from the formula sheet to solve the following: remember to show your work, inclu
ID: 112303 • Letter: F
Question
from the formula sheet to solve the following: remember to show your work, including ALL unit conversions, and use scientific notation if appropriate. On May 30, 2016, Mars reached opposition with Earth: on that date, it was 0.503 AU from Earth had an angular size in the sky of 18.4 arcseconds. Estimate the actual diameter of Mars in km. Calculate the distance from the Earth to the Moon at perigee (closest) and apogee (furthest) given the actual diameter of the Moon as 3476 km, and the angular size of the Moon is 0.546 degree (at perigee) and 0.491 degree (at apogee). Compare your two answers using a ratio (distance at apogee over perigee).Explanation / Answer
4. 1arcsec = 1/3600 arcdegree
18.4 arcsec = 18.4/3600 arcdegree = (2pi/180) * (18.4/3600) radian = 1.784 x 10-4 radian
we know, Mars diameter = theta * distance
mars diameter = 1.784 x 10-4 x 0.503 x1.496 x 108 [1 AU= 1.496 x 108 km]
= 13424.38 km
5) answer
at perigee, theta= 0.549 ° = 0.549 * (2pi/180) = 0.0191601
at apogee, theta = 0.491 ° = 0.491 * (2pi/180) = 0.0171359
distance r= diameter / theta
distance at perigee = 3476 / 0.0191601 km = 181418.677 km (Answer)
distance at apogee = 3476 / 0.0171359 km = 202848.989 km (Answer)
apogee / perigee in distance = 1.1181 (Answer)
Note: if all calculation is done in calculator without eliminating higher decimal value then, ration will be nearer to 1.034.
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