It's like something out of Children of the Corn. Everyone standing in the broad park at the top of a hill not far from my house looking upward in the same direction, facing north, distanced. Spread out, silent, waiting for twilight to darken into night. They wait to see a new visitor to our part of the solar system: Comet NEOWISE C/2020 F3. It was discovered by the satellite of the same name (the acronym for Wide-field Infrared Survey Explorer) designed to search for objects that could pose a danger to earth. According to the NASA JPL database (at https://ssd.jpl.nasa.gov/sbdb) this is the fifteenth comet discovered by that satellite. Comet NEOWISE passed perihelion (its swing around the sun) on July 3rd and is now outbound. For a while it’s been circumpolar, never setting, hanging out on the fringes of Ursa Major. It’s slowly moving each day from East to West under the celestial pole. That explains why I saw it in the Northeast in the morning sky, and why I’m now looking toward the northwest in the evening sky. Standing here among dozens of still people, silouetted, silent, like Easter Island statues. I double check the alt-azimuth coordinates of the comet in my https://www.heavens-above.com/ app.
At last as the sky darkens it gradually emerges, a slight wisp of light. It’s visible to the naked eye though seen much better in binoculars through the wash of our city sky. Many see nothing and leave, presumably disappointed; better to go to the country!
A few days later, on July 23rd, NEOWISE comes closest to Earth (at .69 au from Earth and .63 au from the sun). It’s now moving up and out on a fairly steep path over the ecliptic plane (the earth-sun orbital plane).
That day I drive an hour out of the city to darker skies. I do want to see and photograph this thing away from city lights. Sadly, the Oregon Star Party in the dark dark Eastern Oregon desert was canceled due to the virus. It would have been the perfect venue for seeing this wonderful comet. So instead I approach one of my favorite ‘near’ observing sites, once a mountain now eroded to a respectable range of hills. Off on a dirt side-road I haven’t tried before, I’m hoping to find a clearing. No luck. I stop. I say hello to a waddly porcupine. They are nocturnal too. I bid him on his way. Back on the main road, through the trees, a slim moon hovers low. Almost near the top, a problem: Uh oh, blinking lights, trooper in the road. Waives me over. He’s masked. I put on mine; roll down my window. Due to Covid, he says, I can’t do stargazing. Place is closed.
Ok. Serious glitch in my plan. I’m about a hundred meters from a large clearing and a majestic view of dark skies. I know the comet is up there, poised and waiting for me to observe it, to photograph its bright nucleus and long split tail before it is forever gone – gone anyway for about seventy centuries. I try another strategy.
“I’m not really here to stargaze” I say. “I’m a photographer.” It's true the back of my car is full of camera stuff. “I just want a quick picture.” He can’t possibly object to that, there isn’t another soul on this mountain.
“No, ‘fraid not sir.”
“Nobody else is here” I say, pointing to the blackness ahead.
“No sir.”
“How about if I just go over there and take a glimpse through my binoculars?”
“No sir.”
Polite but firm, he is. “If I let you in I’ll have to let everybody in.” He isn’t going to budge. I thank him for his demeanor, reverse course and start the drive back down. Another day, I’ll try another site.
Back home my wife was still up. “Any luck?” she asked. I was home unusually early for such outings. “Did you see the comet?”
“I saw a porcupine.” When I told a neighbor of my results, he said, "Did you try looking up?"
The Story Two Numbers Can Tell
Many can’t see the comet in these strange times, and it isn't for want of looking up. So let’s try to get a glimpse of it mathematically. I’ll keep the vocabulary simple and straightforward. I always like to look first at two simple elements of an orbit: eccentricity of the orbit, denoted by e, and perihelion distance, denoted by q, of the comet’s closest approach to the sun.[1] If we were to know only these two parameters of Comet NEOWISE, what would that tell us? How much information about the orbit can we squeeze out of these two numbers? The answer is, quite a lot.
With just e and q we can learn the shape and vital characteristics of the comet’s orbit, in 2D. We will not know its 3D orientation in space. For that, we’ll need other elements, which I’ll talk about another day. For Comet NEOWISE, we have,
e = .999208
q = .2946 au
Let’s look at each number in turn.
Eccentricity : Eccentricity is a dimensionless number, a kind of scale to tell you the shape of an orbit. A perfect circle has eccentricity of zero, and a parabola has an eccentricity of 1. So somewhere between zero and just shy of one lies all of the elliptical orbits that ever were and ever will be in the universe. If an eccentricity is exactly one, it is a parabola. A comet on the parabolic path will never return. If it is greater than one the trajectory is a hyperbola. It will not return either. Comet NEOWISE C/2020 F3 has an eccentricity of less than one, so we know it’s orbit is an ellipse and it will return, unless later encounters with planets (especially Jupiter or Saturn) change its orbit. (Feel free to check out my blog on interstellar object ‘Oumuamua as a refresher on these orbit types and how they are determined by the balance of energies in orbit.)
