# Stationary or not?

by Grimstone
Tags: stationary
 P: 69 stationary or not? I understand that satellites orbit the earth at a speed and angle that allows them to "free fall" the entire time. That is they are going so fast that they are always cresting the edge of the planet and always in a state of free fall. isn't it possible to place a satellite or station that is pretty much stationary over the poles? yes the orbit of the earth is not round. yes the earth tilts.
 Sci Advisor P: 6,106 Satellites can be placed stationary over a point on the equator, not at the poles. The satellite must orbit the earth - over the equator, the orbital period can be made coincident with the earth's rotation.
 Sci Advisor PF Gold P: 9,488 A stable orbit is impossible unless the satellite is traveling at least at escape velocity wrt to the body it orbits - this is orbital mechancis 101.
P: 2,504
Stationary or not?

 Quote by Grimstone stationary or not? I understand that satellites orbit the earth at a speed and angle that allows them to "free fall" the entire time. That is they are going so fast that they are always cresting the edge of the planet and always in a state of free fall. isn't it possible to place a satellite or station that is pretty much stationary over the poles? yes the orbit of the earth is not round. yes the earth tilts.
No. As mathman said, an orbiting body can only remain stationary with respect to a point on the Earth's surface when it is in the geocentric orbit (more specifically geostationary). That is, an orbit in the equatorial plane at a distance of about 40,000 km where the orbital speed matches the Earth's rotation in terms of a fixed point on the surface.

Any other orbit must lie in a plane which contains the Earth's center of gravity (mass) so polar orbits are possible, but they cannot be geostationary.
 P: 69 thank you.
Mentor
P: 22,313
 Quote by Chronos A stable orbit is impossible unless the satellite is traveling at least at escape velocity wrt to the body it orbits - this is orbital mechancis 101.
Er, what? No it isn't! Orbital speed is of course lower than "escape" velocity!
Mentor
P: 15,201
 Quote by russ_watters Er, what? No it isn't! Orbital speed is of course lower than "escape" velocity!
Emeritus
PF Gold
P: 5,196
 Quote by D H Google the term "hyperbolic orbit".
Like russ, I don't understand either. If you just apply the virial theorem to the simple system of a satellite in a circular orbit around some parent body, you get that the speed at the orbital radius is exactly half of what the escape speed would be at that radius. You can also derive this result just by using centripetal force, of course.

So, regardless of what a hyperbolic orbit is (and I haven't googled it), the statement that the escape speed is a minimum speed required for a stable orbit seems manifestly wrong.
 Sci Advisor PF Gold P: 9,488 Agreed, I was thinking of escape velocity at the surface of earth vs orbital velocity around earth. Obviously orbital velocity is always less than escape velocity by a factor of sqrt 2.
Mentor
P: 15,201
 Quote by cepheid Like russ, I don't understand either.
I misread. I thought Chronos was talking about a radial orbit directly away from the pole. The satellite isn't stationary in terms of distance, but it is in terms of angular position. Such an orbit is of course of no use for communications or Earth observations.

 Quote by Chronos Agreed, I was thinking of escape velocity at the surface of earth vs orbital velocity around earth. Obviously orbital velocity is always less than escape velocity by a factor of sqrt 2.
Still not right. (Closed) orbital velocity is always less than escape velocity. There's no factor of sqrt(2). Escape velocity by definition is that speed at which a trajectory changes from a closed orbit to an open orbit (or escape trajectory, if you don't like using the word "orbit" for things that aren't "orbiting").
Emeritus
PF Gold
P: 2,361
 Quote by Chronos Agreed, I was thinking of escape velocity at the surface of earth vs orbital velocity around earth. Obviously orbital velocity is always less than escape velocity by a factor of sqrt 2.
The sqrt 2 factor holds when comparing orbital velocity for a circular orbit to escape velocity. For an elliptical orbit, orbital velocity changes throughout the orbit, and approaches escape velocity at periapsis as the eccentricity approaches 1. This leads to an interesting fact: If you are already in an elliptical orbit, it takes less delta v to achieve escape velocity at periapsis than it does apoapsis
HW Helper
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 Quote by Grimstone stationary or not? I understand that satellites orbit the earth at a speed and angle that allows them to "free fall" the entire time. That is they are going so fast that they are always cresting the edge of the planet and always in a state of free fall. isn't it possible to place a satellite or station that is pretty much stationary over the poles? yes the orbit of the earth is not round. yes the earth tilts.
It's not possible to put a single satellite into an orbit that's stationary over the poles, but it is possible to accomplish the same result using several satellites.

With a constellation of satellites in Molniya orbits, you can stagger their orbits so there's always some satellite in the same given location all of the time. From the point of view of the tracking station, they point their antenna roughly in one direction and each satellite moves into that location in a kind of relay race. The antenna barely has to move to pick up the next satellite coming along.

Typically, this is done with six satellites in a semi-synchronous orbit (two orbits per day, which means each satellite is used for two periods per day, giving you the equivalent of a 12 satellite relay race). You could do this with a minimum of four satellites if you were willing to move your antenna just a bit further to pick up the next satellite coming along.

And, the satellites wouldn't be directly over the poles. They have to have an inclination angle of 63.4 degrees, so you'd actually always have a satellite at about 63.4 degrees latitude with some nearly constant longitude.

The 63.4 degree requirement is because you create this relay race with satellites in highly elliptical orbits. The satellite is used when its at apogee and is moving very slowly. Because of the equatorial bulge, perigee and apogee will move forwards or backwards depending on the inclination angle, with 63.4 degrees being the angle where perigee and apogee remain stationary.

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