Will the Emirate Mars Mission, Tianwen-1 and Mars 2020 Mission get closer to each other or spread out on their way to Mars?

Question

Background & Introduction: On August 2, 2020 the brand new Where Is Roadster page Spacecraft launched to Mars in 2020 (announced here) said that it had been:

• 13 days, 3 hours, 47 minutes and 13 seconds since the Emirates Mars Mission launched.
• 9 days, 21 hours, 4 minutes and 27 seconds since Tianwen-1 launched.
• 2 days, 13 hours, 55 minutes and 27 seconds since Mars 2020 launched.

The Solar System map extends out to pars of Ceres' orbit and at this scale the three spacecraft are on top of each other. Of course they also appear on top of Earth at the moment but that will change.

Question: Roughly how far apart from each other are they at the moment, and will they drift closer together or farther apart from each other during their interplanetary transfer between Earth's and Mars' orbit?

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related: China, UAE and US all sending missions to Mars in 2020 (Summer of L̶o̶v̶e Mars); how far apart are their frequencies?

Answer 1

Only the mission operations team for each mission can answer that question.

During an interplanetary mission, spacecraft perform Trajectory Correction Maneuvers (TCMs). These are used to better target the B-Plane target (as explained in the documentation for FreeFlyer). The selection of the B-Plane depends on many factors, such as the thrust capability of the spacecraft, the attitude control authority, and more crucially the targeted injection orbit.

If a Mars mission adhered by the NASA Planetary Protection rules, then the spacecraft is not allowed to be on an orbit which intercepts Mars directly: the operations team must prove to NASA that the spacecraft is behaving well enough throughout the interplanetary leg.

Moreover, each mission design team has their reference trajectory which is built prior to launch. After launch, the navigation team will determine where exactly a spacecraft is for the mission design team to re-optimize the interplanetary trajectory: at that moment, the mission designers may decide whether to modify a planned TCM, or even remove it entirely.

Therefore, unless the mission designers publish this information, we cannot know whether EMM, Tianwen-1 and Mars 2020 will get closer or not for sure.

However, we can answer determine whether these spacecraft will get closer or not using their current orbit states if neither performs any TCMs. Another option would be to attempt to back-propagate their known Mars orbits and rebuild a trajectory to match their current states.

Answer 2

The hopelessness of my question expressed in this answer now seems "greatly exaggerated".

Only the mission operations team for each mission can answer that question.

Of course for detailed and reliable trajectories one will need TCM data, but to answer this question, I think we have enough now.

Will the Emirate Mars Mission, Tianwen-1 and Mars 2020 Mission get closer to each other or spread out on their way to Mars?

Answer: Yes! Both!

While EMM Hope and Tianwen-1 will continue to move further apart until late in their missions when they approach Earth, both of them will have a first minimum distance during their interplanetary travels before moving away from each other again.

All inter-spacecraft distances remain greater than about 1 million kilometers until they reach Mars.

JPL's Horizons now has nominal trajectories for all three spacecraft. These of course are preliminary trajectories as indicated by some of the spacecraft flying past Mars and continuing into deep space!

Below is a plot of 1) Earth/Mars distance, 2) Inter-Spacecraft distances, and 3) Planet-Spacecraft distances.

Original 18-Aug-2020

Python script that plotted Horizons data: https://pastebin.com/7evPAprS

"Extra Crispy" 06-Jan-2021

Mars 2020 and EMM Hope calculated trajectories have been updated based on official tracking data as DSN is involved. Tianwen-1 calculated trajectories have been updated on an "as-is" bases based on tracking data from skilled but unofficial contributors.

 TRAJECTORY: 
  This trajectory is an UNOFFICIAL one based on optical and radio ground 
  observations collected by numerous volunteers. 

  It does not include FUTURE maneuvering events that will take place en-route 
  to Mars (no information on them has been made public), so will likely be 
  accurate only for days or weeks into the future past the "revision date" 
  noted above. 

  This as-is trajectory is being made available through Horizons by request, 
  to support volunteer ground-based radio tracking efforts described here:

   https://destevez.net/2020/07/tracking-tianwen-1s-orbit-to-mars/
   http://www.r00t.cz/Sats/Tianwen1
   https://amsat-dl.org/chinese-mars-probe-tianwen-1-successfully-received-by-amsat-dl/

  References for trajectory segment data:
   Jul23-Aug01: https://www.projectpluto.com/pluto/mpecs/tianwea.htm#o001
   Aug01-Sep20: https://destevez.net/2020/08/tianwen-1-tcm-1/
   Sep20-Oct09: https://destevez.net/2020/09/tianwen-1-tcm-2/
   Oct09-Oct28: https://destevez.net/2020/10/tianwen-1-dsm-final-trajectory/
   Oct28-Mar21: https://destevez.net/2020/11/tianwen-1-tcm3-final-trajectory/

  Trajectory (data from ground-based volunteers)       Start         End 
  -------------------------------------------------  -----------   -----------
  tianwen-1_p-mpec     (Bill Gray)                   2020-Jul-23   2020-Aug-01
  tianwen-1_post_tcm-1 (Amateur DSN)                 2020-Aug-01   2020-Sep-20
  tianwen-1_post_tcm-2 (Amateur DSN)                 2020-Sep-20   2021-Oct-09    
  tianwen-1_post_dsm   (Amateur DSN)                 2020-Oct-09   2021-Mar-21
  tianwen-1_post_tcm-3 (Amateur DSN)                 2020-Oct-28   2021-Mar-21
*******************************************************************************

Answer 3

Would not really make sense, because the were launched at different dates and will arrive at mars on different dates. That means the speed of each spacecraft is different. They drift away.