Orbiting the Sun beyond the Hill sphere

[xpell]

I was wondering if a spacecraft (or any other object) could 'co-orbit' the Earth by orbiting the Sun beyond our Hill sphere. For example, could this object 'hover over' the North (or South) Pole at >1,500,000 km?

Thanks in advance!

 

[tiny-tim]

hi xpell!

yes, see http://en.wikipedia.org/wiki/Lagrangian_point

(one theory of the origin of the moon is that it formed from the collision of the Earth with a another body orbiting near the L4 or L5 Lagrangian point, see http://en.wikipedia.org/wiki/Giant_impact_hypothesis#Possible_origin_of_Theia)

 

[D H]

For example, could this object 'hover over' the North (or South) Pole at >1,500,000 km?

No.

Well shoot. That response was too short. No, it can't.

 

[xpell]

hi xpell!

yes, see http://en.wikipedia.org/wiki/Lagrangian_point

(one theory of the origin of the moon is that it formed from the collision of the Earth with a another body orbiting near the L4 or L5 Lagrangian point, see http://en.wikipedia.org/wiki/Giant_impact_hypothesis#Possible_origin_of_Theia)

Thank you, Tiny-tim. Rather than positioning "my" spacecraft in the Lagrangians, which I understand they're on the Body 1-Body 2 plane (in this case, the Sun-Earth plane), I was thinking in positioning it in a solar orbit with a slightly different inclination relative to the Sun-Earth plane. The (fancy) idea is having an Earth observatory 'hovering over' the ecliptic poles. I assumed that we must leave the Hill sphere to achieve this.

No.

Well shoot. That response was too short. No, it can't.

Thank you too, D H. May I please ask why?

 

[Janus]

Thank you, Tiny-tim. Rather than positioning "my" spacecraft in the Lagrangians, which I understand they're on the Body 1-Body 2 plane (in this case, the Sun-Earth plane), I was thinking in positioning it in a solar orbit with a slightly different inclination relative to the Sun-Earth plane. The (fancy) idea is having an Earth observatory 'hovering over' the ecliptic poles. I assumed that we must leave the Hill sphere to achieve this.



Thank you too, D H. May I please ask why?

Think about it. Even if you could ignore Earth's gravity, a solar orbit with a different inclination would still cross Earth orbit at 2 points. The spacecraft would try to go from above the North pole to above the South pole and back again over the course of one orbit. However, the Earth would be in the way.

 

[xpell]

Think about it. Even if you could ignore Earth's gravity, a solar orbit with a different inclination would still cross Earth orbit at 2 points. The spacecraft would try to go from above the North pole to above the South pole and back again over the course of one orbit. However, the Earth would be in the way.

I had actually thought about it. For the sake of the thought experiment, let's assume it's a short mission, just a few weeks, or an asteroid in a temporary orbit approaching the Earth.

I am actually not so interested in the spacecraft or asteroid thing as in understanding if the Hill sphere is the absolute limit of a body's gravitational influence or you must still need to take it into account.

 

[mfb]

There is no absolute limit of influence. Even the planets influence each other in a measurable way. The Hill sphere gives the opposite: Outside the hill sphere (or close to it), you have to take the third object (here: sun) into account, while you can neglect it for objects deep inside (like low Earth orbits). So yes, you have to take Earth into account. But a mission for a few weeks with that trajectory looks possible. On the other hand, take two satellites in eccentric orbits, and you get observations with much better resolution for years.