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If there were a kind of a fireman's pole from the Moon down to the Earth, how long would it take to slide all the way from the Moon to the Earth?  

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ekkoirving
(@ekkoirving)
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24/12/2019 1:32 am  

My son (5y) asked me today: If there were a kind of a fireman's pole from the Moon down to the Earth, how long would it take to slide all the way from the Moon to the Earth?

                                                                                                                                                                                          Ramon Schönborn, Germany

 

First, let's get a few things out of the way:

In real life, we can't put a metal pole between the Earth and the Moon. The end of the pole near the Moon would be pulled toward the Moon by the Moon's gravity, and the rest of it would be pulled back down to the Earth by the Earth's gravity. The pole would be torn in half.

Another problem with this plan. The Earth's surface spins faster than the Moon goes around, so the end that dangled down to the Earth would break off if you tried to connect it to the ground:

There's one more problem: The Moon doesn't always stay the same distance from Earth. Its orbit takes it closer and farther away. It's not a big difference, but it's enough that the bottom 50,000 km of your fire station pole would be squished against the Earth once a month.

But let's ignore those problems! What if we had a magical pole that dangled from the Moon down to just above the Earth's surface, expanding and contracting so it never quite touched the ground? How long would it take to slide down from the Moon?

If you stood next to the end of the pole on the Moon, a problem would become clear right away: You have to slide up the pole, and that's not how sliding works.

Instead of sliding, you'll have to climb.

People can climb poles pretty fast. World-record pole climbers can climb at over a meter per second in championship competition. On the Moon, gravity is much weaker, so it will probably be easier to climb. On the other hand, you'll have to wear a spacesuit, so that will probably slow you down a little.

If you climb up the pole far enough, Earth's gravity will take over and start pulling you down. When you're hanging onto the pole, there are three forces pulling on you: The Earth's gravity pulling you toward Earth, the Moon's gravity pulling you away from Earth, and centrifugal force from the swinging pole pulling you away from Earth. At first, the combination of the Moon's gravity and centrifugal force are stronger, pulling you toward the Moon, but as you get closer to the Earth, Earth's gravity takes over. The Earth is pretty big, so you reach this point—which is known as the L1 Lagrange point—while you're still pretty close to the Moon.

Unfortunately for you, space is big, so "pretty close" is still a long way. Even if you climb at better-than-world-record speed, it will still take you several years to get to the L1 crossover point.

As you approach the L1 point, you'll start to be able to switch from climbing to pushing-and-gliding: You can push once and then coast a long distance up the pole. You don't have to wait to stop, either—you can grab the pole again and give yourself a push to move even faster, like a skateboarder kicking several times to speed up.

Eventually, as you reach the vicinity of the L1 point and are no longer fighting gravity, the only limit on your speed will be how quickly you can grab the pole and "throw" it past you. The best baseball pitchers can move their hands at about 100 mph while flinging objects past them, so you probably can't expect to move much faster than that.

Note: While you're flinging yourself along, be careful not to drift out of reach of the pole. Hopefully you brought some kind of safety line so you can recover if that happens.

After another few weeks of gliding along the pole, you'll start to feel gravity take over, speeding you up faster than you can go by pushing yourself. When this happens, be careful—soon, you'll need to start worrying about going too fast.

As you approach the Earth and the pull of its gravity increases, you'll start to speed up quite a bit. If you don't stop yourself, you'll reach the top of the atmosphere at roughly escape velocity—11 km/s—and the impact with the air will produce so much heat that you risk burning up. Spacecraft deal with this problem by including heat shields, which are capable of absorbing and dissipating this heat without burning up the spacecraft behind it. Since you have this handy metal pole, you can control your descent by clamping onto it and controlling your rate of descent through friction.

Make sure to keep your speed low during the whole approach and descent—and, if necessary, pausing to let your hands or brakepads cool down—rather than waiting until the end to try to slow down. If you get up to escape velocity, then at the last minute remember that you need to slow down, you'll be in for an unpleasant surprise as you try to grab on to the pole. At best, you'll be flung away and plummet to your death. At worst, your hands and the surface of the pole will both be converted into exciting new forms of matter, and then you'll be flung away and plummet to your death.

