Where would the Pascal B manhole cover be now?

Question

As part of the Operation Plumbbob series of nuclear tests, on August 27th, 1957, at 22:35 UT (15.35 Pacific Daylight Time), at the Nevada Test Range at 32°N 116°W, a 300 ton-yield atomic device was detonated at the bottom of a shaft dug for the purpose. This was Test Pascal B. The testers were expecting a fizzle, a mis-fire, but they got their physics wrong and it detonated, blowing the 900 kilo steel cap to the shaft into the air.

A 1000-frame-per-second camera set up to film the results of the test caught the cap in one frame as it flew past, from which it was later estimated that it was moving at a speed of more than 66 km/s. The cap (or manhole cover, as it is sometimes characterised) probably burnt up in the atmosphere as it ascended. But if it hadn't, where would it plausibly be right now?

I've gotten as far as finding what stars would have been overhead at "launch" — Cor Caroli, more or less — and the vector the cap would have been moving at — 53 km/s relative to the Sun at 129° away from Earth's direction of orbit, so clockwise around the Sun in a hyperbolic orbit. I feel like a younger me would have been able to work out how far away the cap would have travelled by now, call that part A; but my grammar school math classes are 42 years behind me. For part B, any idea how much Kentucky windage I'd have to apply to the course as it travels past the Sun?

Answer 1

The sea level speed quoted in the question for the Pascal-A manhole cover is likely in error. It came from an informal conversation between Bill Ogle and Dr. Robert R. Brownlee about back-of-the-envelope calculations (done by Brownlee) concerning the upcoming Pascal-B test. Brownlee, himself, denies the speed is valid.

The US-manhole-beats-Sputnik-into-space-story is firmly entrenched in Cold War mythology. Questionable information has morphed into hard fact by frequent retelling. But calculating the trajectory of the manhole cover using erroneous estimates is like calculating Santa Clause’s trajectory from the North Pole: it provides quantitative validation to a mythical flying object.

Original sources (including the cine frame) are scant, but this conversation is reported by Brownlee in the Nuclear Weapons Archive, http://nuclearweaponarchive.org/Usa/Tests/Brownlee.html

“Ogle: "What time does the shock arrive at the top of the pipe?"

RRB: "Thirty one milliseconds."

Ogle: "And what happens?"

RRB: "The shock reflects back down the hole, but the pressures and temperatures are such that the welded cap is bound to come off the hole."

Ogle: "How fast does it go?"

RRB: "My calculations are irrelevant on this point. They are only valid in speaking of the shock reflection."

Ogle: "How fast did it go?"

RRB: "Those numbers are meaningless. I have only a vacuum above the cap. No air, no gravity, no real material strengths in the iron cap. Effectively the cap is just loose, traveling through meaningless space."

Ogle: And how fast is it going?"

This last question was more of a shout. Bill liked to have a direct answer to each one of his questions.

RRB: "Six times the escape velocity from the earth."

Bill was quite delighted with the answer, for he had never before heard a velocity given in terms of the escape velocity from the earth! There was much laughter, and the legend was now born, for Bill loved to report to anybody who cared to listen about Brownlee's units of velocity. He says the cap would escape the earth. (But of course we did not believe that would ever happen.)

The next obvious decision was made. We'll put a high-speed movie camera looking at the cap, and see if we can measure the departure velocity. In the event, the cap appeared above the hole in one frame only, so there was no direct velocity measurement. “

Dr. Brownlee was later quoted, "I have no idea what happened to the cap, but I always assumed it was probably vaporized.”

The fate of the manhole is dealt with in this excellent posting on our favorite website: https://physics.stackexchange.com/questions/488151/could-the-end-cap-of-the-pascal-b-1-survive-its-trip-through-the-atmosphere

Without a reliable launch velocity, the hypothetical orbit cannot be calculated.

Answer 2

Where would the manhole cover be now? Answer it would be in the ocean.

Any object like a manhole cover accelerated to 66 km/s at Earth's surface would be vaporised by such high velocity travel through such a dense medium. However the question specifically asks us to assume that it did not burn up.

In this case the kinetic energy would still be bled away but instead of vaporizing the cap it would raise the temperature of the cap without vaporizing it. As the cap ascended It would also have to accelerate an increasing mass of air encountered on the way up because there would not be time for any the molecules to get out of the way.

At some arbitrarily high temperature the kinetic energy of the cap would be entirely bled away and the cap would fall back towards the ocean radiating energy in all directions possibly at UV or even X-ray frequencies at least initially.

Answer 3

If the manhole cover reached orbital speed just above the surface of Earth, it would be vaporized before the Kármán line. There was no heat shield at all and unlike to a reentry, the maximum speed was achieved at surface air pressure. The extreme heat load would have destroyed the cap. If the cover survived partially, it would have lost so much speed that an orbit was impossible.

But an orbit around Earth could not be achieved if the cover was shot vertically from the surface of Earth without a second acceleration to enter a circular or elliptical orbit.

So the cover would never reached an orbit.