I wrote an MFD that displays the distance of the ship from the 5 Lagrange points.
I used the formulas found at the link
https://en.wikipedia.org/wiki/Lagrangian_point#Mathematical_details
rewritten for the 3D space.
Now I would improve the calculations but it’s not clear to me what happens in a Lagrange point.
For example, consider the instant 2017-10-05 18:15:07 UTC when Sun, Earth and Moon are almost in a straight line (their angular distance is about 0.00967 deg, this is to make the calculations easier).
For L2 point of the Earth-Moon system, I get a distance = 436158.875344 km from the Earth and 62681.581136 km from the Moon.
The Moon’s angular speed for the above instant is 13.998 deg/day and it’s the same for L2; hence, the centripetal acceleration at L2 is 3.48743 mm/s2.
The accelerations at L2 exerted by the celestial bodies are:
Moon: 1.24786 mm/s2
Earth: 2.09531 mm/s2
Sun: 5.89786 mm/s2
the sum is 9.23615 mm/s2.
I thought to find centripetal acceleration = gravitational acceleration.
Please, could anyone explain what I’m doing wrong?
I used the formulas found at the link
https://en.wikipedia.org/wiki/Lagrangian_point#Mathematical_details
rewritten for the 3D space.
Now I would improve the calculations but it’s not clear to me what happens in a Lagrange point.
For example, consider the instant 2017-10-05 18:15:07 UTC when Sun, Earth and Moon are almost in a straight line (their angular distance is about 0.00967 deg, this is to make the calculations easier).
For L2 point of the Earth-Moon system, I get a distance = 436158.875344 km from the Earth and 62681.581136 km from the Moon.
The Moon’s angular speed for the above instant is 13.998 deg/day and it’s the same for L2; hence, the centripetal acceleration at L2 is 3.48743 mm/s2.
The accelerations at L2 exerted by the celestial bodies are:
Moon: 1.24786 mm/s2
Earth: 2.09531 mm/s2
Sun: 5.89786 mm/s2
the sum is 9.23615 mm/s2.
I thought to find centripetal acceleration = gravitational acceleration.
Please, could anyone explain what I’m doing wrong?