Professor of Mathematics Jan Vrbik explains the math and science behind the total solar eclipse happening on Monday, April 8.
The rarity of a total solar eclipse, set to take place over Niagara and select areas across North America April 8, can be better understood by breaking down the math and science involved, says a Brock University expert.
The celestial phenomenon, in which the moon completely blocks the sun and turns the daytime sky dark enough to see stars for several minutes, will be a once-in-a-lifetime experience for many who witness it next month.
Jan Vrbik, a Professor of Mathematics who studies the movement of the sun, planets and moons, says there are four factors that make witnessing a total solar eclipse quite rare.
The distances of the sun and moon from the Earth
“Even though the sun is 400 times larger than the moon, when we look at them in the sky, they appear to be practically the same size,” says Vrbik. “This is because their distances from Earth are roughly in the same 400 to one ratio.”
It’s why the moon can obscure the sun, either partially or fully, to create a solar eclipse.
The tilt of the moon’s orbit
The moon’s orbit around the Earth is not a perfect circle — it’s an ellipse — so the distance of the moon from Earth fluctuates depending on where it is along its orbit.
“It varies by 11 per cent each month, which implies that the moon’s disk also fluctuates in size compared to the sun,” says Vrbik.
About 35 per cent of the time, the moon’s disk is bigger than the sun’s disk, and the other 65 per cent of the time, it’s the reverse, he says.
An illustration of a solar eclipse, in which the sun, moon and Earth align so that the moon blocks light from the sun and casts a shadow on parts of the Earth. The smaller inner shadow is the umbra, the darkest part of the moon’s shadow. People in this small area will see a total solar eclipse, lasting about three minutes, in which the day turns into night and stars and planets become visible. The much larger outer shadow is the penumbra, the moon’s lighter shadow. People in this area will see a partial eclipse for several hours.
The intersection of the sun and moon’s orbits
The Earth orbits the sun once a year, while the moon circles the Earth once a month. If the sun and moon’s orbits were on the same plane, an eclipse would happen every month, but the moon’s orbit is tilted by about five degrees from the sun’s orbit.
“This means that at most new moons, the moon is either visibly higher or lower in the sky than the sun,” says Vrbik. “Nevertheless, the moon needs to cross the plane of the sun’s orbit twice during its monthly cycle, at an intersection called a ‘node.’ Eclipses happen only when, during a new moon, the sun’s direction is closely aligned with one of these nodes, which happens regularly twice a year.”
He says 23 per cent of solar eclipses are ‘total,’ when the moon fully covers the sun, and 42 per cent are ‘annular,’ when the moon’s disk is smaller than the sun’s disk and a ‘ring of fire’ is seen.
“Thirty-five per cent of solar eclipses run so much off the Earth’s centre that only a partial eclipse is observed on one side of the globe — with the actual path of totality missing the Earth entirely,” he says.
The moon’s shadow along the path of totality
For both an annular and total solar eclipse, the moon’s shadow needs to cross the Earth’s surface.
The size of the moon’s shadow varies depending on how close in time the event is to when the moon is at its closest to Earth. Typically, the shadow is 150 kilometres (km) in a circular area. A much larger part of the Earth’s surface, about 7,000 kms across, will at the same time experience a partial eclipse, in which only a part of the sun’s disk is covered by the moon.
Vrbik says the shadow’s path across the globe is a combination of the moon’s straight-line motion of about one km per second and the Earth’s rotation of close to 0.5 km per second, complicated more by the fact that the Earth’s axis is tilted.
If people are in the right place at the right time, they can witness a total solar eclipse for three to four minutes.
Brock University Professor of Mathematics Jan Vrbik
Adding it all up
“When one considers the movement of the sun, the Earth and the moon, as well as their orbits, speed, distance and alignment from each other, it is easier to understand why a total solar eclipse is so rare,” says Vrbik.
While a total solar eclipse occurs on Earth every 18 months, it usually occurs over water. The last time a total solar eclipse occurred over Ontario was in 1979. The next one won’t happen again over the province until 2099.
“If you know the length of each celestial body’s cycle, you can easily predict when an eclipse will happen again,” he says. “Experiencing a total solar eclipse from a specific location is a rare privilege, typically separated from the next such occurrence by several centuries.”
Vrbik will be among a group of Brock experts leading discussions and educational exhibits around the solar eclipse during ‘Eclipse on the Escarpment,’ a free community event being held on Brock’s main campus Monday, April 8.
NAIROBI, Kenya (AP) — The body of Ugandan Olympic athlete Rebecca Cheptegei — who died after being set on fire by her partner in Kenya — was received Friday by family and anti-femicide crusaders, ahead of her burial a day later.
Cheptegei’s family met with dozens of activists Friday who had marched to the Moi Teaching and Referral Hospital’s morgue in the western city of Eldoret while chanting anti-femicide slogans.
She is the fourth female athlete to have been killed by her partner in Kenya in yet another case of gender-based violence in recent years.
