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David Sims

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    astronomy, celestial mechanics
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    Hillsboro, West Virginia

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  1. Time to Fall in a Plunge Orbit The moon doesn't fall on Earth because it has enough transverse velocity to remain in an orbit around Earth, and because angular momentum is conserved as a natural law. Now, if you removed all of the moon's transverse velocity when the moon reached its aphelion, leaving the moon momentarily stationary with respect to Earth, then the moon and Earth would indeed fall together. How long would it take? 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
  2. Determining the Keplerian Elements of an Elliptical Orbit from Four Observations Presented hereafter is a method for determining a preliminary heliocentric orbit from four geocentric directions of a sun-orbiting object at four distinct times of observation. I take this method after that presented in chapter six of The Determination of Orbits by A.D. Dubyago. The initial data t₁, X⊕₁, Y⊕₁, Z⊕₁, α₁, δ₁ t₂, X⊕₂, Y⊕₂, Z⊕₂, α₂, δ₂ t₃, X⊕₃, Y⊕₃, Z⊕₃, α₃, δ₃ t₄, X⊕₄, Y⊕₄, Z⊕₄, α₄, δ₄ The times of observation, tᵢ, are given in Julian date format. The vectors [X⊕ᵢ,Y⊕ᵢ,Z⊕ᵢ] are t
  3. Elliptical Transfer-Intercept Orbits Non-Hohmann Transfer Orbits that Take You Somewhere Most of the time, when someone speaks of transfer orbits, he's referring to a special case known as a Hohmann transfer orbit. Hohmann transfer orbits have a departure occurring at one of its apsides (perihelion or aphelion) and an arrival occurring at the other apside. Thus, I could describe Hohmann transfer orbits as transfer orbits having two anchored apsides. In this essay, I will treat a more general case of transfer orbits that have only one anchored apside, which turns out to be enough
  4. If you are a serious amateur astronomer, then there probably will be occasions when you have photographic observations of an asteroid moving through a star field, and you might think that there's a chance that it is one that hasn't been discovered by anyone else. So you will want to calculate the asteroid's orbital elements, both so that you can find it again, and so that you can prove your claim as the discoverer should that be the case. For situations such as this, I've written a program so that you can easily calculate the Keplerian elements of your asteroid's orbit. The type and manne
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