PCalc and HP 50g: Period of Orbit Around the Sun

To determine the period of a satellite's orbit around the sun (mainly planet), Newton's version of Kepler's Third Law is used.

T = 2 π √(a^3 /(G * (MS + m)) )

Source: Astronomy 801: Planets, Stars, and the Universe - Penn State University
https://www.e-education.psu.edu/astro801/

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PCalc Program: Period Around the Sun
5/19/2014

G = 1.0690441604e-9 ft^3/(s^2 lb)
Mass of the Sun = MS = 4.384e30 lbs

T = 2 π √(a^3 /(G * (MS + m)) )

Input:
Y: mass in pounds
X: distance in miles

Output:
X: period in years

Program:
Decimal Mode
Multiply X By 5280
X To Power of 3
Add 4.384e30 To Y
Multiply Y By 1.0690441604e-9
Divide X By Y
X of Power of 0.5
Multiply X By 2
Multiply X By Pi
Divide X By 31556925.9747

Example:
Input:
Y: 1.3170e25 pounds (Mass of the Eath)
X: 9295400 miles (average semi-major axis between Earth and Sun)

Output:
X: 1.0000102186
It takes about 1.00001 years for Earth to orbit the Sun

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HP 50g: Period Around the Sun:

Input:
2: mass of orbiting object in pounds
1: distance from sun in miles

Output:
1: period of orbit in years

Program PERSUN
<< 5280 * 3 ^ SWAP 4.384E30 +
1.0690441604E-9 * / √ 2 * π *
→NUM 31556925.9747 / >>

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This blog is property of Edward Shore. 2014