Tuesday

July 22, 2014

July 22, 2014

Posted by **anonymous** on Monday, December 7, 2009 at 8:50pm.

According to Kepler's Laws, planets have elliptical orbits, with the sun at one of the foci. The farthest Pluto gets from the sun is 7.4 billion kilometers. The closest it gets to the sun is 4.4 billion kilometers. Find the equation of the orbit of Pluto.

- MATH ANALYSIS -
**drwls**, Monday, December 7, 2009 at 10:25pmLet us center the ellipse at (0,0) with the major axis along the x axis. The semimajor axis is a = (7.4 + 4.4)/2 = 5.9 . We will call that "a" in the general equation

x^2/a^2 = y^2/b^2 = 1

(x, y, a & b are in billions of miles).

The minor axis b is given by

b^2 = a^2 - c^2, where c is the distance of either focus from the middle, which in this case is 5.9 - 4.4 = 1.5. That means b^2 = 32.56; b = 5.71

The orbit equation is

(x/5.9)^2 + (y/5.71)^2 = 1

- MATH ANALYSIS (correction) -
**drwls**, Monday, December 7, 2009 at 10:26pmMake those distances billions of km, not miles. The equation stays the same

- MATH ANALYSIS -
**anonymous**, Monday, December 7, 2009 at 10:33pmthank you!

**Related Questions**

Science - Have I matched the right Scientists with these famous sayings: ...

science - write T if the statement is true or F if it is false. a.)All the ...

college algebra - Kepler’s third law. According to Kepler’s third law of ...

science - i'm not sure witch statement is true .The earth has a stronger ...

Physics - Halley's comet moves about the Sun in a highly elliptical orbit. At ...

science - According to Kepler's law of harmonies, which of these planets takes ...

science - According to Kepler's law of harmonies, which of these planets takes ...

science - Our solar system consists of_____? a) the moon and the planets b) the...

physics - Halley's comet moves about the sun in an elliptical orbit with its ...

Astronomy - 1. Sun-grazing comet ISON disintegrated on November, 2013. ...