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/

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

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 / >>

This blog is property of Edward Shore. 2014

Best add a zero to 9295400 (miles). All the best, J.

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