• Collin Cherubim

Close Encounters of the Venereal Kind

How fast are you moving right now?

I’m guessing you’re sitting still. But the Earth is rotating at 1,670 km per hour about its axis. It’s revolving around the Sun at over a hundred thousand km per hour, and the Sun is whizzing around the center of the Milky Way at nearly three quarters of a million km per hour, and the Milky Way is... Never mind.

Why do you think you’re sitting still then? Why don’t we feel that motion? Let that marinate for a bit and we’ll come back to it later.

If you’re in the Northern hemisphere, you may have noticed a bright object in the sky at twilight over the past month or so. That's Earth’s hot sister, Venus. You may have seen her dancing with the crescent moon on the first day of Ramadan, bearing a staggering resemblance to the symbol of Islam. I was enjoying the sunset and the perfect view of Venus from my apartment in Casablanca, Morocco the other night when a thought suddenly wrinkled my brain. I thought, is water wet?

Ok not really. Actually I was trying to get a grip on my cosmic bearings. Standing still, I wanted to feel the Earth’s motion, or at least orient myself to it. Of course we can’t feel the Earth’s rotation, but we can see it as the Sun sets and Venus retires on the horizon after her dance with the moon. I imagined myself sitting on the giant rock that is Earth, spinning away from the Sun as it disappeared.

Then I took it a step further. I wondered how the orbital plane of our system was oriented with respect to the horizon. What would our orbital path look like if it were projected into the sky? This sent me down quite a rabbit hole. Fortunately I came up with a satisfying answer. Before I show you, I want you to try and figure it out for yourself.

If you’re near a window, go take a look outside for a moment. Look at the horizon and riddle me this: Where is the plane of Earth’s orbit? Is it horizontal, that is roughly parallel with the horizon? Is it vertical? Or is it at some angle? Try to visualize it.

The answer depends on the time of day, the time of year, and your geographic latitude on Earth. Regardless, I think most of us intuit that the Earth's orbit is in a plane – called the “ecliptic” – parallel to the horizon, along with the other planets' orbital planes, which are roughly parallel to ours. At least that was my gut reaction, and that of many others polled on Facebook (yes I know, quite a representative sample). After thinking about it a bit longer, I realized that the Sun had set on the horizon mostly vertically with Venus following close by. If we’re orbiting the Sun with Venus, it seems the plane is mostly vertical. But isn’t the apparent “setting” of objects like the Sun on the horizon a result of our rotation, not our orbital path? To help disentangle this mess, let’s look at a diagram.

Figure 1 - Casablanca's latitude, Earth pictured during Spring (Gregorian)

Casablanca’s latitude is 33.6 degrees North. The image shows Casa’s relative position at sunset, moments after the brain wrinkle occurred on my terrace. Imagine the Earth rotating counterclockwise as little bald me in Morocco slowly vanishes behind the globe. The figure shows that the ecliptic is approximately 10 degrees from the vertical, leftward leaning relative to the horizon at sunset.

Ultimately I wanted to be able to picture this in the sky next time I watched the sunset. So here is a visualization of the ecliptic projected into the sky, Pink Floyd laser light style.

Figure 2 - Ecliptic projection

What I really wanted was to visualize the Earth careening through space, just past Venus. I wondered what the apparent distance from our orbital path was from Venus. In other words, what would it look like if I were able to shine a giant laser pointer into the sky that curved past Venus, tracing our orbit? From this distance, would it look as if the laser nearly touches Venus? Would it shoot really high into the sky, several feet above Venus in my field of view? I already knew the laser would arc through the sky, 10 degrees left of the vertical. But to answer the question fully, I needed to know Earth’s current distance from Venus as well as the distance of closest approach.

An astronomical unit – or 1 AU – is the average distance from Earth to the Sun and is equal to 149,597,870,700 m, or about 150 million km (that’s about 93 million miles for you Imperialists out there). The AU is like an astronomical meter stick. The time of the brain wrinkle was about 8:30 pm April 13, 2020. According to theskylive.com, which provides solar system data in real time, our distance from Venus at that time was 0.555041 AU. To determine the apparent position of closest approach to Venus in the sky, I used the Earth-Venus distance of 0.28859 AU predicted for June 4, 2020. This is as close as the two planets will get. Finally, using NASA's live tracking of our solar system, I mapped this all out (shown below, Figure 3). Note that the use of 0.28859 AU on June 4 as a proxy for the distance 'AB' shown below in Figure 3 is an assumption that limits my calculations, but it is a good approximation given the relative shapes of the Earth's and Venus' orbital paths.

