a.
Write an equation for the orbit of each planet.
a.
Answer to Problem 62SR
Explanation of Solution
Given information:
The table at the right shows the closest and farthest distances of Venus and Jupiter from the Sun in millions of miles.
Write an equation for the orbit of each planet. Assume that the centre of the orbit is the origin and the centre of the Sun is a focus that lies on the
Calculation:
Consider the standard equation of the horizontal ellipse which is centred to the origin,
Length of major axis,
The valid equation is,
Consider the table for distances,
Assume that planet Venus revolves around the Sun in an elliptical orbit with the Sun at its one of its focus on
The length of major axis will be the sum of closest and farthest distances and diameter of the Sun which is
Now find
Now put values of
Now put
Hence, the equation of the orbit of Venus is ,
Now consider the closest and farthest distance of Jupiter from the Sun,
Now substitute
Now put
Hence equation for orbit of Jupiter is
b.
Which planet has an orbit that is closer to the
b.
Answer to Problem 62SR
Explanation of Solution
Given information:
The table at the right shows the closest and farthest distances of Venus and Jupiter from the Sun in millions of miles.
Which planet has an orbit that is closer to the circle?
Calculation:
Consider the standard equation of eccentricity of ellipse is,
For Venus planet put
For Jupiter planet,
Thus lesser the value of
Hence, the orbit of
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