Question

Orbit of the Sagittarius dwarf galaxy View edge-on to the Milky Way disk 16 kpc 8 kpc Sun Sag dwarf 210 km/s a) By how many metres does the Sagittarius galaxy move in a year? In 100 years? (Your answers may sound like a lot, but compare them to its distance from us in metres). b) By how much does the angular position of the centre of the Sagittarius Dwarf as seen from Earth change over a year? Over the course of 100 years? Do you think this change be detected by (i) the naked eye over a year? (ii) in two photographs taken 100 years apart from ground-based telescopes?

Answer 1

Velocity of sag galaxy = 210 km/s distance moved in one year = 210 times 3.154 times 10^7 km = 6.62 times 10^12 m distance moved in 100 year = 6.62 times 10^14 m now distance of sag galaxy from us = 24 kpc 24 times 10^3 times 3.08 times 10^16 m = 7.4 times 10^20 m so distance moved by sag galaxy in 100 years is 10^6 times smaller then distance from as (b) angular position change once a year delta theta = 6.62 times 10^12/7.4 times 10^20 = 89 times 10^-9 red hence eye was angular resolution ~ 3 times 10^-4 red so naked eye can't detect the change now angular position charge in 100 year delta theta = 6.62 times 10^14/7.4 times 10^20 = 8.9 times 10^7 rad According to the angular resolution telescope is given as theta = 1.22 lambda/D so with wavelength of few and diameter of lenses of few