Heýssukai.

Problem 1：Sundial.

The following diagram represents a sundial, for which the triangle, called a gnomon, casts a shadow onto the surrounding surface, which has markings and numbers representing important information. It is known that this sundial is located either between the Tropic of Cancer and the Arctic Circle or between the Tropic of Capricorn and the Antarctic Circle.

Problem 1：Neptune.

Given that Neptune will be at opposition on 21 September 2024, calculate in which year Neptune was last at opposition near the time of the nort hern-hemisphere spring equinox. Assume that the orbits of Earth and Neptune are circular.

$(5points)$

Problem 2：Magnetic field.

An emission line of wavelength $ \lambda =600nm $ was observed in the spectrum of a white dwarf.Assuming that it originates from the interaction of a free non-relativistic electron with a magnetic field

$(a).$ calculate the magnetic flux density of the field;

$(b).$ estimate the wavelength of another spectral line, the discovery of which could confirm that the lines originate from particles of a plasma interacting with the magnetic field.

$(5points)$