### Is Earth's Surface "In orbit"?

• I'm having trouble understanding relative angular/tangential speeds at increasing altitudes above Earth's surface. In particular, I find this comparison of tangential velocities on Wikipedia very confusing. According to it, the tangential speed of Earth's surface (465.1 m/s) is different from the tangential speed required to "orbit" at Earth's surface (7.9 km/s). Why are these different values? My understanding of the Earth was always that material on and within the Earth is orbiting the center of the Earth just like satellties do. Time for multiple questions in one post...

1. Is material on Earth's surface not in free fall around Earth's center?

2. How are geostationary orbits even a thing? Seems like the only orbit that could be geostationary would be standing on the Earth's surface.

3. What changes as you orbit further above the Earth's surface? Does your angular speed increase or decrease? Does your tangential speed increase or decrease?

4. Is magma near the center of the Earth not rotating faster than material in the crust, like in an accretion disk?

5. Can two objects be orbiting (circularly) at the same altitude but with different tangential speeds?

Consider what happens if you're standing at the North or South poles, and how you move relative to the centre of the Earth.

If we were in orbit, we'd be floating.

Earth's speed of rotation is simply not the required orbital speed. That's more a question of how much angular momentum Earth has left-over from its formation.

Consider that you can have celestial bodies that rotate pretty fast (Jupiter 9 hrs 56 minutes, Saturn = 10 hrs, 42 minutes) or pretty slowly (Venus 116 days, 18 hrs, Earth's moon 27 days, 8 hrs), irrespective of the speed needed to orbit them - which is a function of mass and distance.

As to #1, free fall is kinda the opposite of "being on Earth's surface". The former means **not** experiencing the forces associated with gravity, such as the force of your seat against your chair or your feet against the ground while standing. Even sky diving is not really "free fall" once air resistance builds up.

Consider that if Earth was rotating fast enough for you to be in orbit at the surface, then the surface itself would also not be held by gravity and the planet would throw itself apart - at least until the remaining surface was sufficiently below orbital velocity to remain stuck to the planet.

*::blink::* I'd be interested in hearing how you came by the understanding that *"material on and within the Earth is orbiting the center of the Earth"*. No reputable source should say anything like that which leaves me wondering about plausible-sounding chains of conjecture.

Oh, and let's not forget neutron stars, the fastest known of which spins at 43,000 RPM - which means the equator is moving at more than 20% of the speed of light.

@dmckee I think my confusion came from descriptions of tidal forces (e.g., https://en.m.wikipedia.org/wiki/Tidal_force). They always show opposite "bulges" facing toward and away from the Moon, which I assumed was due to crust material being pushed into a higher, elliptical "orbit" by the Moon's gravity. I think I see now how the Earth's crust is not in orbit, but now I don't really understand tidal bulges lol

It might be helpful to imagine the Earth as airless and *not spinning*. The orbital velocity at a given height around an airless, uniform body does not change whether the body is spinning or not, right?

If playing around with absurd scenarios like "an earth-mass planet spinning fast enough that objects on the surface are thrown into orbit", there is a mod to Kerbal Space Program that adds a planet like that to the game. I have not tried it myself but apparently it is quite difficult to land on.

The Moon provides a force of gravity on the Earth, the same as the Earth does on the Moon, and that force is stronger on the Moon side, and weaker on the opposite side. If it helps, think of the Moon as pulling the ocean on the near side away from the Earth, and pulling the Earth *away from the ocean* on the far side.

@PM2Ring Aren't we all orbiting the Sun?

@EricDuminil Fair point, although my solar orbit is slightly modified since I'm gravitationally attached to the Earth. But sure, Earth (and everything on it) is floating in freefall "above" the Sun.

If it did, we'd have flying cars for quite a while already ;-). Also, we wouldn't need a space elevator (and couldn't build one; it would fly away).

• Peter Erwin Correct answer

2 years ago

1. Is material on Earth's surface not in free fall around Earth's center?

No. Material on the Earth's surface -- or inside it -- is not in orbit, and so is not in free fall. You can temporarily put yourself into an orbit (and thus into free fall) by jumping up into the air, or jumping off a higher surface. When you do this, you are briefly in a very eccentric orbit (one which would take you very close to the center of the Earth, if the Earth wasn't a solid body) -- but then you hit the ground and are no longer in orbit.

The Earth rotates in the same way that a spinning top rotates; this has nothing to do with orbits.

2. How are geostationary orbits even a thing? Seems like the only orbit that could be geostationary would be standing on the Earth's surface.

Again, the surface of the Earth is not orbiting. The Earth rotates as a rigid body, with (as AtmosphericPrisonEscape noted) residual angular momentum left over from its formation, like a spinning top.

Because your angular speed in an orbit decreases the further away you are from the Earth, there will be a point where it happens to match the Earth's spin rate. If you arrange the orbit so it is above the equator and in the same direction as the Earth's spin, then you will always be above the point on the equator: a geostationary orbit.

3. What changes as you orbit further above the Earth's surface? Does your angular speed increase or decrease? Does your tangential speed increase or decrease?

