Margin of Error

7 February 2020

“What went wrong?”

“Nothing, Mr. President.” James said.

“Nonsense! My spacecraft’s gone, Mr. Ngueyn, and I demand answers!”

“It’s Doctor, actually.” James muttered. He could ignore the President’s claim that he owned a NASA spacecraft, but being called Mister was a bridge too far. James sighed, and tried to explain.

“Mr. President, every research mission carries a certain degree of risk. We are working at the edge of human engineering.”

“A billion dollars! All for nothing.”

One hundred and thirty-five million was hardly a billion, but James moved on. “Mr. President, Planet Nine is the most distant object a human spacecraft has ever reached. It is ten times more distant than Pluto. Sir, just reaching it is a huge success.”

The real name of Planet Nine was Kauket, after the Egyptian goddess of darkness, but the President wasn’t fond of foreign-sounding names, so James stayed with Planet Nine.

“The spacecraft was supposed to orbit Planet Nine, not just reach it.” the President grumbled. “Now it’s lost, and I demand to know why.”

“Let me explain.” James said. “Remember that we’ve never seen Kauket…Planet Nine…before this mission. That’s because even though it has a mass 5.3 times that of Earth, it is only about the size of an apple. Technically it’s not even a planet. It’s a primordial black hole.”

Never seen it.” the President mocked. “I’ve seen pictures of it for years.”

“Those were artistic renderings, Sir.” James replied. “They were just ideas of how it might look.” The President was frustrated and confused. Never a good sign. “But we do have pictures of it now. Let me show you.”

James pulled up an image on his tablet, then flicked it to the wall monitor. The image was mostly purple, speckled with dots that clustered around a small dark region. “This is an infrared image taken by the Eddington spacecraft.” James said. “The purple dots are stars in the background.”

False-color images typically used red or orange to represent infrared light, but purple was the President’s favorite color, so James thought he’d find purple more appealing.

“And the dark spot is the black hole.” the President said.

“Technically it’s the shadow of the black hole, but yes, Mr. President. From this and other images we’ve confirmed the black hole mass and its orbit.”

“But we already knew those things.”

“To within a certain margin of error. The Eddington data let us measure them more precisely.” James sighed quietly. Oh, for the days of a scientifically literate President.

“Okay, but if we’ve never seen it before, how did you know where to send the spacecraft?” The President smiled, as if the question would stump James.

“Planet Nine has the mass of five Earths. Even though it’s at the edge of the solar system, its gravity tugs a bit on other solar system bodies.”

“Good God, could it eat us?”

“No, Sir, it’s too far away for that.” James replied. “But its gravity shifts the orbits of small bodies, particularly those beyond the orbit of Neptune. Comets and the like. We’ve known Kauket was out there since the 2020s. In the last two decades we’ve been able to calculate its orbit well enough to send a probe.”

“Just from its gravity?”

“Yes Sir, Einstein’s gravitational equations are very precise.”

“So how was it lost?”

“Well, Mr. President, the Eddington spacecraft went off course.”

“Ah ha! So you did make a mistake!” Again that gotcha smile.

“Not at all, Sir. The trajectory of the spacecraft was precisely calculated, and Eddington operated perfectly.”

“Then how was it lost?”

“It was actually destroyed, Sir.” James said. “Eddington followed its calculated trajectory until it was about 60,000 kilometers away. Then it drifted closer to the black hole than expected and the black hole ripped it apart.”

“So how was that not a mistake?”

“Up until 60,000 kilometers the spacecraft followed Einstein’s equations almost perfectly. To within a margin of error. As it got closer to the black hole, its trajectory deviated from prediction. The closer it got, the more it deviated.”

The President looked confused again. “Either way,” he said, “the spacecraft is destroyed and you’ve learned nothing.”

“Not at all, Mr. President. We’ve learned a great deal.” James replied.

“And what did you learn?”

“After nearly two centuries we’ve finally done it.” James said. “We’ve finally proven that Einstein was wrong.”