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I was never great at math but now I wish I would have taken it more seriously.

We have an office bet going and I need to come up with a formula to figure out the future velocity the JWST. I was able to pull data from Twitter of all places but all the Velocity formulas I've seen don't help me.

Here's the office bet.

How fast will the JWST be going in MPH on L+ 26:00:00:00

Today at L+ 23:03:09:56 V= 0.1619 mi/s x 3600 = 582.84 mph. What will it be on L+26:00:00:00? We have till 5pm to give the answer.

I've tried the simple calculation of substraction every 24 hours but that leaves errors and it's different every time I'm guessing because Earth's gravity is less and less as it's traveling further and further away and it's altitude increases, I don't know how accurate the answer has to be but I would like to know how to do the math. I know most of you on here will probably laugh at my question but I'm happy to be laughed at to learn something new.

I was guessing that you get the mass of the earth the mass of the JWST and the distance between them to get the gravitational pull on jwst in N but then getting future velocity with that info is where I get lost.

Jwst total Mass 6,500 kg

JWST velocity data in K/ps

Any help would be greatly appreciated.

mountainbikebc
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  • To answer your question, you must specify speed in relation to what? On land, sea and air, speed is motion relative to the medium. In space, no medium so you need to pick an object like the earth or Sun, The Sun's gravity field will be stronger than the Earth's, but earth will be closer so either one would be a choice, – Woody Jan 17 '22 at 16:35
  • So let's say earth, I'm still a bit confused as how to put this into an equation to solve the future speed. Thanks for taking the time to help me out. – mountainbikebc Jan 17 '22 at 19:08
  • Check out diagram in https://space.stackexchange.com/questions/57635/what-are-the-characteristics-of-jwsts-orbit-around-l2 . Once in a stable halo orbit, JWST will be at a constant average distance from Earth for the next 10+ years. So it will have no net speed WRT Earth in that reference frame. But it will be doing a (average) 600,000km halo orbit every 6 months. That's 440 km/hr. It also orbits the Sun once a year. That's about 100,000 km/hr. – Woody Jan 17 '22 at 21:39
  • @Woody that's not right; JWST's halo orbit is not perpendicular to the Earth's orbital plane; there will be a large, ~6 month oscillation in JWST-Earth distance. See this side view: https://i.stack.imgur.com/rSuD8.png from here The Moon's motion around the the Earth is green (Earth in the center) and the JWST halo orbit is substantially tilted wrt the Earth's orbital plane, being much closer when it's north and further when it's south. – uhoh Jan 17 '22 at 22:37
  • @uhoh --- you're right. The orbit is not flat, its not perpendicular to the X axis and its not even an "orbit" in the Keplerian sense. That's why all the wiggle words like "net" and "average" in the description. – Woody Jan 18 '22 at 00:45
  • @mountainbikebc --- Check out https://directory.eoportal.org/web/eoportal/satellite-missions/j/jwst for a good graphic on the JWST orbit. Scroll down to fig. 6. ---- BC: world's best mountainbikin' – Woody Jan 18 '22 at 01:23
  • @mountainbikebc --- and if that wasn't enough, there are some great graphics here: https://space.stackexchange.com/questions/57822/is-jwst-halo-orbit-prograde-or-retrograde-and-why – Woody Jan 18 '22 at 02:09
  • Thank you everyone! I really appreciate the help! You have been great! I think I have the info I need to make this equation. I'm a bit late on the due date but we got a bit more time to solve it. Woody, if you're ever in North Vancouver BC, I'll take you riding on the best trails on the planet. Haha thanks again everyone for your input and data. – mountainbikebc Jan 19 '22 at 07:59

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