Conversation started Jan 30, 2016 at 23:24.
TildalWave
TildalWave
Jan 30, 2016 23:24
@Hohmannfan Are you sure about this part:
> The angular velocity of the orbit is larger for 25.5 degrees before and after perihelion, making the total retrograde motion 19.5 degrees.
I get ~ 0.5 r
0.50000031459364351900956416685623 :D
Hohmannfan
Hohmannfan
Quite, wiki gives an equation for calculating the radius from true anomaly en.wikipedia.org/wiki/True_anomaly
TildalWave
TildalWave
then I don't get it what you mean with 19.5
Hohmannfan
Hohmannfan
putting 25.5 degrees into that gives me a radius from (A + P) / 2 (1 - e²) / (1 + e cos(v))
46778000 km radius
that has an equal angular velocity as the rotation
TildalWave
TildalWave
ah geez yes OK I get it, I thought that 19.5 was total angular displacement during the retrograde motion
for that I get 0.5 r (about 0.853°)
Hohmannfan
Hohmannfan
51 degrees is 0.0876 of the orbital period
TildalWave
TildalWave
Jan 30, 2016 23:30
yes OK we were talking about different things
because the Sun definitely doesn't have apparent diameter of more than 19.5° on Mercury's sky LOL
but it would be larger than 0.853°
Hohmannfan
Hohmannfan
geez did I say 19.5? obviously the angular displacement is 3.5 degrees
TildalWave
TildalWave
minimum Sun's size from Earth is 0.52527...°
Hohmannfan
Hohmannfan
the planet rotates 47.5 degrees in 0.0876 times the Mercurian year
51 - 47.5 is 3.5
TildalWave
TildalWave
hmmm where did I drop the 3 then?
dunno, I guess it's too late for me to do these things
or maybe I should change my music for something faster
Hohmannfan
Hohmannfan
user image
@TildalWave I get 1.73 degrees for the solar diameter at Mercury periapsis.
Retrograde displacement angle > solar diameter, so two complete sunsets are possible
TildalWave
TildalWave
Jan 30, 2016 23:46
yes me too... 1.73449435 deg and now I'm trying to figure it out why that doesn't match
Hohmannfan
Hohmannfan
At what true anomaly do you get an equal angular velocity? I get 25.5 degrees, as stated before
TildalWave
TildalWave
@Hohmannfan I'm reasonably sure I remember that part correctly, and that Wiki quote kinda suggests there wouldn't be a complete sunset
dunno, I'll sleep on it, I can only think of lighter things now like pancakes and such :)
Hohmannfan
Hohmannfan
It says "approximately 4 days before perihelion". I get 3.87 days, so the 25.5 degrees is correct. In 7.74 days, Mercury rotates 47.5 degrees around its axis.
51-47.5 is 3.5 [citation needed], and that is greater than the 1.7345 angle. BTW, the quote can be interpreted in at least three ways :)
TildalWave
TildalWave
yes, 3.49° and the Sun's angular diameter is 1.73° so almost exactly half that
Hohmannfan
Hohmannfan
@TildalWave We agree on the same numbers? Yes!
TildalWave
TildalWave
Jan 31, 2016 00:01
@Hohmannfan yes, they seem correct to me now that it isn't 19.5°
Hohmannfan
Hohmannfan
The 19.5 deg was for another quantity, Retrograde displacement angle makes a lot more sense
TildalWave
TildalWave
OK so how come that (0.265 - 0.256) * 24 * 3.87 * 2 is 1.67184, and that's even way too big because that's max retrograde displacement per hour?
something still isn't quite right
Hohmannfan
Hohmannfan
something is fishy...
TildalWave
TildalWave
I'll let you check that if you want, but I'm off for tonight. I'm simply too knackered. I'll recalculate tomorrow.
Hohmannfan
Hohmannfan
Jan 31, 2016 00:28
0.0919 * 3/2 *360 is 49.6 degrees..... So 1.4 degrees retrograde motion is correct. Never thrust me with numbers again
TildalWave
TildalWave
ha! well this will make sleeping a bit easier :)
I'll still recalculate tomorrow just to double check
night then ;)
Hohmannfan
Hohmannfan
night
0.0923 * 3/2 *360 is 49.8 degrees. So 1.2 degrees after my recalc. with more accurate data. The angular velocities are very close to each other, so any error is important
 
Conversation ended Jan 31, 2016 at 0:37.