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Assuming that a method was found to teleport objects, and at huge range, if an object was teleported from the surface to a location at the correct height (Wikipedia says about 42,164 km from the earth's center of gravity, if I'm reading it correctly) and directly above its point of origin and maintained all momentum, would it arrive in a geosynchronous orbit? The momentum transferred from its surface velocity should be exactly the velocity of an object in geosynchronous orbit, if my understanding of orbital mechanics is correct, and, thus, it should be in geosynchronous orbit.

Teleporting the object to a location closer to earth should result in it being at the apoapsis of an elliptical orbit and on its way back down towards earth, and, if it was teleported low enough, it would eventually collide. Teleporting an object further would result in it being at the periapsis of an elliptical orbit, and, if teleported far enough, it would actually leave earth's orbit.

The question comes as a result of me thinking over design concepts for a physics-heavy game involving space travel and ultimately future technology and trying to wrap my head around how all of these various types of science-fiction technology would actually interact with orbital mechanics.

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    $\begingroup$ Astronomy and World building $\endgroup$
    – Muze
    Commented Apr 18, 2018 at 16:31
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    $\begingroup$ Teleporting an object to any given orbit while maintaining momentum is no different than teleporting your object to a position a few feet above the protagonist's head. What happens next? Gravity takes over. $\endgroup$
    – Saiboogu
    Commented Apr 18, 2018 at 18:13
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    $\begingroup$ @Saiboogu You are correct in that 'gravity takes over', but keep in mind that orbiting is essentially falling but constantly missing. If your forward momentum is sufficient, you should 'fall' due to gravity, but still miss and establish an orbit. Unfortunately, it looks like earth's surface velocity is insufficient to establish a circular orbit within it's SOI, though it may be able to establish an elliptical orbit. I'm uncertain there still. $\endgroup$
    – Darinth
    Commented Apr 18, 2018 at 22:43
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    $\begingroup$ Play KSP for at least another year first. Click on the speed indicator to swap between surface, orbit, and target: relative velocities. $\endgroup$
    – Mazura
    Commented Apr 19, 2018 at 0:27
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    $\begingroup$ At least you think a little before you try to teleport, and ask if you are not sure ;-). Most don't, and that's why we hear so little about it. $\endgroup$
    – Peter - Reinstate Monica
    Commented Apr 19, 2018 at 10:02

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I'm afraid you are incorrect. An object on the equator of Earth has a velocity of ~460 m/s. A satellite in geosynchronous orbit has a velocity of ~3000 m/s.

You may be confused by the fact that both objects complete an "orbit" in 24 hours. But consider the fact that the satellite travels a significantly greater distance in that time.

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    $\begingroup$ And the second I read the answer I realized the mistake I made. An object in geosychronous orbit has a "surface velocity" of zero because it stays above the same spot, but the orbital velocity is still much higher. Theoretically if an object were teleported high enough, would it enter orbit since objects at higher orbits do have slower velocities? $\endgroup$
    – Darinth
    Commented Apr 18, 2018 at 19:00
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    $\begingroup$ The Moon's orbital velocity is about 1000 m/s so there may theoretically be an Earth orbit further than that with a 460 m/s velocity. But I am a LEO guy...don't know what perturbations such high orbits are subject to. $\endgroup$
    – Organic Marble
    Commented Apr 18, 2018 at 19:59
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    $\begingroup$ My research at the moment indicates that in principle, a faster spinning planet (or one with more gravity) could allow for this phenomenon, but based on wikipedia's indicated SOI for earth of 924,000 km and CalcTool's estimated earth orbit to achieve a orbital velocity of 460 m/s of about 1,870,000 km this wouldn't be possible on earth as you'd be well outside of it's SOI. $\endgroup$
    – Darinth
    Commented Apr 18, 2018 at 20:03
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    $\begingroup$ @Darinth yes, in geostationary orbit, the surface velocity is 0, the orbital velocity is greater than on the surface. The surface velocity is really just a ∆(rotational) and they do have the same rotational velocity, but that isn't carried over with your 'teleport' $\endgroup$
    – Baldrickk
    Commented Apr 19, 2018 at 12:58
  • $\begingroup$ @PeterCordes I think you're failing to take into account that orbital speed decreases with distance. An object can be moving fast enough on the surface of a planet that it would be in a stable orbit if it were high enough up, but not in a low orbit or enough to be ejected into orbit. The moon only has a mean orbital speed of about 1000 m/s, not enough to reach LEO but enough to remain in a stable orbit further away. $\endgroup$
    – Darinth
    Commented May 22, 2018 at 14:14
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As Organic Marble indicates, you'd have insufficient orbital velocity.

However, even if you haven't increased the orbital velocity with your teleport, you have increased the orbital energy by increasing the altitude.

If your game allows the object to be teleported a 2nd time you can still achieve geosynchronous orbit by allowing the object to fall towards earth until its velocity has increased to around 3070 m/s, then teleport it again back to 35,786 km over the equator at the correct phase such that its velocity is tangential to the target geosynchronous orbit.

Alternately, considering this teleportation machine can somehow profoundly increase the gravitational potential energy of an object, I see no strong argument (besides "teleportation does not exist", which we have already suspended) that it could not also increase the kinetic energy of the object and teleport directly to the desired orbit with the necessary velocity.

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  • $\begingroup$ And this is the a great example of the kinds of emergent gameplay that will be fascinating to watch. One teleport to get into space, then use gravity to slingshot an object up to orbital velocity and into position. $\endgroup$
    – Darinth
    Commented Apr 20, 2018 at 16:19
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To have an 460 meter/s velocity in a circular orbit, an object would need to orbit the earth at an altitude of 1.9 million kilometers. Which is outside Earth's Hill Sphere so the sun would wrest it from Earth's influence and it would be in a heliocentric orbit.

If you have a 300 km perigee, an elliptical orbit with an 150,000 km apogee would be moving about 460 m/s at apogee.

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  • $\begingroup$ Thank you! I wasn't certain how to calculate what apogee/perigee you'd end up at with different starting speeds and points. So it sounds like establishing an eliptical orbit utilizing a single teleport about 150,000 km above your point of origin is feasible. $\endgroup$
    – Darinth
    Commented Apr 20, 2018 at 16:27

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