Solution Whitehouse part 3

Sam stared in disbelief and finally got up to move unsteadily to the window. She pulled back the curtains with her good arm and tried to look out the windows to see the moon. Or moons. Her room faced another wing of the hotel so she couldn't see much of the sky. What blue sky she did see contained no moon, real or otherwise. She craned her to the side so much to see south that her bad arm banged into the window and she screamed. Blackness engulfed her vision and she nearly fell onto the floor.
She was able to grope blindly, nearly doubled over, with her good arm to the edge of the bed. She took a long time to settle back into the hotel bed and prop herself up with a pillow.
Over the course of the next hour, news reports flooded in about the double moons. Pundits who knew nothing of astrophysics held forth on the cause of the optical illusion (for it must be an optical illusion; there was no way it could be a real phenomenon). Sam scoffed at them but didn't know what to believe. She jotted down some calculations on the hotel stationery pad.
The earth and moon exert approximately 2x10^20 Newtons of force on each other. Since the force equation for two objects is the product of their masses times a constant and divided by the square of the distance between them, doubling the number (and hence mass) of the moons would double the force between them. So Sam reasoned that two moons and one earth would put 4x10^20 Newtons of force. Of course, the angle of the interaction between the two moons and earth could make a big impact on the calculations.
The two moons in the camera images appeared to be about six diameters of moons apart. That is, using the diameter of the moon as a reference, like a coin, Sam guessed you could fit six moon-coins between the two. The moon rises approximately 1 hour later per day on average (a little less perhaps, her father had told her), which was approximately 12 degrees. The moon covered a part of the sky that was approximately half a degree. So Sam's guess at six moon diameters between them appeared to confirm the moons were lagging each other in orbit by one earth day.
This angle of 12 degrees meant that the moons were pulling on each other at an angle while the earth pulled both at a different angle. Assuming an isosceles triangle at the distance from the earth to the moon of 384,000 kilometres (or, a little more than 2.5 seconds round trip from the earth to the moon at the speed of light), with an acute angle of 12 degrees, Sam calculated 84 degrees offset for the force from earth to each moon. With two objects, the angle would be 90 degrees dead on, so 84 degrees would reduce the force of 4x10^20 Newtons by about 93%.
Given the two sides of the isosceles triangle of 384,000 kilometres, you can construct two right triangles by bisecting the original and find out half the calculated side using the Pythagorean Theorem:
A^2 + B^2 = C^2
Which yields a distance between the moon of 271,500 kilometres. Using Newton's gravitational formula:
F = (G * m1 * m2) / r^2
Would yield a force between the two moons of 4.5x10^17 Newtons. This was 10,000 times less than the force between the earth and the two moons. So it might be possible that the orbits would remain stable, Sam thought. She was not an orbital mechanics expert, however.
The news reports continued all day and into the night to discuss the problems that multiple moons would pose, including doubling the tides and increasing earthquakes. The earth's crust could warm up from the friction, one expert claimed. It was possible this could increase the effects of climate change. Sea ice could break up more quickly and melt faster, said another expert.
The stock market had swung into the largest sell-off of the last two centuries, only to come roaring back by bulls buying into the decline. The NASDAQ decided to close the markets early while the New York Stock Exchange struggled to keep up with orders. The NYSE was technically able to stay open, although most major stocks had collars and freezes in place that prevented most transactions from occurring.
On television, an expert from the Catholic Church said that this was predicted by a dead woman in Guadalajara some 2,500 years ago. The old guy who always predicted the end of the earth got quite a bit of airtime to discuss how this was surely the final sign of the end of the earth. This old guy believed that God's wrath would visit us due to sins such as allowing recreational use of marijuana, gay marriage, and the abolishing of daylight savings. He seemed to have convinced the CNN hosts that this was the case.
Most channels that had local news showed static shots of the sky with both moons clearly visible on a field of blue sky. Samantha flicked through these channels because the hosts usually said inane things along the lines of "Stay calm. There is no immediate danger." If there were danger, they wouldn't admit to it obviously. One oblivious local channel on the hotel network showed a daytime show of two children dressed as Mario and Luigi sporting ridiculously racist fat mustaches. The spun round cloth towels that were supposed to represent pizza doughs. The audience cheered as the kids threw the dough into the air and caught them on their hands.
"Oh please," said Sam to no one. "Do people really watch this?"
Samantha eventually fell asleep fitfully among her notes. The light from the television flickered over the wall and her bedspread, filling her dreams with hate and pain from her injuries.
----
The next morning, Samantha hobbled into the lobby. Over her right pants leg she wore a metallic knee brace. While struggling to walk and with her left arm in a cumbersome cast, she heard a familiar voice behind her that said, "Ms. Griffen! Ms. Griffen!"
Sam froze in horror and tried to shift to the left, then the right to try to hide. She nearly toppled over. Mark rushed up and helped steady her by her good arm.
"Ms. Griffen," he repeated. "I'm so glad to see you. What a coincidence! I was supposed to be staying at the Harrison, but my father's secretary made a mistake and I'm here." He paused, then continued, "Wow, you look terrible. No  offense."
"Of course I'm offended," Samantha said. "I'm in a lot of pain, only one week out from an airplane crash, and I've met one of the most despicable people on the planet. That was my mom. But you are a close second."
"Well, shit on me," Mark said bemused. "Listen, I'm serious. Let's talk. This coincidence can't be an accident. Also, the whole moon thing. I've been up all night looking at it on T.V. Here, sit down," he said and motioned to a lobby couch.
"I can't sit down," Sam said. "I need to get to a cab. The Secret Service said I shouldn't be late. I need to talk to the president immediately."
"Let me get you a cab," Mark offered. "I'll help you. I can back you up when you talk to the president. I read your email and I want to help you solve the mystery of the problems we're seeing."