The accuracy required for parking spacecraft at Lagrange points L1, L2, and L3 is critical, with the James Webb Space Telescope (JWST) maintaining a distance of 250,000 to 832,000 km from L2. These points are inherently unstable, necessitating a balance between proximity and fuel consumption for orbital corrections. Instruments and techniques for achieving precise positioning include gravitational balance and continuous adjustments to maintain orbit. The recent addition of the Euclid spacecraft to the L2 point further emphasizes the importance of these calculations in space missions.
PREREQUISITESAerospace engineers, astrophysicists, mission planners, and anyone involved in spacecraft navigation and positioning at Lagrange points will benefit from this discussion.
You can have a look at this, a practical example.RobbyQ said:TL;DR Summary: What is the accuracy of parking craft into Lagrange points
I often wonder what the accuracy is when dealing with spacecraft and wondered how accurate a craft needs to be positioned into the Lagrange (L1,L2,L3) positions. Are we talking plus or minus 1km/100km/1000km etc. It's just that the system is so vast and what instruments are used to achieve a good L sweet spot?
Those three Lagrange points are unstable, so there is a trade-off between staying close versus the fuel required to stay there. (L4 and L5 are stable). A big consideration is whether sunlight is needed for power. L2 is in the shadow of the Earth. JWST stays near, but orbiting the L2 Lagrange point so that its solar cells will get sunlight. The distance of JWST from the L2 point varies between 250,000 to 832,000 km. (see this). If you think that is a lot, remember that the Sun is over 100 million km away.RobbyQ said:TL;DR Summary: What is the accuracy of parking craft into Lagrange points
I often wonder what the accuracy is when dealing with spacecraft and wondered how accurate a craft needs to be positioned into the Lagrange (L1,L2,L3) positions. Are we talking plus or minus 1km/100km/1000km etc. It's just that the system is so vast and what instruments are used to achieve a good L sweet spot?
Wow that's crazy. It actually orbits the L2FactChecker said:Those three Lagrange points are unstable, so there is a trade-off between staying close versus the fuel required to stay there. (L4 and L5 are stable). A big consideration is whether sunlight is needed for power. L2 is in the shadow of the Earth. JWST stays near, but orbiting the L2 Lagrange point so that its solar cells will get sunlight. The distance of JWST from the L2 point varies between 250,000 to 832,000 km. (see this). If you think that is a lot, remember that the Sun is over 100 million km away.
Yes. It is roughly following the Earth's orbit but it is farther from the Sun than the Earth is. My understanding is that the combined gravity of the Sun and Earth (the component in the direction of the Sun) balance the centrifugal force of its orbit around the Sun so that part is in balance. Then it can essentially orbit the Earth at an offset distance around L2 (since there is a component of Earth gravity pointing toward L2). The orbit is a little unstable so it takes small corrections occasionally. There is a lot more to it that I am not knowledgeable enough to comment on.RobbyQ said:Wow that's crazy. It actually orbits the L2
Thanks. This video I found very interesting too as it discusses the component forces leading up to the JWST orbit around L2. And even this is simplified.FactChecker said:Yes. It is roughly following the Earth's orbit but it is farther from the Sun than the Earth is. My understanding is that the combined gravity of the Sun and Earth (the component in the direction of the Sun) balance the centrifugal force of its orbit around the Sun so that part is in balance. Then it can essentially orbit the Earth at an offset distance around L2 (since there is a component of Earth gravity pointing toward L2). The orbit is a little unstable so it takes small corrections occasionally. There is a lot more to it that I am not knowledgeable enough to comment on.
RobbyQ said:Thanks. This video I found very interesting too as it discusses the component forces leading up to the JWST orbit around L2. And even this is simplified.
I agree . Very informative. Also what's interesting (about 5mins into video) is that they keep it slightly Earth side of L2 so it has tendency to fall Earth wards and so the thrust burners to correct it back towards L2 are always Sun facing so as not to have to turn it around and get burnt up.FactChecker said:That is a great video! Thanks!
Euclid joined L2 too last month.RobbyQ said:I agree . Very informative. Also what's interesting (about 5mins into video) is that they keep it slightly Earth side of L2 so it has tendency to fall Earth wards and so the thrust burners to correct it back towards L2 are always Sun facing so as not to have to turn it around and get burnt up.