Breaking News; Mercury, Not Venus is Closest Planet to Earth

[Frank Kenney]

How did we miss this one?

https://gizmodo.com/mercury-not-venus-i ... 1833290616

https://youtu.be/GDgbVIqGADQ

https://physicstoday.scitation.org/do/1 ... 312a/full/

In fact Mercury is the closest to all seven of the other planets.

[Ron Schmit]

Nice, Frank!

Interesting that this story comes out on Pi Day when it's all about the round.

As his graphic shows the planets orbiting in the wrong direction, I say his argument is void.

OK, yes, when your definition of "closest" does not include which one GETS closest... Then, yeah, I'm good with that.

In fact, if you want to play that game, Neptune stays "closer" to the Sun than the Earth, because its eccentricity (0.009) is almost half that of the Earth's (0.017.) HA!

“Anyone can speak Troll. All you have to do is point and grunt.”

― J.K. Rowling, Harry Potter and the Goblet of Fire

[tugger]

As his graphic shows the planets orbiting in the wrong direction, I say his argument is void.

In fact, if you want to play that game, Neptune stays "closer" to the Sun than the Earth, because its eccentricity (0.009) is almost half that of the Earth's (0.017.) HA!

“Anyone can speak Troll. All you have to do is point and grunt.”

― J.K. Rowling, Harry Potter and the Goblet of Fire

What if he's looking at it upside down?!

[Dale Smith]

The basic idea is that average distance includes both nearest and farthest distances and all points inbetween. I can see where that might yield a closer average for Mercury than for Venus.

Having said that, the graphics in the Youtube video should be taken with a grain of salt.

In the middle of the video there was a page of text. The first equation was:
Distance = √(R2² + R1² + R1R2cosΘ)
From the diagram R2=Earth/Sun distance, R1=Mercury/Sun distance, Θ=angle formed by Earth-Sun-Mercury.

The equation is wrong. If this is the equation he actually used in his calculations, the calculated distances will be incorrect. The term +R1R2cosΘ should be replaced with -2R1R2cosΘ.

The Law of Cosines (found in any geometry book) is
c² = a² + b² - 2ab cos(C)
where C is the angle opposite the side with length c.

Replacing c, a, b and C with Distance, R2, R1 and Θ and taking the square root we get
Distance = √(R2² + R1² – 2R1R2 cos(Θ))

In polar coordinates the form of the equation I just gave remains the same, except Θ is replaced with (Φ2 – Φ1) (i.e. the difference between the angular portions of the coordinates).