Escape from Earth with Professor Dirac and Doctor Pauli (IV)

Chapter 4: Going Round in Circles

Matt King

All passengers of the spacecraft had gathered on the observation deck. This was not a day to miss the view. Just before them, looming out as one of the few sights amongst the seemingly eternal blackness of space, was the planet that the crew had been sent to investigate. And what a planet it was. Doctor Pauli, who currently had his face pressed against one of the windows, wondered if he had felt the same way looking at Earth as they left. It had been a spectacular sight, no one could deny that. The knowledge that this was where the entirety of humankind had lived was certainly a powerful thought. But getting to see a new planet? This was special. He scanned its shape, trying to peek through the swirling white clouds covering the surface. A hint of some deep blue was visible – maybe even water! A tense silence had fallen over the whole group and the excitement was palpable.

Captain Bohr broke the silence. “We will, of course, have to prepare for the worst. There may well be hostile life forms on the planet, and so I will be activating our defence systems.” He was doing his best to appear disinterested in the planet before them, but wasn’t succeeding as he still hadn’t looked away.

“Don’t be silly,” said Professor Dirac, “there are much more important things to consider than starting a war with the first planet we meet outside of Earth. We need to make the most of this opportunity to explore it!” Dirac was becoming more animated by the second. After spending most of his life reading the discoveries of others, he was thrilled by the chance to study something no one else had ever seen.

“Well we definitely can’t land on the planet,” replied Bohr. “Not only is it not safe, but taking off again would waste so much fuel.”

The crew looked around at each other, thinking about their predicament. After taking so long to get here, they didn’t want to just turn around straight away. But the captain had made good points. There was no way they would be able to land.

Suddenly Pauli shouted out, breaking the quietness. “We’re about to crash!”

Everyone followed his gaze and saw a huge rock hurtling towards them, its ominous figure growing by the second. As it drew ever closer, dominating their vision, the huge craters covering its grey surface threatened to swallow the ship whole.

“Engaging evasive manoeuvres,” beeped a robotic voice. “Please ensure all personal belongings are secured. Please enter the brace position.” The voice seemed completely calm, yet that provided no comfort to its listeners. They grabbed onto anything they could, hoping that at least something they were holding wouldn’t be thrown across the room taking them with it. And then it happened. Pauli felt the force of the movement across his whole body. His stomach flipped, his vision went black, and his arms ached for freedom from his body. But the handles on the wall he was gripping remained firm. It was all over in a brief moment. Had there been a collision? Pauli thought about this, lying on his back breathing heavily. Given he was breathing oxygen, rather than just the emptiness of space, he suspected there was no collision.

“We made it!” breathed Dirac, still trying to recover. He seemed to have had the worst time – the table he grabbed was clearly not well secured enough to the ground and had now been reorganised to sit sideways in the corner of the room. Thankfully the professor was generally unscathed other than some bruises, which would definitely hurt tomorrow.

“What was that?” Asked Bohr, who had rapidly regained his composure.

“That,” answered the professor, still lying on the floor, “was a moon. Look, we can see it going back behind the planet just over there.” He pointed out of the window. “And I think it might be how we can stay close to the planet without landing.”

Pauli watched as he dragged himself across the floor to one of the touchscreens, and began to draw. “We just have to orbit the planet.”

“I’ve heard people talk about orbiting, but what actually is it? Why doesn’t the moon just fall back towards Earth?” interjected Pauli. He was sure Dirac would have good answers but was presently very confused about the whole idea.

“Great question!” answered Dirac with a smile. “We know that gravity is pulling the moon towards Earth. But the moon is travelling very fast, and it’s also very massive. This makes it very hard to make it change direction. Imagine a small pebble and a big boulder rolling down a hill. Which one would be easier to stop?”

“The boulder would be much harder to stop,” replied Pauli. He was now imagining a moon-sized rock and decided that would be almost impossibly hard to stop.

“Exactly,” continued Dirac, “so the force of gravity, even though it is very strong, isn’t enough to pull the moon in. All it does is keep changing the direction of the moon by exactly the right amount so that it keeps going around in a circle. In fact, I can tell you the formula we use to find out what force we need to keep something moving in a circle.”

F is the force, m is the mass of the object, v is the speed that it’s travelling and r is the radius of the orbit.”

Pauli looked at the equation for a moment. “The speed of the rocket is 500 m/s at the moment, it weighs 75,000 kg and the force is 20,000 N. So how far away from the planet do we need to be to orbit? And if we speed up, how would the force need to change to keep us orbiting?” he asked.

“I can work that out, but I think we’ll need more accurate numbers if we want to be sure the rocket will orbit. We know we covered the last 1526 miles in an hour exactly, so we should use that value for our speed. And also we’ve burnt 46% of our mass as fuel, so the value you said isn’t quite right,” replied Dirac.

Scroll down for the solution!

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Dirac pressed around on the screen until a calculator appeared in front of him. “To solve that we need to multiply both sides of the equation by the radius, and then divide both sides by the force, which gives us this equation:

Then, putting in the values, that would mean we have to orbit 937,500 metres or almost 1000 km above the planet. But, to use the more accurate values, we need to recalculate our speed in metres per second. This would be 682.2 m/s. We also need to recalculate the mass – 46% is fuel, so we only have 54% left. That’s 40,500 kg left of the original value of 75,000 kg. Then we put these numbers into the equation and get our more accurate value of the radius as 942,429 km. And if we were going faster then the force would have to be much bigger in order for us to still be orbiting – at least at the same radius.”

Bohr, who had been listening along carefully, suddenly began talking. “That sounds like a great plan. I’ll get the computer on it now!” He said, before hurrying away. Dirac and Pauli, however, went back to staring at the planet. Pauli, as always, was prepared and pulled out a pair of binoculars from his jacket. Looking through, he peered around the clouds until he could make out the sandy dirt below. Then, out of the corner of his eye, he saw movement. He adjusted his gaze and looked carefully at the ground. There it was again – something was moving on the ground below. Perhaps the adventure was only just beginning after all…

Chapter 1

Chapter 2

Chapter 3

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