Of Particular Significance

Tag: Mars

Mars Meets the Moon

A break from all these wormholes and strings; let’s take a moment to look at the sky. In the US, sadly, most of the country will be under cloud, but for those who aren’t, you have a spectacle tonight, at around 10-11pm Eastern Time in the US, roughly 5-6 am UT in Northern Europe.

It’s not terribly unusual for the Moon to pass in front of a planet and block it, from the point of view of some of us on Earth. This time it is Mars’ turn. You’ll be able to see the Moon eclipsing Mars (a “lunar occultation” of Mars), weather permitting, in the region shown below. This map is taken from in-the-sky.org, where you can enter your location and find out exactly when you’ll see Mars disappear behind the Moon and then reappear.

*Visibility of tonight’s occultation of Mars by the Moon. See in-the-sky.org for more details.*

This should be fun even with the naked eye — Mars won’t disappear in an instant but will do so gradually — but it will be better with binoculars, and great in a small telescope. It will give you a chance to see that yes, the Moon is in slow, steady motion in the sky relative to the planets, which (being further) seem to move more slowly. Lunar and solar eclipses provide a similar opportunity to observe this motion, but I think occultations provide the clearest sense of it.

The Full Moon can be seen from south to north across the Earth. Why isn’t the occultation visible everywhere? It is because the Moon is smaller than the Earth, as I explained here as part of my series on “Do It Yourself Astronomy”. In a sense, the light of Mars effectively (though not literally) casts the Moon’s shadow onto the Earth, and the shadow’s width — the width of the region over which the occultation is visible — would be the same as the diameter of the Moon, were the occultation visible close to the Earth’s equator. (As I pointed out, you can use this fact to measure the Moon’s size without ever leaving the Earth.) Because tonight’s occultation is visible closer to the poles, the region of visibility on the Earth’s surface is distorted by the Earth’s curvature, making it larger than the Moon by about 50% — about 3000 miles (5000 km) or so. (That’s yet more evidence that the Earth’s not flat, in case you needed some.)

Finally, there’s something quite remarkable about this occultation. It occurs close to two special moments:

almost at full Moon (within a few hours);
almost at “Mars opposition” (within a few hours) — when Mars is (nearly) closest, brightest and highest in the midnight sky, as brilliant as it gets over its cycle.

Since (1) happens once a month, and (2) happens once every two years, and occultations don’t occur all the time, this seems like quite a coincidence!

Only… it’s not as big a coincidence as it looks. A puzzler for you: why isn’t it a coincidence that (1) and (2) happen at the same time? That is, if there’s an lunar occultation of Mars at full Moon, why must Mars be nearly at opposition? [Hint: it’s just geometry.]

POSTED BY Matt Strassler

ON December 7, 2022

How to Estimate the Distance to the Outer Planets Yourself

Now, the last step in mapping out the other planets, before heading for more intriguing territory.

In a previous post I showed you how you can measure the distance between Venus and the Sun, R_VS, relative to the distance between Earth and the Sun, R_ES. Under the assumption that Venus’s orbit around the Sun is circular (or nearly so), you can use the fact that when the angle between Venus and the Sun reaches its maximum (the moment of greatest elongation, and also approximately the moment when Venus appears half lit by the Sun), there’s a simple right-angle triangle in play. High school trigonometry then gives you the answer: R_VS/R_ES ≈ 0.72 ≈ 1/√2. The same trick works for Mercury, which, like Venus, is a near Sun-orbiting planet, closer to the Sun than Earth.

But there’s no maximum angle for Mars, Jupiter, or the other far planets. These planets are further out than Earth and can even appear overhead at midnight, when they are 180 degrees away from the Sun. Fortunately there’s another right triangle we can use, again under the assumption of a (almost-)circular orbit, and that can give us a decent estimate.

The Triangle for the Far Sun-Orbiting Planets

Let’s focus on Mars first, although the same technique will work on the outer planets. Mars has a cycle in which it disappears behind the Sun, from Earth’s perspective, on average every 780 days. (That start of the cycle is called “solar conjunction,” or just “conjunction” when the context is clear.) About half a cycle later, after on average 390 days, it is at “opposition”: closest to Earth, largest in a telescope, appearing overhead at midnight, and at its brightest. But if we wait only a quarter cycle, on average 195 days after conjunction, then the Mars-Sun line is at a 90 degree angle to the Earth-Sun line. That means that Mars, Earth and the Sun form a right-angle triangle with the right angle at the location of the Sun.

