Choochoo_baloo
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I am struggling to visualise why the plane of a satellite's circular orbit has to be coplanar with the Earth's equatorial plane, in order for the orbit to be geostationary. I cannot 'work out' in my mind why an orbital plane at a non 0 angle to the equator would cause the satellites to follow the familiar vertical '8' shape / "analemma".

i.e. what is it about the orbit and equator being non-planar they causes an Earth's surface observer to see motion of the satellite over a sidereal day?

Thanks in advance.
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Jammy Duel
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The principle is that the satellite is at such a distance that the outward acceleration from the circular motion balances with the attraction from gravity while orbiting in the geostationary manner.
Although that's largely irrelevant. Consider the vectors of all the forces.
If you want the satellite to be positioned over a point and to orbit parallel to the plane passing through the equator you have to prove some form of constant thrust.
Gravity will be drawing the satellite to the center of the planet, the force from the circular motion will cancel the force drawing the satellite towards the axis, however it won't compensate for the part of the force drawing it down to the equatorial plane unless you have a constant force from a thruster which isn't particularly feasible.

I'll draw a diagram in a sec.
Image
Unless I didn't understand the question, the net force would draw you into an equatorial orbit.
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Desk-Lamp
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(Original post by Jammy Duel)
The principle is that the satellite is at such a distance that the outward acceleration from the circular motion balances with the attraction from gravity while orbiting in the geostationary manner.
Although that's largely irrelevant. Consider the vectors of all the forces.
If you want the satellite to be positioned over a point and to orbit parallel to the plane passing through the equator you have to prove some form of constant thrust.
Gravity will be drawing the satellite to the center of the planet, the force from the circular motion will cancel the force drawing the satellite towards the axis, however it won't compensate for the part of the force drawing it down to the equatorial plane unless you have a constant force from a thruster which isn't particularly feasible.
...
Unless I didn't understand the question, the net force would draw you into an equatorial orbit.
Be VERY careful here. You're answer is mostly correct, but it looks like you've got lucky with intuition and then slapped some bogus physics on top.

In your diagram you've invented some sort of outwards acting force which you call the 'force from the circular motion,' which simply doesn't exist. If you consider the earth to be stationary in a rotating frame of reference then you could use inertial forces (i.e. centrifugal force), but you're not really justified in doing that given that the satellite isn't stationary relative to the earth.

Basically, since the force due to gravity is towards the centre of the earth rather than the earth's axis, the only possible stable circular orbits circle the Earth's centre of mass. If you try to start a satellite in an orbit such as you drew in your diagram, it wouldn't be drawn into a circular orbit around the equator. rather it would oscillate about that orbit on an angled path that may or may not be stable
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lerjj
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(Original post by Choochoo_baloo)
I am struggling to visualise why the plane of a satellite's circular orbit has to be coplanar with the Earth's equatorial plane, in order for the orbit to be geostationary. I cannot 'work out' in my mind why an orbital plane at a non 0 angle to the equator would cause the satellites to follow the familiar vertical '8' shape / "analemma".

i.e. what is it about the orbit and equator being non-planar they causes an Earth's surface observer to see motion of the satellite over a sidereal day?

Thanks in advance.
Because the orbits have to go around the Earth's centre of mass. That means the a non-equatorial orbit that is at geostationary distance would have to be a 'titled' version of the equatorial one. That means that one side of it's orbit is at a lower latitude to the other side, whilst any point on the Earth maintains a fixed latitude during the day. Thus it would appear to go up and down in the sky.
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Choochoo_baloo
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(Original post by lerjj)
Because the orbits have to go around the Earth's centre of mass. That means the a non-equatorial orbit that is at geostationary distance would have to be a 'titled' version of the equatorial one. That means that one side of it's orbit is at a lower latitude to the other side, whilst any point on the Earth maintains a fixed latitude during the day. Thus it would appear to go up and down in the sky.
Ah ok I think I follow you. I've drawn a sketch of what I understand by your answer - attached to this post.
Vertical dashed line is the Earth's axis. Green lines are lines of latitude. Black ellipse is the equatorial plane (black hexagon is an equatorial satellite), same labelling goes for blue but as a tilted plane of orbit.

Image

So the key point is: ONLY an equatorial plane will be parallel with an observers motion (latitude lines), thus the satellite is fixed within our view of the sky. Whereas all tilted planes will arc across the sky - not a fixed position?
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lerjj
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(Original post by Choochoo_baloo)
Ah ok I think I follow you. I've drawn a sketch of what I understand by your answer - attached to this post.
Vertical dashed line is the Earth's axis. Green lines are lines of latitude. Black ellipse is the equatorial plane (black hexagon is an equatorial satellite), same labelling goes for blue but as a tilted plane of orbit.

Image

So the key point is: ONLY an equatorial plane will be parallel with an observers motion (latitude lines), thus the satellite is fixed within our view of the sky. Whereas all tilted planes will arc across the sky - not a fixed position?
To my understanding, yes. By being at geostationary distance, you automatically are fixed above a certain longitude, but only an equatorial orbit will also be fixed above the same latitude. If you drew a polar orbit at the same distance it would be reasonably obvious that the satellite does not appear to be in a fixed point.
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Choochoo_baloo
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Ok thanks a lot.
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