英语日期多了个农历,该怎么表达?

公元1405年农历7月11日,地球蓝色的海洋上出现了一支庞大的船队,前后有208艘船

On July 11th, lunar calendar, 1405 AD, a huge fleet of 208 shipsappeared in the blue sea of the earth.
On lunar (calendar)July 11th 1405 AD, a huge fleet of 208 shipsappeared in the blue sea of the earth.
上面两种表达是否都行?calendar在第二句可加可不加
还有这句的表达:中秋节在农历八月十五,是人们拜月的节日。
The Mid-Autumn Festival, which falls on the 15th
of lunar August, is a festival when people worship the moon.
.........................................,which falls on the lunar August 15th,............................
这两个表达都可以吗?

实际上中国农历不是严格意,义上的 lunar year calendar(在西方这种说法是指伊斯兰教国家的历法)。中国农历通常译为 traditional Chinese calendar。
第一句的表述方式更适合英语读者的思维方式:
On the date of traditional Chinese calendar July 11th, 1405 AD, a huge fleet of 208 ships appeared on the blue seas on earth.

which falls on the 15th of the lunar August 比 which falls on the lunar August 15th 更顺耳。
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