Both your angular speed and your tangential speed decrease the further away you get. (Your angular speed would decrease even if your tangential speed stayed the same, because the circumference of your orbit increases with altitude; but in fact the tangential speed decreases as well.)

4. Is magma near the center of the Earth not rotating faster than material in the crust, like in an accretion disk?

The Earth rotates approximately as a rigid body, so in general, no. The molten outer core (which is not magma) may rotate slightly slower, while the solid inner core might rotate a little faster, but we're talking about $$\sim 0.1$$ degrees per year differences, and this has nothing to do with orbits. (The Earth is nothing like an accretion disk.)

5. Can two objects be orbiting (circularly) at the same altitude but with different tangential speeds?

Ignoring minor deviations due to things like the non-spherical nature of the Earth, mass concentrations in the crust, etc., the orbital speed for a circular orbit is a function of the altitude only. So two objects in circular orbit at the same altitude must have the same tangential speed. (Note that they can have different velocities, because velocity is a vector quantity -- so you can have two object orbiting in different -- even opposite -- directions at the same altitude, at least until they run into each other.)

Nice answer, but minor correction from geophysics: the Earth's Outer Core is molten (mostly made out of iron) and convecting according to magnetohydrodynamics, maybe(!) rotating slightly more slowly on average. The Earth's Inner Core consists (mostly) of solid iron and may be rotating slightly faster then the mantle/surface (but no more than 0.1 deg/year or so faster - with the years this estimated number went down substantially)

frederik -- Good points; I'll edit the answer.

"You can temporarily put yourself into an orbit (and thus into free fall) by jumping up into the air, or jumping off a higher surface...but then you hit the ground and are no longer in orbit." To paraphrase Douglas Adams, "The knack [to flying] lies in learning how to throw yourself at the ground and miss."

I think the idea that anything can be "in orbit" in Earth's atmosphere is at least confusing if not inaccurate. "Orbit" implies a cycle, and objects in low-earth orbit, e.g., are considered to be "de-orbiting" when they encounter the atmosphere at any significant density. And aircraft are not considered to be orbiting either (Star Trek dialog notwithstanding (Tomorrow is Yesterday).) In short, no vehicle has the thrust resources (nor the necessary heat shielding) to maintain orbital velocity in the atmosphere.

@PeterErwin fantastic answer, marked as correct! If you get a minute, I'd love to see some links to back up your claims. E.g., the math behind #3 and where you (or rather @frederik) got the ~0.1 deg/year in #4 from. Thanks again either way!

Also @PeterErwin, regarding #5... What if a rocket was in orbit, and fired diagonally so that its acceleration had a tangential component _increasing_ its tangential speed, and a perpendicular component pushing back in toward Earth...could it not reach a faster tangential speed at the same altitude? I guess that isn't really true orbiting though...presumably once it turned off the engines, its tangential speed would send it up into a higher, elliptical, "true" orbit

@JeffY You're using a more restricted definition of an orbit. In general, anything that follows geodesics is an orbit (or in Netwonian models, any trajectory curved mostly by gravity), and we usually allow for orbits that don't _perfectly_ follow geodesics too (e.g. satellites around Earth do not follow geodesics perfectly, because they're accelerated by their collisions with air). In the same sense, a person jumping off a cliff is imperfectly following a geodesic (until he hits the ground). The main point is that objects in orbits move exactly the same way regardless of how many orbits you do

@Rabadash8820 The rocket wouldn't be in free fall; you would feel acceleration onboard the rocket ship (in fact, the same as if you were standing on a surface - you basically made a very silly airplane). That's not an orbit. Being in orbit means you're following geodesics - your trajectory is curved only by gravity (to a reasonable approximation). The crucial point is that as soon as you turn off that engine, you're going to be on a highly eccentric orbit where your altitude when you turned off the engine is the lowest point, and the highest point depends on your velocity at that time.

@JeffY I've run into that frustration here over the term "orbit" as well - even the NASA website defines an orbit as "a regular, repeating path", and says that "all orbits are elliptical". A more general definition is given by Wikipedia, which is simply a "gravitationally curved trajectory". Most people use "orbit" as shorthand for "orbital trajectory" (which is repeating and elliptical), but it could also refer to a suborbital or escape trajectory (which are non-repeating and non-elliptical), particularly among such a precise and knowledgeable crowd as you'll find here.

@JeffY Even in the two-body problem, there are hyperbolic orbits (like extrasolar comets!) which are not "cyclic". And more generally, there are chaotic orbits which are not cyclic, either. (As Luaan noted: geodesics!)

Again, it's highly confusing (read counterproductive) to include "any geodesic path" in the definition of "orbit", **especially when there is another perfectly good term** for describing such trajectories **as distinct** from orbits: ballistic. Alan Shepard was not the first American to orbit. Insisting otherwise is, frankly, divisive, crankish, and unnecessary.

"5. Can two objects be orbiting (circularly) at the same altitude but with different tangential speeds?" Can't let that go without mentioning horseshoe orbits

@Rabadash8820 I added a link in the answer to #4 pointing to a Nat.Geo. article (which has links to the original papers) summarizing recent work on the core's rotation.