Because of the presence of Jupiter, the Sun moves in a small orbit of radius 742,000 km with a period of 11.86 years. (a) Calculate the Sun's orbital speed in meters per second.
(b) An astronomer on a hypothetical planet orbiting the star Vega, 25 light-years from the Sun, wants to use the astrometric method to search for planets orbiting the Sun. What would be the
angular diameter of the Sun's orbit as seen by this alien astronomer? Would the Sun's motion be discernible if the alien astronomer could measure positions to an accuracy of 0.001 arcsec?
(c) Repeat part (b), but now let the astronomer be located on a hypothetical planet in the Pleiades star cluster, 360 light-years from the Sun. Would the Sun's motion be discernible to this astronomer?
The text offers the answers but I am not coming up with them using the formulas, please assist with the proper formula and calculations needed to get the answer.
Sun's orbital speed = orbit distance / time
orbit distance = 2*pi*radius = 2*pi*742,000 km = 4,662,123 km
time = 11.86 years = 433 days = 103,894 hrs = 6,233,616 min = 374,016,960 sec
Sun's orbital speed = 4,662,123 km / 374,016,960 sec
= 0.0125 km / sec
= 12.47 meters / ...