我如何计算木星和土星的位置？

Question

木星和土星刚刚在天空相遇。我在哪里可以找到它们？他们什么时候再来一次

PyEphem似乎是执行这种计算的标准编程工具，但如何在这种情况下使用它呢

Answer 1

生成行星数据（代码）

首先，我用pyephem生成了很多关于行星相对位置的数据：

#!/usr/bin/env python3

#Running this script produces a CSV file containing information about the
#positions of Jupiter and Saturn

import ephem

from datetime import datetime, timedelta

my_lat      =   40.0150           # Boulder, Colorado is a space-y place
my_lng      = -105.2705
ephem_tdfmt = '%Y-%m-%d %H:%M:%S' # Used for formatting PyEphem strings

p1            = ephem.Jupiter()   # Planet of interest
p2            = ephem.Saturn()    # Second planet of interest
observer      = ephem.Observer() 
observer.lat  = str(my_lat)       # PyEphem takes lat/lng in strings
observer.lon  = str(my_lng)
observer.elev = 1624              # Elevation in metres

# We'll generate a large amount of data, one point for each day,
# starting at the time below. We choose the hour/minute to be a
# time when we're interested in looking at the sky
base_time = datetime(year=2018, month=12, day=21, hour=23, minute=0, second=0, microsecond=0) 

# Let's print a CSV to stdout with info about the planets
print("date time Planet az alt sep mag")
for x in range(2000*365):  # 365 days a year for 2000 years
  calc_time = base_time + timedelta(days=x)
  observer.date = ephem.date(calc_time.strftime(ephem_tdfmt))
  p1.compute(observer)
  p2.compute(observer)
  sep = ephem.separation(p1, p2)
  print(calc_time, "Jupiter", float(p1.az), float(p1.alt), float(sep), float(p1.mag))
  print(calc_time, "Saturn",  float(p2.az), float(p2.alt), float(sep), float(p2.mag))

分析和绘制数据（代码）

接下来，让我们用R来计算数字并绘制一些图

library(directlabels)
library(dplyr)
library(ggplot2)
library(ggrepel)
library(lubridate)
library(reshape2)
library(tidyr)

# Used for numbering the conjunctions
get.groups = function(x) with(rle(x),rep(1:length(lengths),lengths))

# Read the data
dat = read.table("output", header=TRUE)
dat = dat %>% mutate(date=lubridate:::date(date), sep=sep*180/2/pi)

# Plot angular separation for the next 2,000 years
# Since `sep` is common to both planets, we arbitrarily choose one
sep_over_time = dat %>% filter(Planet=="Jupiter")
ggplot(sep_over_time, aes(x=date, y=sep*180/2/pi)) +
  geom_line()                                      +
  xlab("Date")                                     +
  ylab("Separation (degrees)")                     +
  scale_y_log10()                                  +
  ggtitle("Angular Separation over time of Jupiter and Saturn (2018-4017)")
ggsave("/z/sep_over_time.png", width=10, height=6)

# Data used to plot the "shape" of a number of future conjunctions
conjunctions_time_normalized = dat   %>%
  group_by(Planet)                   %>%
  mutate(cnum=get.groups(sep<1.5))   %>%
  ungroup()                          %>%
  filter(sep<1.5)                    %>%
  group_by(cnum)                     %>%
  mutate(days=date-first(date))

# Get information about the 2020 conjunction
this_year = conjunctions_time_normalized      %>%
  filter(year(date)==2020 | year(date)==2021) %>%
  ungroup()

# Minimal angular separation of the 2020 conjunction
this_year_sep = min(this_year$sep)

# Plot the "shape" of future conjunctions by angular separation
ggplot(conjunctions_time_normalized %>% filter(Planet=="Jupiter"), aes(x=days, y=sep, group=as.factor(cnum))) +
  geom_line(color="blue", alpha=0.3)                                            +
  geom_line(data=this_year, aes(x=days, y=sep), color="green")                  +
  geom_hline(yintercept=this_year_sep)                                          +
  xlab("Days from first <1.5deg separation")                                    +
  ylab("Separation (deg)")                                                      +
  ggtitle("Angular Separation and Timing of Jupiter-Saturn Conjunctions (2018-4017)")

ggsave("/z/all_conjunctions.png", width=10, height=6)


# Get positions of the planets for the current (2020) conjunction
temp = this_year %>% mutate(az=az*180/2/pi,alt=alt*180/2/pi) %>% mutate(date=ifelse(wday(date)==1,as.character(date),NA))

ggplot(temp, aes(x=az, y=alt, color=Planet, label=date)) +
  geom_point()                                           +
  geom_text_repel(nudge_y=2)                             +
  xlab("Azimuth")                                        +
  ylab("Zenith")                                         +
  theme(legend.position="bottom")                        +
  ggtitle("2020 Conjunction of Jupiter and Saturn (16:00 local time)")

ggsave("/z/conjunction_timing.png")

# Get times of next conjunction
print("Times of next conjunctions")
print(dat %>% filter(sep<this_year_sep))

当前连词

这是木星和土星穿过天空的路径。请注意，如果你错过了21日最接近的分居点，今晚（22日）和23日也会很好。在那之后，你可以尽情地看着他们彼此拉开距离

什么时候会再次发生

虽然木星和土星经常彼此靠近（周期约为20年），但下面的图表显示，它们很少如此接近

事实上，在接下来的2000年中，它们只有几次如此接近：

         date     time  Planet       az         alt        sep   mag
1  2080-03-14 23:00:00 Jupiter 4.565937 -0.31129250 0.05045080 -1.86
2  2080-03-14 23:00:00  Saturn 4.564148 -0.31174162 0.05045080  0.76
3  2417-08-24 23:00:00 Jupiter 4.923358  0.27409384 0.04687376 -1.70
4  2417-08-24 23:00:00  Saturn 4.922710  0.27258733 0.04687376  0.24
5  2874-12-24 23:00:00 Jupiter 3.558560  0.49130434 0.04148634 -1.83
6  2874-12-24 23:00:00  Saturn 3.557792  0.49258307 0.04148634  0.63
9  3271-08-14 23:00:00 Jupiter 4.730337  0.46493667 0.03977666 -1.70
10 3271-08-14 23:00:00  Saturn 4.728929  0.46435314 0.03977666  0.13
13 3669-02-27 23:00:00 Jupiter 4.407206 -0.08765785 0.05079357 -1.73
14 3669-02-27 23:00:00  Saturn 4.408436 -0.08571938 0.05079357  0.58
15 3728-12-29 23:00:00 Jupiter 3.501876  0.55620575 0.04263970 -1.83
16 3728-12-29 23:00:00  Saturn 3.500159  0.55650318 0.04263970  0.61

连词总是这样吗

不！如下图所示，木星和土星非常接近的合相持续时间很短。然而，它们有点接近的连接可以持续近一年。在这里，我用亮绿色突出显示了当前连接，并用黑线突出显示了最小角度间隔

快乐的星星/行星凝视