Chapter 2: Time flies when you’re having fun
Captain Bohr stared out of the spacecraft window in front of him. When he signed up for the military, he’d expected to face all kinds of difficulties – walking for hours in the hot desert sun, camping in unexplored wilderness, and even enduring dangerous shootouts. However, he never thought of the possibility of space travel.
“They never included this in the adverts!” he grunted. Many times he had travelled by boat and plane, and as a hardened veteran, he was not the type to suffer from motion sickness. That was a weakness he scathed his subordinates for. Surely space travel was no different? Sadly his stomach had a different opinion and was currently expressing that through a vague twisting feeling that was slowly worsening.
“Good morning, hope you’re doing well!” came Doctor Pauli’s cheerful voice.
The captain thought for a moment – it was now 10am which did not, in his opinion, constitute the morning, and the feeling of his insides being upside down was not giving him a great sense of “doing well”. Nevertheless, there was no need to let the doctor know this.
“Never been better,” he replied gruffly.
“Glad to hear. I was just wondering when we would be reaching our destination?” asked Pauli.
“Well the planet is 5 light-years from Earth, and we’ve just set off, so work it out for yourself.”
“Um… ok I’ll get on that,” said Pauli again, getting the feeling that Bohr may not be as happy as he had claimed. He backed away, leaving the captain to stare miserably at the array of stars laid out before him.
Back in his room, Pauli sat hunched in his chair gazing at the calculator in front of him. He stood up and began to pace around the room, brushing past the heavily laden bookshelves plastering the walls. Sharing his room with Professor Dirac had advantages and disadvantages, but at least he was never out of reading material. Currently, however, his mind was solely focused on one thing.
“Are you that desperate for exercise?” chuckled the professor, peering over his book. He suspected something was on the doctor’s mind, but from the comfort of his armchair, he saw no reason for worry.
“The planet is 5 light-years away. And we’re travelling about the speed of light,” said Pauli hurriedly, “So that would make our journey about 5 years. We packed supplies for around 2 years – we’re going to run out of food!” His brow was furrowed and his mind was racing. He had 16 different calendars to keep organised, how had he not thought of this sooner? Surely someone in charge should have noticed – this is why he never relied on anyone else’s planning ability.
“Don’t panic!” said Dirac. Pauli turned to him in disbelief. The professor had only packed his own belongings 2 days before launch, and with Pauli’s help. There was no way he knew about the supplies on the ship.
Scanning his bookshelves, Dirac continued talking. “First of all, I know we aren’t going any faster than the speed of light. We are probably going very close to that speed, but we actually can’t go any faster. Now, if you’ll just let me find the right b-”
“Wait, that makes the problem worse!” the doctor interrupted, “That means we won’t have supplies for at least 3 years!”
Dirac didn’t respond and was merely flicking through the pages of a well-worn book, still somewhat out of breath from lifting its huge weight onto his lap.
“Why can’t we go faster than the speed of light anyway?” asked Pauli.
“Aha!” Dirac answered, “I’ve found it. It’s all explained right here.” Dirac pointed at the open page, then continued. “The speed of light is like the speed limit of the universe, as nothing can go any faster. But light itself always travels at the same speed relative to you, no matter how fast you’re going. Albert Einstein discovered this, and it’s called special relativity. But it has some other strange properties too. When you’re going really fast, time actually goes slower for you, to make sure that you still measure light going at the same constant speed.”
“What? That’s a bit confusing,” replied the doctor.
“I know, it’s very strange, but we know it’s true because we’ve tested it so many times. Look, here’s the equation we use to find the time between 2 events:
where Δt’ is the time for the people on Earth, γ is a number that increases depending on the speed but can never go below 1, and Δt is the time for us experiencing the journey.” Explained Dirac.
“So if the people on earth expect the journey to take 5 years, and we’re travelling at a speed such that γ = 8, then how long will the journey take for us in the spaceship?” asked Pauli. He was hoping that someone had already done these calculations to make sure they wouldn’t starve, but then again he couldn’t be sure…
“We should check that the value of γ is correct too. If γ = 8, then what speed are we going?” asked the professor, pointing to a different equation. “This is the formula”
Scroll down for the solution!
Dirac decided he would work this out properly as he didn’t like seeing his friend so worried. Picking up the calculator, he plugged in 58. “The trip should take us 0.625 years, or around half a year. So we have plenty of food to get there and back. I told you not to panic.” He said with a smile.
“Now for the speed. We have to rearrange the equation. First, we square both sides and then multiply up by (1 – v2/c2) to get:
Next we divide both sides by -γ2 (don’t forget the minus sign), and then we add 1 to both sides and square root. Our final equation is:
which we plug in our value of γ to find our speed, v, divided by the speed of light. Usually, we like to keep our speed divided by the speed of light, because the speed of light is so important. Anyway, this will give us our answer for the speed: v/c = 0.9922 or v = 297,600,000 m/s.”
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