With an orbit eccentricity just shy of one, it is an extremely squished circle. Take a rubber band and put it on your desk to form an approximate circle; its eccentricity is about zero. (For reference, Earth’s orbit has a .017 eccentricity, nearly circular. Even Mercury’s fairly eccentric .206 orbit is far more circular than your average comet.) Now take it between two fingers and stretch it apart so that the rubber band is skinny and long, far longer than it is wide. The rubber band now has an eccentricity that is much closer to one. (It’s an imperfect analogy, of course, because the stretched rubber band has no curvature along the long sides.) If we imagine it to be a true ellipse, it’s length measured through the center is called the major axis and its width is called the minor axis. We normally deal with semi-major axis and semi-minor axis which are half those dimensions. Now, an eccentricity of .99208 seems pretty close to one. It’s not one, so it’s not a parabola, but it is very far from being a circle. Even if some comet’s eccentricity were .999999 its orbit would still not be a parabola. But with NEOWISE’s e at .99208, that rubber band is stretched mightily, so it must be a very elongated ellipse. How does it compare with the orbits of other high-eccentricity comets? Below I’ve compared the eccentricity of NEOWISE with those of some of my favorite comets. You will recognize them as some spectacular comets of recent history, with Isaac Newton’s Great Comet of 1680 thrown in for comparison. They are arranged in order of increasing e (toward higher and higher orbit ellipticity):
I added ISON as the hyperbolic case, with its e >1 just for comparison. (You may remember it disintegrated as it rounded the sun.) As you can see, NEOWISE’s eccentricity holds its own against some of the more showy comets of recent times. With three 9s to its e you know it had the potential to be quite interesting! But this, of course, isn’t the full story. We need to look next at perihelion distance.
Perihelion distance: The short distance from the end of the ellipse to the sun is one focus of the ellipse, and that distance is q. (Kepler coined the Latin term for ‘hearth’ in calling that point the focus.) q is measured in astronomical units (au), the astronomers standard measuring stick. Let’s look at the perihelion distances for the same comets to see how NEOWISE stacks up, q-wise. They are arranged in order of decreasing q (toward closeness to the sun in the comets’ perihelion passage):
Again, a respectable showing for its perihelion distance. You can see NEOWISE was not a “sungrazer“ like Comet Lovejoy – the kind of comet that dives in screamingly close to the sun and emerges around it, boiling, releasing multi-million mile long jaw-droppingly beautiful streamers of gas and dust, as in the top picture of Lovejoy on my NEWTON’S GRAVITY page. The most impressive comets have very low q, often thousandths of an au, coming incredibly close to the sun’s surface, and an eccentricity only a hair’s breadth this side of one. While Comet NEOWISE glided by the sun’s surface like a responsible commercial pilot at a ‘distanced’ 43 million kilometers, Lovejoy buzzed it like a crazed test pilot at an insane 135 thousand kilometers. Low-q-high-e comets typically have very long orbital periods. They’re not regular, periodically-appearing members of the solar system (like Encke or Halley). They drop in (literally) from the Oort cloud after astonishingly long and patient journeys, gradually gaining speed by the slightest of increments as they near their fateful encounters with the sun – either for a nose dive into it or, if not big enough to survive the boil-off, disintegration. The few lucky ones survive to give us a spectacular show. But NEOWISE, shown in my simple (but mathematically accurate) simulation below, with the sun depicted at twice its relative size for clarity, traded fame for security and rounded the sun at a highly appropriate distance, well away from the most intense solar heat.
Other factors will also account for a comet’s actual appearance in the sky. Even if a comet is potentially spectacular, it may not be seen as such if the earth is not well placed during the comet’s brief voyage through the solar system. The rather distant 1986 apparition of Halley’s comet was nothing like the 1910 apparition, where to the great consternation of the public the earth passed through its tail. NEOWISE did not come so close to the earth like Hyakutake whose ghostly nucleus and tail seemed to fill half the sky when it came by.
Some math . . .
So we’ve gotten at least a rough sense of NEOWISE’s e and q in comparison with some other well-known comets. Now we can take those numbers and put them into a geometrical context and come out with some other characteristics of its orbit. If math isn’t your thing, close your eyes for the next few paragraphs and join me later. Look at this sketch:
The semimajor axis a is the distance from the center to the perihelion point P or to the aphelion point A. It is also the distance from the focus F (the sun here) to the perpendicular drawn from the center (that’s the semi-minor axis, b, though not marked as such in the picture). The distance between focus F and the perihelion point P is the perihelion distance q that we’ve been talking about. Since q + ae = a, we can find the semi-major axis, a, for Comet NEOWISE from the e and q. The equation is a = q/(1-e ). So,
a = 372.0589651 au.
You might’ve guessed that we can find the semi-minor axis b for NEOWISE by using the Pythagorean theorem. See if you can solve for b. The result is:
b = 14.80463156 au.
The ratio of these two axes a : b is about 25 to 1. If we were to draw the NEOWISE ellipse on a piece of paper, as Newton did with his Great Comet of 1680 (by “scale and compass”) we could make it about a foot long by half-an-inch wide. By comparison, the long-to-short axis ratio for Newton’s 1680 comet was about 69 to 1. That would be harder to draw!
Before we go, let’s find the orbital period P of NEOWISE by using Kepler’s simple Harmonic Law (his famous Third Law of planetary motion, which applies not just to planets!), where the square of the period is equal to the cube of the semi-major axis a. Using the semi-major axis of NEOWISE a that we found above, you can do it on your calculator:
P = 7,176.58 years
That’s a long time! What will our world be like when it returns?
[1] There are of course other elements of any orbit I’m not mentioning here. If you go to the NASA/JPL site https://ssd.jpl.nasa.gov/horizons.cgi you’ll see the “Horizons” database system. Click on “Bodies” then “Comets” then “Small-Body Browser” and you’ll see a search engine. Type in “Neowise” and you’ll see a list. Select the C/2020 F3 at the bottom and it will take you to our comet. You’ll see all the “Orbital Elements” and a legend for reading them. Here I am talking about only two of the elements, e and q. It’s a fun site. Try playing around with its features.
The picture of NEOWISE at the top was taken by the talented Austrian astrophotographer Michael Jaeger.
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