2. (7 points) On the night of January 21st, 2019, there was a total lunar eclipse during a supermoon. At the time, the moon was close to perigee, at a distance of $$351837 km$$ from the earth, which was $$1.4721\times 10^8$$ km from the sun. The gamma (γ) of a lunar eclipse refers to the closest distance between the center of the moon and the center of the shadow, expressed as a fraction of the earth’s radius. For this eclipse, $$γ = 0.3684$$. Given this information, find the closest estimate for the duration of totality of the eclipse.