every orbit! $\endgroup$
    – jdunlop
    Commented Oct 25 at 22:08
  • $\begingroup$ @jdunlop: Yes it would. The geometry is either given in the question, or at least implied. $\endgroup$
    – AlexP
    Commented Oct 25 at 22:30
  • $\begingroup$ Oh, I wasn't suggesting the calculation was wrong. More that I'd expect some wild consequences of this orbital arrangement for the occupants of the earth-like moon. $\endgroup$
    – jdunlop
    Commented Oct 25 at 22:36

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