Bye-Bye, BepiColombo

On 20 October 2018, ESA launched its Mercury Mission BepiColombo. This space probe will follow a rather complex path to the innermost planet. This path leads past the Earth on Friday, 10 April 2020.

So … can we see Bepi one last time?

That’s a tricky question. The answer depends on many parameters. But luckily, as is often the case with science, just doing the math already tells us quite a lot. 

To do the math, we need BepiColombo’s trajectory. That can be obtained from the JPL HORIZONS Web Interface. That web site accesses a repository of data files called Spice Kernels that contain the trajectory data for a large number of natural bodies and spacecraft. Each and every body is identified by a unique number. BepiColombo’s is -121. 

If you know how to use JPL Horizons and how to process the data you get from there you won’t need any further explanations from me. Conversely, if you aren’t comfortable with astrodynamics, don’t bother with that web site right now and just read on. 

Altitude and ESSA

The altitude of BepiColombo during the hyperbolic flyby is shown in the following diagram. The point of closest approach is called the perigee. This has an altitude of 12678 km and is passed at 4:25 UTC.

Right after the perigee, there is a gap – that is when the spacecraft will be in the Earth’s shadow cone. The eclipse pass begins at 5:00 UTC and lasts 35 minutes. Almost all of that time is passed in the core shadow, with brief periods in the penumbra at eclipse entry and exit.

I left out that part of the trajectory because it is of no interest here – you can’t see BepiColombo if it is not in sunlight. The distance is an important parameter – the closer Bepi is, the better you can see it. At half the distance it will be twice as bright.

Just as important as the distance is the Earth-Spacecraft-Angle (ESSA). Imagine a line from the spacecraft on its trajectory to the Sun, and another from the spacecraft to the Earth. The large solar arrays on the transfer module contribute more than any other component to the visual brightness. The arrays are oriented towards the sun.

If the ESSA is small, much of that portion ofthe sunlight that is reflected from the arrays wil be sent in the direction of the Earth. Conversely, if the ESSA is close to 90 degrees, we’re looking at the arrays edge on, so we won’t be able to see them.

In the ESSA plot, the altitude is colour-coded. As Bepi approaches the Earth and goes below 20,000 km distance, the ESSA will still be large, and Bepi will be virtually invisible. But then around perigee and just before entering the Earth shadow, the ESSA dips. It goes below 20 degrees right before entering eclipse. Then it goes down even more, but that is no help, as there won’t be any sunlight reflected from its surfaces.

What does the ground track tell us?

The ground track is simply the projection of a space trajectory onto the Earth surface. At any given time, compute the location at which an observer would have to look straight up (astronomers would say “towards the zenith”). One moment later, again compute the location at which an observer would have to look straight up. Mostly, but not always, that will be a different location. Do that for a number of times that span the period of interest, and you get a bunch of locations, each with its own longitude and latitude. Then just draw a line through all these locations and you get a line. That’s the ground track.

Here, I drew the ground track on a world map. The colour (and thickness) of the line represents the altitude, Ticks are added at 30 minute intervals. The ground track starts and ends when the altitude (Bepi’s distance from the Earth surface) is 300,000 km.

It starts in Africa, just between the republics of Chad and Niger. From there,  it moves towards the West, out over the Pacific, reappears on the other side (180 deg West is the same as 180 deg East). Bepi appears to move from East to West because its orbit is retrograde. The altitude will dip below 20,000 km near Madagascar, then cross southern Africa and the South Atlantic. After perigee, Bepi will be flying above South America.

And now, again the ESSA. But this time not as function of universal time (or Dynamic Barycentric Time, which is close to UTC), but of the local solar time at the location just below where the spacecraft happens to be. Again, the altitude is colour-coded.

Daylight times are no good. You can’t see a spacecraft against a bright sky. Luckily, the lowest parts of the trajectory are during local night, after and then before local midnight. So that’s good. There still may be a chance to observe Bepi for some of us.

Visibility from Sample Locations

All of the above indicates that the best locations to observe BepiColombo’s final Earth visit will be in South America. Now follow two diagrams that show the elevation and range seen from some sample locations as function of the local time at each of those locations.

Definitely, South America is the place to be. Rio de Janeiro will see Bepi passing almost directly overhead. Observers at the VLT on the Cerro Paranal in the Atacama desert in Chile too. Mexico City and Los Angeles aren’t too bad too, but the observing range from there will be much larget than from the South American sites.

Again, the parts of the trajectory where BepiColombo is in the Earth shadow cone from 05:00 to 05:35 UTC have been excluded from the plots.

Where to Look in the Sky

I am not going to include the viewing tables for many different observer locations here. Please refer to JPL Horizons to obtain tables of right ascension and declination or azimuth and elevation values for wherever you are. 

However, I do need to point out one more thing – 10 April 2020 is two nights after full moon. On that night there will be a bright moon in the sky that obliterates all fainter objects in the vicinity. 

The night sky over Rio de Janeiro is shown here at 04:35 UTC, the time when BepiColombo will be at minimum range from that city. This is 10 minutes after perigee and 25 minutes before eclipse entry. The angular distance from the Moon is less than 20 degrees and will further decrease in the minutes to come.

Here is the equivalent plot for the location of the VLT on Cerro Paranal, Chile, shown for 4:41 UTC, 19 minutes before eclipse entry. The range is 15054 km, the elevation 42.5 deg. Unfortunately, the angular distance to the moon is again only around 20 degrees, and closing. 

Mexico City. The time is 04:51, 9 minutes to eclipse entry. BepiColombo is rising in the sky and will have reached an elevation of 10 degrees above the horizon, at a range of 19203 km. In addition to possible haze issues close to the horizon, again we have the problem of the vicinity to the moon.

Los Angeles, California. No chance to observe BepiColombo before eclipse entry, when it will still be close to the perigee of the flyby hyperbola. The view simulated here is for 05:37 UTC, shortly after eclipse exit. The range is 28213 km but the Moon distance is larger and will grow with every minute. 

One more thing to do would be the calculation of the apparent magnitude from each of the locations. For that I would need the range from the location (given here for  and not the ESSA, but the Observer-Spacecraft-Sun Angle (OSSA), which might slightly differ. Calculation of the OSSA is straightforward. 

However, what I don’t know is how to take into account the extinction due to the brightness of the still nearly full moon in the immediate vicinity. I need to figure out how to factor that in.