Question 1167713: 1. Kepler observed that Pluto orbits the sun in an elliptic motion. With the
sun at one focus, nearest that Pluto gets to the Sun is 4,400,000,000 km, and the farthest that it goes to the Sun is 7,400,000,000 km.
a) Assuming that the center of Pluto’s orbit is at (0, 0), find the equation
that models Pluto’s orbit.
b) If an unidentified planet is located in the other focus, how far is this
planet from the Sun?
Found 2 solutions by htmentor, ikleyn:
Answer by htmentor(1343)   (Show Source):
You can put this solution on YOUR website! The equation for an ellipse centered at the origin is x^2/a^2 + y^2/b^2 = 1, where a, b are the semi-major and semi-minor axes, respectively.
The sun is located at one focus with coordinates (-c,0), with c^2 = a^2 - b^2.
For simplicity, we will express the distances in billions of miles.
The distance of the furthest approach is 7.4 = c + a, and the closest
approach is 4.4 = a - c. Solving for a gives 2a = 11.8 -> a = 5.9.
Solving for c gives 2c = 3 -> c = 1.5.
b^2 = a^2 - c^2 -> b^2 = 5.9^2 - 1.5^2 = 32.56.
Thus, the equation is x^2/34.81 + y^2/32.56 = 1.
If another planet is placed at the other focus, the distance between them
will be 2c = 3.
Answer by ikleyn(52781)  (Show Source):
You can put this solution on YOUR website! .
1. Kepler observed that Pluto orbits the sun in an elliptic motion. With the
sun at one focus, nearest that Pluto gets to the Sun is 4,400,000,000 km, and the farthest that it goes to the Sun is 7,400,000,000 km.
a) Assuming that the center of Pluto’s orbit is at (0, 0), find the equation
that models Pluto’s orbit.
b) If an unidentified planet is located in the other focus, how far is this
planet from the Sun?
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The problem's formulation is MONSTROUS.
To part (a)
Kepler lived 1571 - 1630.
Pluto was discovered in the year 1930.
So, Kepler (as a person) could not observe Pluto and did not know about Pluto's existence.
To part (b)
If another planet is " placed " in the other focus (in the standard meaning of the word " placed "),
then, according to Physics, this planet will fall to the Sun.
So, this formulation in (b) is MONSTROUS, too.
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