Viola Cheptoo, the founder of Tirop Angels – an organization that was formed in honor of athlete Agnes Tirop, who was stabbed to death in 2021, said stakeholders need to ensure this is the last death of an athlete due to gender-based violence.
“We are here to say that enough is enough, we are tired of burying our sisters due to GBV,” she said.
It was a somber mood at the morgue as athletes and family members viewed Cheptegei’s body which sustained 80% of burns after she was doused with gasoline by her partner Dickson Ndiema. Ndiema sustained 30% burns on his body and later succumbed.
Ndiema and Cheptegei were said to have quarreled over a piece of land that the athlete bought in Kenya, according to a report filed by the local chief.
Cheptegei competed in the women’s marathon at the Paris Olympics less than a month before the attack. She finished in 44th place.
Cheptegei’s father, Joseph, said that the body will make a brief stop at their home in the Endebess area before proceeding to Bukwo in eastern Uganda for a night vigil and burial on Saturday.
“We are in the final part of giving my daughter the last respect,” a visibly distraught Joseph said.
He told reporters last week that Ndiema was stalking and threatening Cheptegei and the family had informed police.
Four in 10 women or an estimated 41% of dating or married Kenyan women have experienced physical or sexual violence perpetrated by their current or most recent partner, according to the Kenya Demographic and Health Survey 2022.
TEL AVIV, Israel (AP) — A rare Bronze-Era jar accidentally smashed by a 4-year-old visiting a museum was back on display Wednesday after restoration experts were able to carefully piece the artifact back together.
Last month, a family from northern Israel was visiting the museum when their youngest son tipped over the jar, which smashed into pieces.
Alex Geller, the boy’s father, said his son — the youngest of three — is exceptionally curious, and that the moment he heard the crash, “please let that not be my child” was the first thought that raced through his head.
The jar has been on display at the Hecht Museum in Haifa for 35 years. It was one of the only containers of its size and from that period still complete when it was discovered.
The Bronze Age jar is one of many artifacts exhibited out in the open, part of the Hecht Museum’s vision of letting visitors explore history without glass barriers, said Inbal Rivlin, the director of the museum, which is associated with Haifa University in northern Israel.
It was likely used to hold wine or oil, and dates back to between 2200 and 1500 B.C.
Rivlin and the museum decided to turn the moment, which captured international attention, into a teaching moment, inviting the Geller family back for a special visit and hands-on activity to illustrate the restoration process.
Rivlin added that the incident provided a welcome distraction from the ongoing war in Gaza. “Well, he’s just a kid. So I think that somehow it touches the heart of the people in Israel and around the world,“ said Rivlin.
Roee Shafir, a restoration expert at the museum, said the repairs would be fairly simple, as the pieces were from a single, complete jar. Archaeologists often face the more daunting task of sifting through piles of shards from multiple objects and trying to piece them together.
Experts used 3D technology, hi-resolution videos, and special glue to painstakingly reconstruct the large jar.
Less than two weeks after it broke, the jar went back on display at the museum. The gluing process left small hairline cracks, and a few pieces are missing, but the jar’s impressive size remains.
The only noticeable difference in the exhibit was a new sign reading “please don’t touch.”
VICTORIA – The British Columbia government is partnering with a bear welfare group to reduce the number of bears being euthanized in the province.
Nicholas Scapillati, executive director of Grizzly Bear Foundation, said Monday that it comes after months-long discussions with the province on how to protect bears, with the goal to give the animals a “better and second chance at life in the wild.”
Scapillati said what’s exciting about the project is that the government is open to working with outside experts and the public.
“So, they’ll be working through Indigenous knowledge and scientific understanding, bringing in the latest techniques and training expertise from leading experts,” he said in an interview.
B.C. government data show conservation officers destroyed 603 black bears and 23 grizzly bears in 2023, while 154 black bears were killed by officers in the first six months of this year.
Scapillati said the group will publish a report with recommendations by next spring, while an independent oversight committee will be set up to review all bear encounters with conservation officers to provide advice to the government.
Environment Minister George Heyman said in a statement that they are looking for new ways to ensure conservation officers “have the trust of the communities they serve,” and the panel will make recommendations to enhance officer training and improve policies.
Lesley Fox, with the wildlife protection group The Fur-Bearers, said they’ve been calling for such a committee for decades.
“This move demonstrates the government is listening,” said Fox. “I suspect, because of the impending election, their listening skills are potentially a little sharper than they normally are.”
Fox said the partnership came from “a place of long frustration” as provincial conservation officers kill more than 500 black bears every year on average, and the public is “no longer tolerating this kind of approach.”
“I think that the conservation officer service and the B.C. government are aware they need to change, and certainly the public has been asking for it,” said Fox.
Fox said there’s a lot of optimism about the new partnership, but, as with any government, there will likely be a lot of red tape to get through.
“I think speed is going to be important, whether or not the committee has the ability to make change and make change relatively quickly without having to study an issue to death, ” said Fox.
This report by The Canadian Press was first published Sept. 9, 2024.