Figure 3 - Orbital geometry and angular separation, courtesy of 'NASA's Eyes'

As it turns out I got super lucky. It just so happened that on April 13, Earth, Venus, and Earth’s position of closest approach to Venus (point A; Earth's location about a month earlier) formed almost a perfect isosceles triangle. My task was reduced to a simple trigonometry problem. If I could find the angular separation of Earth and Venus at closest approach, I would know how close Earth’s orbit is to Venus in my field of view when looking at the night sky. The method is outlined below in Figure 4 where the diagram above (Figure 3) is replicated on the left. The right side of Figure 4 shows how to use the angular separation to determine the distance between Earth and Venus at closest approach using a ruler held at arm’s length.

Figure 4 - The orbital geometry is used to solve for alpha, which is then used to determine the angular separation of Earth from Venus at closest approach

Aha! So the laser outline of our orbit in the sky would arc over Venus, passing it by at 32.82 cm or 12.93 inches – about a foot. To visualize the orbital path, I needed an image for scaling:

Figure 5 - Scaling the apparent distance of Earth's closest approach to Venus. Note that I actually used the correct length of 32.82 cm in the images that follow

And we’ve emerged from the Venereal rabbit hole:

Figure 6 - Earth's orbital path projected into the sky above Venus

And to enjoy the show without subtitles:

Figure 7 - Earth's orbital path sin subtítulos

By the time I’ve posted this, our orbital geometry has changed a bit. However the image will remain relatively accurate for those of us living 33.6 degrees North of the equator until mid-late May. It will then become relevant again in August, except only during sunrise, and the orbit will become mostly horizontal relative to the horizon.

Can you repeat this exercise using your own latitude? Use Figure 1 and Earth's axial tilt of 23.5 degrees to guide you. Tell us your location and the orientation of the ecliptic relative to the horizon in terms of degrees in the comments section. The results will be similar for North Americans. Can you also figure out for which latitudes the ecliptic will appear perfectly horizontal and at what times of the day for which seasons? Let me know in the comments! One more challenge: Determine if Earth is moving toward Venus or away from Venus along the orbital path in Figure 7 ( Figure 3 should help). Now you'll be able to picture yourself spinning around this massive rock, hurling through space just past Venus in the night sky.

Let’s circle back to the opening question: Why can’t you feel the motion of our planet (I can’t feel it anyway and if you feel it, go see a doctor)? The answer is that you and every one of your molecules, inside and out, are moving at a constant velocity along with the Earth. Imagine getting double bounced off of a trampoline the size of Texas into outer space. Once you leave Earth’s gravitational field and can’t see anything near you as a frame of reference, how can you tell you’re moving? You can’t because we don’t “feel” constant velocity, we “feel” acceleration. Forces make things accelerate, and we feel forces. You would surely feel the force of the trampoline as it accelerates you into space, but once you achieve constant velocity, there’s no force on you so you feel nothing (provided your internal organs have time to catch up with the rest of your body). Since you rotate about the axis and revolve around the Sun at constant speeds, there's no acceleration - with the exception of the acceleration due to Earth’s gravity, which you certainly do feel - so you can’t feel the motion.

The Earth and the Milky Way are moving through mostly empty space (ignoring the few particles per cubic centimeter of interplanetary space and the quantum fluctuations and field excitations pervading all space, filling it with virtual particles flitting in and out of existence predicted by quantum field theory rendering empty space hardly "empty" at all). Therefore there are no resistive forces to our motion. The Earth plows through approximately 100 metric tons (over 200,000 pounds) of space dust every day as determined by spacecraft measurements and sample collection on Earth, but even that isn't enough to “push back,” giving us a pulse on our velocity.

This is akin to why astronauts feel weightless in orbit around the Earth. Weight is the force on a mass due to gravity. When you step on a scale, it measures the product of your mass and the acceleration due to gravity. Newton’s third law tells us that the scale pushes back up on you with the same force, called a normal force, or reaction force. So do astronauts have mass? And is the Earth’s gravity still exerting a force on them? The answer is yes to both questions, so astronauts have weight. Yet they feel weightless and seemingly stationary relative to space stations when performing space walks outside. This is because they’re missing a reaction force to allow them to feel and experience their own weight.

Want to lose weight? Become an astronaut.