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

How do i do this?

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 10:25pm
Let 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 10:26pm
Make those distances billions of km, not miles. The equation stays the same

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

## Answer This Question

## Related Questions

- science - A comet is in an elliptical orbit around the Sun. Its closest approach...
- 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 ...
- physics - Halley's comet moves about the sun in an elliptical orbit with its ...
- college algebra - Keplerâ€™s third law. According to Keplerâ€™s third law of ...
- Physics - Halley's comet moves about the Sun in a highly elliptical orbit. At ...
- science - i'm not sure witch statement is true .The earth has a stronger ...
- math - 1. Number Sense: write three numbers that are greater than 1,543,000 and ...
- physics - The orbit of Halley's Comet around the Sun is a long thin ellipse. At ...
- Physics - What changed Newton's original work on the movement of the Moon ...

More Related Questions