Assuming you descend slowly and enter the atmosphere in a controlled manner, you'll soon encounter your next problem: Your pole isn't moving at the same speed as the Earth. Not even close. The land and atmosphere below you are moving very fast relative to you. You're about to drop into some extremely strong winds.

The Moon orbits around the Earth at a speed of roughly one kilometer per second, making a wide circle every 29 days or so. That's how fast the top end of our hypothetical fire pole will be traveling. The bottom end of the pole makes a much smaller circle in the same amount of time, moving at an average speed of only about 35 mph relative to the center of the Moon's orbit:

35 miles per hour doesn't sound bad. Unfortunately for you, the Earth is also spinning, and its surface moves a lot faster than 35 mph; at the Equator, it can reach over 1,000 miles per hour.

Even though the end of the pole is moving slowly relative to the Earth as a whole, it's moving very fast relative to the surface.

Asking how fast the pole is moving relative to the surface is effectively the same as asking what the "ground speed" of the Moon is. This is tricky to calculate, because the Moon's ground speed varies over time in a complicated way. Luckily for us, it doesn't vary that much—it's usually somewhere between 390 and 450 m/s, or a little over Mach 1—so figuring out the precise value isn't necessary.

Let's buy a little time by trying to figure it out anyway.

The Moon's ground speed varies pretty regularly, making a kind of sine wave. It peaks twice every month as it passes over the fast-moving equator, then reaches a minimum when it's over the slower-moving tropics. Its orbital speed also changes depending on whether it's at the close or far point in its orbit. This leads to a roughly sine-wave shaped ground speed:

Well, ready to jump?

Ok, fine. There's one other cycle we can take into account to really nail down the Moon's ground speed. The Moon's orbit is tilted by about 5° relative to the Earth-Sun plane, while the Earth's axis is tilted by 23.5°. This means that the Moon's latitude changes the way the Sun's does, moving from the northern tropics to the southern tropics twice a year.

However, the Moon's orbit is also tilted, and this tilt rotates on an 18.9-year cycle. When the Moon's tilt is in the same direction as the Earth's, it stays 5° closer to the Equator than the Sun, and when it's in the opposite direction, it reaches more extreme latitudes. When the Moon is over a point farther from the equator, it has a lower "ground speed," so the lower end of the sine wave goes lower. Here's the plot of the Moon's "ground speed" over the next few decades:

The Moon's top speed stays pretty constant, but the lowest speed rises and falls with an 18.9-year cycle. The lowest speed of the next cycle will be on May 1st, 2025, so if you want to wait until 2025 to slide down, you can hit the atmosphere when the pole is moving at only 390 m/s relative to the Earth's surface.

When you do finally enter the atmosphere, you'll be coming down near the edge of the tropics. Try to avoid the tropical jet stream, an upper-level air current which blows in the same direction the Earth rotates. If your pole happens to go through it, it could add another 50-100 m/s to the wind speed.

Regardless of where you come down, you'll need to contend with supersonic winds, so you should wear lots of protective gear. Make sure you're tightly attached to the pole, since the wind and various shockwaves will be violently battering and jolting you around. People often say, "It's not the fall that kills you, it's the sudden stop at the end." Unfortunately, in this case, it's probably going to be both.

At some point, to reach the ground, you're going to have to let go of the pole. For obvious reasons, you don't want to jump directly onto the ground while moving at Mach 1. Instead, you should probably wait until you're somewhere near airline cruising altitude, where the air is still thin, so it's not pulling at you too hard—and let go of the pole. Then, as the air carries you away and you fall toward the Earth, you can open your parachute.

Then, at last, you can drift safely to the ground, having traveled from the Moon to the Earth completely under your own muscle power.

(When you're done, remember to remove the fire pole. That thing is definitely a safety hazard.)

 

Source from: xkcd.com

This topic was modified 3 months ago by ekkoirving

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