Lagrange Point and orbital velocity

In summary, the Lagrange point 1 in the Sun/Earth system does not have any orbital velocity around Earth. This is supported by the fact that the Earth's position affects the position of L1, and that using the term "in orbit around Earth" in a 3-body system is not entirely accurate. Additionally, the calculations for L1 do not take into account the centripetal force from Earth, which further suggests that L1 does not have any orbital velocity around Earth.
  • #1
_Stew_
7
0
When considering the Lagrange point 1 in the Sun/Earth system, Does Lagrange Point 1 have any orbital velocity around Earth?

I suspect a body at L1 has no orbital velocity around earth.
But consider the Earth's position 6months later when it is opposite the sun. The Lagrange point would also have moved to the opposite side of the earth. This would suggest the orbital period of a body at L1 around the Earth would be one year.

So back to my original question:
Does Lagrange Point 1 have any orbital velocity around Earth?
 
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  • #2
_Stew_ said:
I suspect a body at L1 has no orbital velocity around earth.
You have not supplied any reasons for your suspicion, while supplying a good reason to the contrary in the following two sentences.
As seen from Earth(disregarding daily rotation), the body at L1 will have indeed moved across the celestial sphere at angular velocity equal to that of the Sun - 360deg/sidereal year.

There are, however, issues with using "in orbit around Earth" when talking about a 3-body system. It's similar to saying that the Sun has got some orbital velocity around Earth - it's not entirely without merit(vide: common barycentre), but not entirely correct either.
 
  • #3
_Stew_ said:
I suspect a body at L1 has no orbital velocity around earth.
But consider
I used the word “but” to indicate I was talking about something conflicting with that statement.
The reason I suspected that the orbital velocity of the L1 body around Earth was zero is a bit harder to explain. Which is why I didn’t put it in, but I will now.
When trying to find Lagrange point 1, many calculations/proofs I have seen use 3 forces:
1) The gravitational force between the Sun and the L1 body
2) The centripetal force acting at L1 around the Sun
3) The gravitational force between the Earth and the L1 body
I was thinking that there should be another force, the centripetal force acting at L1 from the Earth?
It must be that introducing this new force is illogical for some reason OR the centripetal force acting at L1 from Earth is zero, making the orbital velocity of the L1 body around Earth = 0.
In light of what you said:
Bandersnatch said:
There are, however, issues with using "in orbit around Earth" when talking about a 3-body system. It's similar to saying that the Sun has got some orbital velocity around Earth
I’m guessing that it is illogical to consider L1’s orbit around earth
 

1. What is a Lagrange Point?

A Lagrange Point is a location in space where the gravitational pull of two larger bodies, such as a planet and its moon, balances out the centrifugal force of a smaller object orbiting them. This creates a stable point in the orbit where a spacecraft can maintain a relatively fixed position.

2. How many Lagrange Points are there?

There are five Lagrange Points in a two-body system, labeled L1 through L5. L1, L2, and L3 are located along the line connecting the two larger bodies, while L4 and L5 are located at the vertices of two equilateral triangles formed by the three bodies.

3. What is the significance of Lagrange Points?

Lagrange Points are significant because they provide stable locations in space for spacecraft to gather data, monitor the environment, and study the interactions between celestial bodies. They also serve as potential locations for future space missions and colonization efforts.

4. How does orbital velocity affect a spacecraft at a Lagrange Point?

The orbital velocity of a spacecraft at a Lagrange Point is very low compared to its velocity in a regular orbit around a planet. This is because the spacecraft is essentially orbiting at the same rate as the planet and its moon, which are much larger and have a stronger gravitational pull. Therefore, a spacecraft at a Lagrange Point requires very little fuel to maintain its position.

5. Can a spacecraft remain at a Lagrange Point indefinitely?

Yes, a spacecraft can theoretically remain at a Lagrange Point indefinitely with minimal adjustments to its orbit. However, due to external factors such as solar wind and perturbations from other celestial bodies, small corrections may need to be made over time to maintain its position.

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