Orbital Mechanics Made Simple

Today’s lesson in orbital mechanics.

I was spending New Year’s Day looking over an old 2017 “Year In Space” calendar before recycling it when I found this statement concerning the Spitzer Space Telescope.

Spitzer travels in Earth’s orbit but at a slower pace; by 2063, Earth will have “lapped” the telescope and Spitzer will reenter the atmosphere.

OK, former Sumerlin astronomy students and fellow space nerds. What is wrong with this statement? Think about it before scrolling past the video that gives you a subtle hint.

If it travels in Earth’s orbit around the Sun, it will travel at the same speed as the Earth, not “at a slower pace.” If it moves more slowly than the Earth, it must be farther from the Sun than the Earth. As an example, Mars’s mean orbital speed is 24 kilometers per second as compared to Earth’s 30 km/s.

So Spitzer travels in an orbit that is similar to Earth’s, but slightly farther away from the Sun. For the serious space geeks, let’s go a little deeper.

Spitzer was launched in 2003, and according to the statement above will be lapped by the Earth 60 years later. So in that time, Spitzer will have completed 59 solar orbits while the Earth has completed 60. Its orbital period is 60/59 of a year, or 371 days. (We’re not trying to be super precise here.) There is a simple formula derived by Johannes Kepler 400 years ago that lets us determine Spitzer’s location.

Capture

Where P is the orbital period in years and A is the mean distance from the Sun in astronomical units (AU). One AU is the mean distance of the Earth from the Sun.

Capture

This puts Spitzer in a Sun-centered orbit that is roughly 1.69 million kilometers (1.05 million miles) farther out than Earth’s. For comparison, the Moon orbits about a quarter of a million miles away from Earth.

Who said orbital mechanics was complicated?

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