Does it seem dim outside? Well, it should—sort of. Because it is dim outside—sort of.
On this past Thursday, July 4, just before the end of the day as seen from London (at 11:10 pm British Standard Time), the Earth was at the aphelion point of its orbit—the point at which it is farthest from the sun. At that time it was 94,513,221 miles from the sun. By contrast, at its perihelion point (closest to the sun), on January 3, Earth was merely 91,403,554 miles from the sun.
The Earth’s orbit around the sun. Can you tell that it is not exactly a circle? Image from University of Nebraska-Lincoln.Earth is over 3,100,000 miles farther away from the sun now than it was in January. Of course, that is only a 3.4% difference. But if you observed the sun carefully, and measured its apparent diameter, you could see that difference. The fact that the distance between the sun and the Earth changes has been known since antiquity.
The apparent size of the sun as seen from Earth at perihelion (left) and six months later, at “aphelion” (right). Images created with Stellarium.The sun is a remarkable object, really beyond our comprehension in many ways. First of all, there is its size. The diameter of the sun is over one hundred times the diameter of the Earth. See the circles in the figure below below? The sun is the big yellow one. The Earth is the little black one, indicated by the arrow. Even many of the sunspots are substantially larger than Earth. Fr. Christoph Scheiner, S. J., was the first person to do a really in-depth, long-term study of the sun, which he published in a huge book called Rosa Ursina Sive Sol (click here for a look at it). The drawing of sunspots at upper right in the figure below is the first sunspot drawing Scheiner ever made (this copy is from an article by Fr. Juan Casanovas, also S.J., who was a Vatican Observatory astronomer—the article is available on the V.O.’s Faith and Science pages—click here to check it out). The sunspot photo at lower right is from NASA.
The power output of the sun is 3.8×1026 Watts of power: 380,000,000,000,000,000,000,000,000 Watts, or 380 septillion Watts. As best science can tell, this power comes from nuclear fusion reactions occurring in the sun’s core. These reactions are converting the sun’s mass into energy via E=mc2. A Watt of power is one Joule of energy per second, so every second the sun generates 3.8×1026 Joules of energy. A Joule is a kilogram times a meter divided by a square second (kgm/s2). The speed of light is 3×108 meters/second, so c2 = 9×1016 (m/s)2. So, using E=mc2, we find that in one second the sun converts
m =E/c2 = {3.8×1026J} / {9×1016 (m/s)2} = 4.22×109 kg
of its mass into energy. 4.22×109 kg is 4,220,000,000 kilograms, or 4.22 billion kilograms, of mass.
How much mass is that? Well, a kilogram is the mass of 1 liter of water. A liter of water weighs 2.2 lbs on Earth. A light truck, like the ever-popular Ford F-150, weighs about 2000 times that much (roughly 4400 lbs, according to Ford). So how many F-150s is 4.22 billion kilograms?
4,220,000,000 / 2000 = 2,110,000
So, that is over two million F-150s. In other words, to generate that 3.8×1026 Watts of power, in each and every second the sun converts into energy a mass equal to two million F-150 pickup trucks. In the time it takes you to read this sentence—whoosh! millions of trucks of mass are gone, turned into E=mc2 energy.
Yet while to us this seems like so much, to the sun it is nothing. The total mass of the sun is 2.0×1030 kg. How long will it take the sun to eat up 1% of that mass? Well, 1% of 2.0×1030 kg is
0.01 x 2.0×1030 kg = 2.0×1028 kg
As we calculated above, every second the sun converts 4.22×109 kg of its mass to energy. So the time to convert 2.0×1028 kg to energy will be
{2.0×1028 kg} / {4.22×109 kg/s} = 4.74×1018 seconds
There are 3.154×107 seconds in a year, so in terms of years, this is
{4.74×1018 s} / {3.154×107 s/yr} = 1.5×1011 years
That is 150,000,000,000 years, or 150 billion years! As best we scientists can tell, the universe itself appears to not even be 15 billion years old. Two million trucks-worth of mass vanishing into energy may seem like a lot to us, but it is truly nothing to the sun.
All of this is taking place 95 million miles above us. But in January, it will only be 91 million miles above us. So enjoy the extra distance while it lasts!