So on the day of first quarter we should measure the angle on the sky between Mars and the Sun. That’s the angle A on the figure below. Then the Mars-Sun distance R_MS and the Earth-Sun distance R_ES are the two sides of a right-angle triangle. That means they are related by the tangent function:

R_MS/R_ES= tan A.

*For a planet whose distance R_PS from the Sun is greater than Earth’s, an estimate of its distance compared to the Earth-Sun distance* *R_ES* can be made using the fact that (were its orbit perfectly circular) it would make a right-angle triangle after the first or third quarter of its cycle, with the right angle located at the Sun. Sizes of Earth, Sun and planet not shown to scale.

(more…)

POSTED BY Matt Strassler

ON March 28, 2022

Who Orbits Who, and Where? Check it Yourself

So far the arguments given in recent posts give us a clear idea of how the Earth-Moon system works: Earth’s a spinning sphere of diameter about 8000 miles (13000 km), and the size of the Moon and its distance are known too (diameter about ¹/₄ Earth’s, and distance about 30 times Earth’s diameter). We also know that the Sun is much further than the Moon and larger than the Earth, though we don’t know more details yet.

What else can we learn just with simple observations? Since the stars’ daily motion is an illusion from the Earth’s spin, and since the stars do not visibly move relative to one another, our attention is drawn next to the motion of the objects that move dramatically relative to the stars: the Sun and the planets. Exactly once each year, the Sun appears to go around the Earth, such that the stars that are overhead at midnight, and thus opposite the Sun, change slightly each day. The question of whether the Earth goes round the Sun or vice versa is one we’ll return to.

Let’s focus today on the planets (other than Earth) — the wanderers, as the classical Greeks called them. Do some of them go round the Earth? Others around the Sun? Which ones have small orbits, and which ones have big orbits? In answering these questions, we’ll start to build up a clearer picture of the “Solar System” (in which we include the Sun, the planets and their moons, as well as asteroids and comets, but not the stars of the night sky.)

The Basic Patterns

If we make the assumption (whose validity we will check later) that the planets are moving in near-circles around whatever they orbit, then it’s not hard to figure out who orbits who. For each possible type of orbit, a planet will exhibit a different pattern of sizes and phases across its “cycle“ when seen through binoculars or a small telescope. Even with the naked eye, a planet’s locations in the sky and changes in brightness during its cycle give us strong clues. Simply by looking at these patterns, we can figure out who orbits who.

(more…)

POSTED BY Matt Strassler

ON March 13, 2022

Physics and Curiosity on Mars

The promised follow-up article on the workshop last week in Waterloo, Canada will have to wait til Monday; I had too many scientific activities and chores to take care of today, and I want to make sure the article, which is a bit complicated, is nevertheless clear. But in the meantime, let’s celebrate Martian Curiosity!

First, a big congratulations to the NASA folks! Very impressive, and fantastically cool. I was a huge fan of the Spirit and Opportunity rovers, especially of their 3D photography. Looking at those photos on a big screen, through red/green 3D glasses. brought me to sweeping Martian vistas and deep Martian craters — as vivid and as close as I’ll ever see them. It was amazing stuff, and I look forward to more from the new rover.

Next: some perspective. (more…)

POSTED BY Matt Strassler

ON August 10, 2012

Buy The Book

Reading My Book?

Got a question? Ask it here.

Media Inquiries

For media inquiries, click here.

Tag: Mars

Mars Meets the Moon

POSTED BY Matt Strassler

How to Estimate the Distance to the Outer Planets Yourself

The Triangle for the Far Sun-Orbiting Planets

POSTED BY Matt Strassler

Who Orbits Who, and Where? Check it Yourself

The Basic Patterns

POSTED BY Matt Strassler

Physics and Curiosity on Mars

POSTED BY Matt Strassler

Recent Posts

Buy The Book

Reading My Book?

Media Inquiries

Order Waves In An Impossible Sea