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 ? 10?5 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 (x e ; 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) FindtheazimuthAandelevationhofUranusattimet,asseenfromWashington 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.)

1

Answer 1