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After reading this article, I was inspired to run some simulations at NASA's JPL Solar System Simulator to see Earth's and Mars' orbits from above.

From what I could visually determine (from the JPEG images), Mars is at opposition on July 26, but its perihelion is sometime around September.

When (and where in their orbits) is Mars brightest from Earth this year?

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JPL HORIZONS gives these values for Mars as seen from Earth. r is the Sun-Mars distance in AU, delta is the Earth-Mars distance in AU, and S-O-T is the Sun-Earth-Mars angle in degrees. I added [] to indicate minimum or maximum values.

Date__(UT)__HR:MN   APmag         r     delta    S-O-T

2018-Jul-23 16:00   -2.75   1.40246   0.38911   172.30
2018-Jul-25 14:00   -2.77   1.40106   0.38730   173.27
2018-Jul-27 12:00  [-2.78]  1.39971   0.38600  [173.51]
2018-Jul-29 10:00  [-2.78]  1.39840   0.38522   172.94
2018-Jul-31 08:00   -2.77   1.39714  [0.38497]  171.73
2018-Aug-02 06:00   -2.75   1.39592   0.38523   170.11

2018-Sep-14 12:00   -1.74   1.38147   0.50640   128.93
2018-Sep-16 12:00   -1.69  [1.38144]  0.51602   127.49
2018-Sep-18 12:00   -1.64   1.38147   0.52588   126.08

Mars is at opposition on Jul 27, closest to Earth on Jul 31, and at perihelion on Sep 16. Mars is at peak brightness for several days between opposition and closest approach to Earth. A difference of 0.01 magnitude is imperceptible to the eye and smaller than the uncertainty of most ground-based CCD photometry. Albedo features and dust storms probably contribute at least that much variation in magnitude anyway.

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The two main factors affecting the brightness of Mars are its distance from Earth, and the phase (ie how much of the planet is illuminated from the point of view of Earth. Both of these are optimal when Mars is at opposition.

Stellarium has Mars reaching maximum brightness on the 28th of July with a magnitude of -2.78, very close to opposition. The distance of Mars from the sun has only a secondary effect on the brightness.

On that date it will be close to the full moon, but low in the sky for Northern Hemisphere observers.

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The key is in "as seen from Earth". Mars is illuminated by the Sun and the distance from the Sun varies only slightly. Therefore, it is always the same brightness. A photo of Mars through a telescope will always use the same exposure no matter how far it is from Earth. The planets do not behave like point sources of light. When Mars is twice as close, it fills 4 times the area in the sky. This exactly counters the inverse square spreading of the light from Mars. The same is true for all the planets. If they got brighter as they get closer, they would get brighter as YOU got closer. The Apollo astronauts would have boiled then vaporized as they approached the Moon. It is a common error. N. D. Tyson makes it with a truly dumb statement near the beginning of his Cosmos series. Something about the brightness of the Moon long ago when it was closer to the Earth. Think of how many people read that script and it still slipped by.

The brightness of an extended object as viewed, is not the same as the illumination it provides. If the Moon filled the sky, it would not look brighter. You would not have to wear welder's goggles to look at it. But the total amount of light reflected on the Earth would be much greater and more like the illumination on an overcast day (and there would never be a full Moon because the Earth would get in the way).

You can easily calculate a brightness compared to the Earth (or Moon) daylight brightness and the ratio of the squares of the distance from the Sun.

When you add that you want brightness as perceived from Earth, it depends on distance and phase. If you think of it as wanting to read by Mars light, it is "brighter" if it is closer and it is "brightest" at "full Mars" or opposition.

There is a gaggle of terms used in optics to describe various ways of describing brightness and intensity and illumination and they get very confusing.

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