# ALG/TRIG

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Orbits and Distance Johannes Kepler (1571–1630)discovered a relationship between a planet’s distance

D from the sun and the time T it takes to orbit the sun. This formula is , where T is in
Earth years and corresponds to the distance
between Earth and the sun, or 93,000,000 miles.
(a) Neptune is 30 times farther from the sun than
Earth . Estimate the number of years
required for Neptune to orbit the sun.
(b) Write this formula with rational exponents

• ALG/TRIG -

T = k D^(3/2)
let x = 93,000,000 miles
for earth
1 year = k x^(3/2)
k = 1/x^(3/2)
for Neptune
T = [1/x^3/2) (30x)^(3/2)
T = 30^(3/2) = 164 years

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