Triangles to Mars

Marianne Dyson, July 2018

At the end of July, Mars will be its brightest in 15 years because it will be only 35.8 million miles (57.6 million kilometers) away. Since no one has ever been to Mars, how do we know this distance so precisely?

Triangles! If the length of one side and two angles of a triangle are known, the length of the other sides can be calculated. Way back in 1673, Giovanni Cassini (1625-1712) used this knowledge of triangles to estimate the distance to Mars. This method is called parallax. [Ref: A Teacher’s Guide to the Universe: Background: Parallax.]

Half the distance (R in the diagram) between two locations on Earth is the known (opposite) side of the parallax triangle. One angle is 90 degrees. The other angle is found by observing the object from the two locations (Cassini in Paris and fellow astronomer Jean Richer in French Guiana in 1673). From the two locations (1 and 2 in the diagram), the object appears in a slightly different place in the sky (A and B in diagram) defined by the distant background stars. The difference in position reveals the angle (ɵ in the diagram). Plugging the known distance and measured angle into the tangent equation*, the answer for D is revealed.

Parallax Shift
The distance (D) to a planet or star can be found by observing it from two locations (1 & 2) whose separation (R) is known, and then determining the angle (ɵ) between the observed position in the sky using distant background stars (A and B). Credit: NASA.

*The tangent of ɵ equals the length of the opposite side (R) divided by the length of the adjacent side (D) which is the distance. Because the angle is very small, the tangent is approximately equal to the angle. So the equation simplifies to D (in parsecs) equals R (in Astronomical Units) divided by ɵ (in arc seconds).

The farther away an object is, the “taller” the triangle and the smaller the angle, making it difficult to measure very accurately. Thus parallax measurements to planets are easier when the planet is at opposition, on the same side of the sun as Earth. Mars opposition occurs every 26 months. But the orbit of Mars is an ellipse. So the closest to Earth Mars can get is when opposition is near periapsis—when Mars is closest to the sun. Opposition and periapsis coincide every 15 years, and 2018 is one of those years.

An Alternate History

The years when opposition and periapsis coincide are also the best years, in terms of fuel and time spent in transit, to send spacecraft to Mars. Back in 1990, I wrote a science fiction story about a group of astronauts preparing for a trip to Mars this year so that they would take the first steps on Mars before the 50th anniversary of Apollo 11’s landing on the Moon. I rediscovered this manuscript (it was not in digital form!) in my closet recently and am in the process of turning it into an alternate history novel.

So when I go out to view Mars later this month, I’ll be imagining my crew on their way there this summer. If they had followed the trajectory of InSight that launched on May 5, they’d be arriving on Mars on Monday, November 26. [Ref: Planetary Society.] But to reduce radiation exposure, they would likely have launched on May 18, “passed” InSight en route, and would be arriving on Mars on September 10, 2018. Would that day become a holiday on Mars?

Imagine if the current crew of six (which includes only one woman) up on the International Space Station were instead on their way to Mars. Would they be worried about the global Martian dust storm in progress right now?  Would every kid in the country know everything there is to know about their planned landing area in Isidis Planitia? I can almost hear my young self proudly telling my mom that this part of Mars was named after the Egyptian goddess of heaven and fertility.

Mars in the Teapot

Though no humans are yet scheduled to travel to Mars, at least we have learned how to measure the distance and send spacecraft there. InSight is a pretty cool little spacecraft, too. It has a probe that is a self-hammering mechanism that will pound itself into the ground, up to 16 feet (5 meters). It relays data back via its tether to the lander. What might it find under the surface?

So later this month, look for Mars in the southeast evening sky near the Sagittarius “teapot.” Mars will be glowing orange below and to the left of the teapot with yellow Saturn above the top. Saturn was at opposition on June 27. How far is it to Saturn? If you have a good telescope, and a friend on the other side of the planet, you can figure it out yourself using triangles. Or you can just Google the answer!

Writing about Space

My guest editorial on Gender Parity is in the July/August issue of Analog. You can read it free online, but you might want to subscribe so you can read my fact article “In Defense of the Planet” in the upcoming Nov/Dec issue. I also did a Q&A with the magazine that should be posted later this month on the Astounding Analog Companion.

My next book, coauthored with Buzz Aldrin, To the Moon and Back: My Apollo 11 Adventure, a pop-up book from National Geographic, is available for preorder now from Amazon. Look for it in stores in October.

Speaking about Space

I offer programs for school-aged children up through senior citizens, as well as science workshops for students and teachers. Please consider me for Author Visits.

September 21-23, Science GOH at FenCon XV in Dallas. See their website for program details. Writer GOH is Larry Niven.

September 29, Attending SCBWI Houston conference.

October 2, Instructor for first class of Women and Space course at Rice University’s Glasscock School of Continuing Studies.

October 12, Featured speaker on Friday at noon at the National Science Teachers Association conference in Reno, Nevada.

See my contact page for a complete appearance schedule and photos from previous events.