Question

Find the position of the planet Uranus at time t D December 4, 2019, 8:00 pm EST. You will do this by following the steps shown below.

(a) Convert the time t to Universal Time (just add 5 hours to EST).

(b) Find the Julian day corresponding to time t (using the result of part (a)).

(c) Find the time elapsed from the epoch time to time t (i.e., find t T0).

(d) Find the mean daily motion n (using Kepler’s Third Law, Eq. 1). (Ans. n D 3:267686 105 rev/day)

(e) Find the mean anomaly M of Uranus at time t (Eq. 2).

(f) Solve Kepler’s equation (Eq. 3) to find the eccentric anomaly E of Uranus at time t. See Section 3 for information on solving Kepler’s Equation.

(g) Find the true anomaly f of Uranus at time t (Eq. 4).

(h) Find the distance r of Uranus from the Sun at time t (Eq. 5).

(i) Find the argument of latitude u of Uranus at time t (Eq. 6).

(j) Find the heliocentric ecliptic cartesian coordinates of Uranus at time t (x; y; z) (Eqs. 7–9).

(k) Find the geocentric ecliptic cartesian coordinates of Uranus at time t (xe; ye; ze) (Eqs. 10–12).

(l) Find the ecliptic longitude and ecliptic latitude ˇ of Uranus at time t (Eqs. 13–14).

(m) Find the right ascension ˛ and declination ı of Uranus at time t (Eqs. 15–16).

(n) Find the Greenwich sidereal time GST for time t at Washington D.C. (Eq. 17)

(o) Find the local hour angle H. (Eq. 18)

(p) Find the azimuth A and elevation h of Uranus at time t, as seen from Washington D.C. (Eqs. 19–20) Is Uranus above the horizon (h>0)? If so, you may wish to go outside and see if you can see it at the place you predict it to be. (You will need a telescope.)

Answer 1

Solutions The position of the planet 48anus at given time (H) - December 6, 2017, 5:00 AMEST a) in universal time t: 5+5 = 10:00 AM b) sulion day number JON = (1461X ( 2017 + 4800+(12- 4+(367*(12. - 2 -12 *((12-14))/12 -(3x(C2017 +4900 +(12-14)) 12 ) 100))/4+6-32075 JDN : 2489544 +361 - 518776 - 32075 - 2452 655 sulion day. ID - JON + ( hout-12)/24 +(min) 1440 + second | 86400 JD - 2452654.91666667 considering TO » 1 Jan, 2000 12:00 AM c) t-to -6541. 43274 d) mean daily motion of means =n ornita 1 period, T2 687 days hence CS Scanned with no 2Xp7 1687 - 9.145x10' peu per day CamScanner