# What makes a planet look bright? It's complicated.

#### rod

The article states, "A planet's distance from Earth is probably the most significant factor governing its apparent brightness. Last October, for instance, Mars shone brighter than Jupiter, thanks in large part because the Red Planet was as close to Earth as it will be until 2035. In contrast, Mars is now sinking into the western sunset sky, falling deeper into the brightening twilight glow, as Earth and Mars are practically on opposite sides of the sun."

Observing the brightness and angular size changes of the planets using quality telescopes can be enjoyable and show clearly dramatic changes in the view. From May 2020 until April 2021, I logged 30 observations of Mars including opposition in October last year. 34x to 216x views. Mars angular size was just < 8 arcsecond, expanded to larger than 22 arcsecond at opposition, and in late April this year, < 5 arcsecond size when I last viewed. Tycho Brahe attempted to refute Copernicus by measuring the Mars parallax at opposition showing Mars was farther away from Earth than the Sun during Mars oppositions. Tycho Brahe did not want the Copernicus heliocentric solar system to be correct.

Helio

#### Helio

A nicely written article, but there is an important error worth mentioning. [It's one I made long ago, actually.]

Article: In calculating a planet's brightness, we have already noted that the first consideration is its distance from the sun. For that we must utilize the inverse-square law, which states that a specified physical quantity is inversely proportional to the square of the distance from the light source. So, from 2 feet away, a candle looks only 1/4 as bright as it does from 1 foot.
Yep, the inverse square law explains this. But it's the inverse square law squared, or inverse 4th power law, that must be used for planets as they aren't similar to glowing candles.

For instance, if you move, say, Jupiter to 2x its current distance, then the inverse square law will determine how much light reaches Jupiter, which in this case, will be diminished by a factor of 4. AND this extra distance for that reflected light to reach Earth will also require the inverse square law to be applied, hence the inverse 4th law. [The orbital distance for Earth makes the math a little more complicated.]

This is why no optical telescope built to date, including the HST, could ever spot Jupiter if someone carelessly moved Jupiter to about 10,000 AU. (inner Oort Cloud). Yet we are able to see a handful of exoplanets that are much farther away as their light is an inverse square law, not an inverse 4th power law application.

Last edited:
Catastrophe

#### Catastrophe

##### "There never was a good war, or a bad peace."
Helio, correct as usual!

Reflected light from here has to get there and back.

Reflected light from there has only to get here.

Cat

#### Helio

Helio, correct as usual!

Reflected light from here has to get there and back.

Reflected light from there has only to get here.

Cat
I too made this mistake, when I first go on to an astronomy forum. I wonder if my error was because the term "law" in "inverse square law" made me think less critically. Anyway, the inverse 4th law is pretty interesting.

This 4th law also is how Rayleigh scattering for colors works. It's why the sky is blue when the Sun doesn't emit any more "blue" photons more than, say, "red" photons.

Catastrophe

#### Helio

There is also another problem I see in the article:

Article: The next factor, how far the planet is from us, again stems from the inverse-square law. The closer a planet is to us, the larger it appears in apparent size. And its apparent surface area correspondingly increases as the square of its diameter.
That is all true but it is not a factor in how bright the object will appear. The change in apparent size will not increase the amount of light we see from it. Mars will not increase in brightness due to a shorter distance between us AND a larger apparent size. [Only the distance is used to determine magnitude (and phase angle for a given albedo).]

It's interesting to me that as objects become closer, or we use magnification with larger telescopes, that the increase in both brightness and apparent size will never increase "surface brightness" of any extended object, no matter how large the scope.

Catastrophe

#### Catastrophe

##### "There never was a good war, or a bad peace."
Yes. We are not concerned with the brightness of the source, per se - only the light 'originating' (reflected) from the distant object.

Cat

Helio

#### Helio

Yes. We are not concerned with the brightness of the source, per se - only the light 'originating' (reflected) from the distant object.

Cat
Right. There is X amount of illuminated light that comes from Mars in the direction of Earth. As it gets closer, more of this light will hit the Earth per the inverse sq. law. Only if Mars physically and magically increased in actual radius would more illuminated light come our direction, exceeding the inv. sq. law illumination calculation for distance.

Catastrophe

#### Helio

Tycho Brahe attempted to refute Copernicus by measuring the Mars parallax at opposition showing Mars was farther away from Earth than the Sun during Mars oppositions. Tycho Brahe did not want the Copernicus heliocentric solar system to be correct.
Yes. I wish there would be a series (HBO, Apple, whatever) made about how Tycho's, Copernicus', Kepler's and Galileo's work moved us from the Geocentric model to the modern heliocentric model. All the players lived within in the warm (sometimes very frigid) embrace of the Church, adding to the drama.