Homework #9 (Due Dec. 6, 2017) Find the position of the planet Mars at time-Dece
ID: 1794693 • Letter: H
Question
Homework #9 (Due Dec. 6, 2017) Find the position of the planet Mars at time-December 6, 2017, 5:00 am EST. You will do this by following the steps shown below (a) Convert the timet to Universal Time (Gust add 5 hours to EST (b) Find the Julian day corresponding to time (using the result of part (a). (c) Find the time elapsed from the epoch time to timet (i.e., findt -To). (d) Find the mean daily motion n (using Kepler's Third Law, Eq. 1). (Ans. 1.455649 x 10-3 rev/day) (e) Find the mean anomaly M of Mars at time(Eq 2). (t) Solve Kepler's equation (Eq. 3) to find the eccentric anomaly E of Mars at time t. See Section 3 for information on solving Kepler's Equation. (g) Find the true anomaly f of Mars at timet (Eq. 4) h) Find the distance r of Mars from the Sun at time t (Eq. 5) (0) Find the argument of latitude u of Mars at time t CEa. 6. (j) Find the heliocentric ecliptic cartesian coordinates of Mars at time 1 (x, y, z) (Eqs. 7-9). (k) Find the geocentric ecliptic cartesian coordinates of Mars at time t xe e) (Eqs. 10-12). (1) Find the ecliptic longitude and ecliptic latitude of Mars at time t (Eqs. 13- 14). Find the right ascension and declination of Mars at time i (Eqs. 15-16). (n) Find the Greenwich sidereal time GST for timer at Washington DC (Eq·17) (o) Find the local hour angle H. (Eq. 18) (p) Find the azimuth A and elevation h of Mars at time t, as seen from Washington (m) D.C. (Eqs. 19-20) Is Mars above the horizon (h o)? If so, you may wish to go outside and see if you can see it at the place you predict it to be.Explanation / Answer
given, t = December 6, 2017, 5:00 AM EST
a. in universal time
t = 5 + 5 = 10:00 AM
b. Julian day number
JDN = (1461 × (2017 + 4800 + (12 14)/12))/4 +(367 × (12 2 12 × ((12 14)/12)))/12 (3 × ((2017 + 4900 + (12 - 14)/12)/100))/4 + 6 32075
JDN = 2489544 + 3675187 + 6 32075 = 2452655
Julian Day, JD = JDN + (hour - 12)/24 + (minute)/1440 + second/86400
JD = 2452654.91666667
c. considering To = 1 January, 2000 12:00 AM
t - to = 6541.43274
d. mean daily motion of mars = n
orbital period, T = 687 days
hence
n = 2*pi/687 = 9.145*10^-3 rev per day
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