1,000 Teslas, 200 years

In my previous post, I simulated my best available information on the SpaceX Tesla roadster. In this post, I investigate a range of possible futures for the Tesla. I started with JPL's HORIZONS ephemeris. It turns out that it can evaluate probabilistic orbits; here are its predictions for close planetary encounters by the Tesla given the current uncertainties in its position:


           Date (TDB)      Body   CA Dist  MinDist  MaxDist   Vrel  TCA3Sg  Nsigs  P_i/p
  ----------------------  -----  -------  -------  -------  ------ ------ ------ -------
  A.D. 2020 Oct 07.26668  Mars   .049589  .047961  .052381   8.153  92.21 1.57E5 .000000
  A.D. 2035 Apr 22.36925  Mars   .014376  .003802  .055862   8.199 601.42 10658. .000000
  A.D. 2047 Jan 11.95105  Earth  .031798  .022547  .040258   4.488 5203.0 24104. .000000
  A.D. 2067 Apr 15.90602  Mars   .043165  .004269  .090230   7.193 3779.8 12481. .000000
  A.D. 2085 Jan 01.97974  Earth  .083090  .007954  .163620   6.224 13899. 32807. .000000
  A.D. 2088 Mar 09.97244  Earth  .049174  .006455  .085995   5.106 13241. 28115. .000000
  A.D. 2123 Mar 13.12397  Earth  .054330  .007470  .501619   5.287 1.98E5 31955. .000000

 The approach distances are in Astronomical Units (about 150,000,000 km). The TCA3Sg field is the variation in time of closest approach, in minutes. Note how that variation increases with each encounter - the position/velocity differences add up significantly over time.

I then spent some time fiddling with various simulation options. I settled on a relatively new entrant - the REBOUND orbital simulation package. Its advantages are two-fold: it already has an OpenGL visualization mode, and it implements a new fast, accurate orbital integrator called "WHFast". The integrator does diverge somewhat from JPL's simulator - it's unclear right now why that is. But it comes reasonably close, and it is very fast, which is an advantage for my next experiment. I modified REBOUND to draw the particles the way I want, and to do screen grabs to make a movie.

I used the package to simulate 1,000 possible Tesla orbits. I varied the position of the Tesla by adding a random distance with a normal distribution and a standard deviation of about 5 km. I also varied the velocity of the Tesla by adding a random velocity with a normal distribution and a standard deviation of about 1.8 m/s. I chose these values as fractions of the then-current Earth-Tesla distance and speed (which was about 1,000,000 km and 3.5 km/s at the time the ephemeris was generated).

The results are entertaining; without further ado, the video:


As I did the simulation, a new paper came out with similar results, finding that it has a 6% chance of colliding with Earth and a 2.5% chance of colliding with Venus over the next one million years.

Comments

Anonymous said…
Dear Mr. Cunnif,

I'm curious about the Tesla that escapes to interstellar space around year 2194; it seems to have gained too much energy for a gravity assist with periapsis outside Earth's crust. A back-of-the-envelope calculation tells me that a gravity assist from the Earth can give at most 5 km/s, which added to the 34 km/s of the original Tesla at perihelion is not enough to reach the 42 km/s needed for solar escape.

Could you tell me what numbers do you get from your simulation? Specifically the Tesla's speed just before the encounter and its perigee? Did you check for collisions in the simulation?

Thanks a lot!
3:04 AM
Post a Comment

Popular posts from this blog

April 8, 2024 Total Solar Eclipse

Image
On April 8, 2024, a total solar eclipse crossed a huge swath of the United States. We had been planning a trip to see it ever since the August 21, 2017 total solar eclipse . Our chosen destination was at Chalk Bluff River Resort and Park , near Uvalde, Texas, due to statistical likelihood of clear skies in South Texas: The main attraction at Chalk Bluff is Nueces River and the the eponymous bluffs that rise above it: Chalk Bluffs The eclipse was widely publicized. Enough so that the state of Texas found it necessary to put warnings on its highway signs: Texas DOT warning sign Texas DOT warning sign We arrived at Chalk Bluff on April 6. As eclipse day approached, it became clear that the weather was not going to be our friend: NWS blended forecast for eclipse day So, what was originally going to be an "Eclipse expedition, with a possibility of some birding" became a "Birding expedition, with a possibility of seeing an eclipse". It is fortunate that we chose thi...
Read more

August 21, 2017 Total Solar Eclipse

Image
Like millions of other people, we went chasing the Great American Eclipse. We chose Nebraska, since everybody we knew was going to Wyoming, and the climate models suggested a good probability of clear weather. Our initial camp was at Lake McConaughy, which is just inside the line of totality. My sister Danielle and her husband Edward got there early to start scouting. Our plan was to check weather forecasts and then go mobile the day of the eclipse. The morning of August 19 I got up early and snapped this shot of the moon on its way to its date with destiny: Sunday morning we checked the forecasts. It was not looking good for Nebraska in general, but east-central Nebraska seemed better than western according to the forecasts. So we packed up camp and headed out to Camp Augustine, a Boy Scout camp near Grand Island, Nebraska: They had camping spots available, and a large field which would be good for observations. After a rather hot, muggy, sleepless night (dry camping wi...
Read more

Pune Adventures

Image
Today, the morning was spent on work email. But this afternoon, Ken and Fred arrived from Germany, and Jeetendra joined us to go on an excursion. We started with some shopping in one of Pune's shopping districts - Ken wanted to buy some things. I may or may not have bought anything - only me and Mr. Visa know for sure. Anyway, I caught this picture of one of the oldest wooden buildings in Pune, with hand-carved wooden decorations: After wrapping our shopping up, Jeetendra took us to a combination theme park / restaurant named Chokhi Dhani - it's kind of like a Rajasthani Cultural Center, or maybe a North Indian Standing Renaissance Faire. The buildings are decorated up like historic buildings in Rajasthan, and there are various exhibits, activities, shows, food, etc. scattered throughout the park. Here are Ken, Fred, and I saying " Namaste " to you all along with Chokhi Dhani's plaster host: This is the main entrance. They really go for the electric light...
Read more