# What is the distance of the Sun-Jupiter L4 and L5 points relative to Jupiter?

What is the distance between Jupiter and the L4 and L5 points of the Sun-Jupiter system? I need it to attempt to calculate the $\Delta v$ needed to reach Jupiter from there.

• The $\Delta V$ has nothing to do with the distance. – Mark Adler Apr 30 '16 at 5:30
• Are you starting exactly at (the Jupiter-Sun) L4 or L5 point without relative motion, or in a stable orbit around the point? (which can be very large!) Also, is total time important (10 years, or 100 or 1000?) The actual answer is complicated because the whole time you are (roughly speaking) in some kind of orbit around the sun, assuming you are using a 'low energy' transfer. You could just blast you way there with a huge thrust, but if you had that, you'd probably be asking a different question. That would be more like "if you have to ask, you can't afford it" sort of thing. – uhoh Apr 30 '16 at 12:09

L4 and L5 are the same distance from Jupiter as Jupiter is from the sun: about 5.2 A.U. L4, the sun and Jupiter form an equilateral triangle. Ditto L5, sun, Jupiter. All together, L4, Jupiter, L5, sun form a 120º/60º rhombus.

As Mark Adler says, distance and delta V are different things.

Describe your scenario in more detail and I might be able to help with the delta V. Are you thinking of going from a Trojan asteroid to one of Galilean moons? What trip time do you have in mind?

• Actually, that was what I was thinking. :D – Future Historian Apr 30 '16 at 17:46
• @FutureHistorian Happy to hear it. In my opinion the Galilean moons and Trojans could be part of an interesting science fiction setting. Do you have any moons in particular in mind? What is the range of trip times you hope for? – HopDavid Apr 30 '16 at 17:57
• Well, lucky for you, that setting has been in place for a month already. I am already working on one the setting's first shorts. Now, if you notice my post history on the Worldbuilding Stack Exchange site, this is using the same scenario. However, the answers all assumed they would depart from Earth. Now, before I decide an asteroid, for both L4 and L5 points, what is the closest Trojan object to Jupiter in either end? – Future Historian Apr 30 '16 at 23:00
• @FutureHistorian Doing the math for a scenario is an investment of my time and effort. And I'm supposed to dig through your world building questions to get a more specific scenario? I withdraw my offer. Do your own homework. – HopDavid May 2 '16 at 13:23
• What? What did I do? sighs Fine.....I will do it myself and then link the starting point. :( – Future Historian May 2 '16 at 16:56

According to this, L4 and L5 for Sun-Jupiter will each be at the same distance from Jupiter as Jupiter is from the Sun (something like 780,000,000 km).