Recent content by Jenab2

I set about trying to use HiPER Calc Pro on my phone to solve the integral for the Bessel function of the first kind and of order one, so that I could get the ordinate value for the first root of the function to 99 significant figures, then divide that by π to 99 significant figures, in order to...

The most recent edition I've found is Cox's 1999 update to CW Allen's Astrophysical Quantities. I'd like to find, and to buy, a more recent edition that contains, among other things, information on the several thousand confirmed exoplanets.

I'm looking for a reference text for astronomy and astrophysics that provides astrophysical and cosmological data since Cox's 1999 update to CW Allen's Astrophysical Quantities. Among other reasons, I'm hoping for statistical data on confirmed exoplanets, which did not exist in 1999.

If you have already learned a programming language, then learning another should be easy. I also learned BASIC, FORTRAN, PASCAL in my youth. When I learned BASIC, I also had to learn coding logic. After BASIC, I knew coding logic, so learning the other languages were only a matter of becoming...

I personally don't know of any physical process that can't be modeled without need for tetration or higher order hyperoperations. In my own experience, exponentiation suffices. Does anyone else know about a physical process that can't be well-modeled unless tetration is used in the math?

Oh I quite agree. The high school approximation is quite good enough in this case. But the equation I presented is even more accurate, and remains good when the acceleration of gravity does vary considerably over the fall. It was, therefore, worth deriving, presenting, and showing how it works...

This is why I have been a latent member of the Physics Forums for most of the ten years I've been here. Every time I work out a difficult problem concisely, in detail, I'm jumped on. As someone else noted, the original post was made many years ago, and he probably graduated long ago. I'm not...

Well, since this is a hypothetical problem, probably presented as someone's homework, then we may proceed as if the initial conditions are exact. I'll admit that I retain a ridiculous number of significant digits, but, as to that, I am merely reporting what my calculator told me. If this were a...

I neglected general relativity, too. But the point is that the solution that I found doesn't have any sources of error that the integrative approximation has, and indeed my solution has one fewer cause of error. And the one-and-done approximation from the high school physics textbook has...

Look closely. The altitude used in my treatment is 105 meters, which is what the question specified. The difference between my method and the approximate method is that I've provided the classically exact solution. No approximation necessary. Naturally, the approximation in this case is very...

How To Reduce Keplerian Orbital Elements and a time to Heliocentric Position and Velocity Definitions a : semimajor axis of orbit, positive for elliptical orbits, negative for hyperbolic orbits e : eccentricity of orbit, between 0 and 1 for elliptical orbits, greater than 1 for hyperbolic...

This is the actual distance of the object (15.4 billion light years), not the distance we would observe it at, which would be nearer to 8 billion light years. The 15.4 Gly has already been corrected for the expansion of the universe since the light we currently can see was emitted.

Gravitational parameter of Earth, GM = 3.986004418e+14 m³/s² Radius of Earth, R = 6371000 meters Altitude of helicopter at bag release, h₁ = 105 meters Velocity of bag at release, v₁ = +5 m/s geocentric radius of bag at release, r₁ = R + h₁ r₁ = 6371105 meters The Vis Viva equation, v₁ =...

This equation, t−t₀ = √[d/(2GM)] { √(rd−r²) + d arctan √(d/r−1) } is the classically exact solution to the time-to-fall problem. It does not depend on the acceleration of gravity being constant throughout the fall. Nor does it approximate the resulting time difference by an approximate method...

Here is the derivation of the equation for the time to fall in a plunge orbit. Two bodies having a total mass M (i.e., M = M₁ + M₂) are initially at rest, separated by a distance d, in vacuum, and isolated from all forces except their mutual gravitational attraction. Find the time elapsed from...