REGENTS EARTH SCIENCE
Eccentricity of Orbits
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Aim: How can we describe and calculate the eccentricity of orbits in our solar system?
Eccentricity =
𝐃𝐢𝐬𝐭𝐚𝐧𝐜𝐞 𝐛𝐞𝐭𝐰𝐞𝐞𝐧 𝐟𝐨𝐜𝐢
𝐋𝐞𝐧𝐭𝐡 𝐨𝐟 𝐦𝐚𝐣𝐨𝐫 𝐚𝐱𝐢𝐬
Overview:
Years ago it was assumed that the planets, comets and other astronomical objects revolved around the Sun in
circular orbits. In time, it was proven that they do not revolve in circular orbits, but in elliptical orbits. These
orbits are not round, but slightly flatten, giving it an oval shape. It’s easy to describe a circular orbit, but how
does one describe an elliptical orbit? This was solved by mathematicians using a term called eccentricity.
Think of eccentricity as a measurement of how much the shape of an ellipse deviates from a circle. Eccentricity
( e ) is a value that is used to indicate how elliptical an orbit is.
1) What is the shape of the orbits of the planets around the Sun?
2) What is the term eccentricity a measure of?
3) What is the mathematical formula of the eccentricity of an ellipse?
The Equation:
To arrive at the eccentricity, the distance ( d ) between the two foci (F1 and F2) is measured. Located at one of
these foci may be a star (like our Sun), while the other focus is at imaginary position in the space. The length of
the major axis ( l ) is determined by measuring the longest axis of the elliptical orbit. Dividing,
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gives us the
eccentricity or e value. This e value has no units. The larger the eccentricity, the more elliptical the orbit will be.
The smaller the eccentricity, the more circular the orbit will be. The eccentricity of a perfect circle is 0, which is
the lowest eccentricity. The eccentricity of a straight line is 1, which is the highest eccentricity. The Solar
System Data Table in ESRT pg15 lists the eccentricity of the planets.
1 4) An ellipse has two foci. One of those foci is a star (Sun). What is the other focus?
5) Which planet has the most elliptical orbit (highest eccentricity)? (ESRT pg15) _______________
6) Which planet has the least elliptical orbit (lowest eccentricity)? (ESRT pg15) _______________
7) What is the eccentricity of a perfect circle? _______________
8) What is the eccentricity of a straight line? _______________
Question 9 and 10 refer to the following:
The accompanying diagram represents the elliptical orbit of a spacecraft’s orbit around the Sun.
9) Calculate the eccentricity of the spacecraft’s
orbit.
a) Write the equation for eccentricity
(ESRT pg1):
e=
b) Substitute the values for distance between
foci (nearest tenth place) & length of
major axis (nearest tenth place) into the
equation and solve for eccentricity
(nearest thousandth place):
e=
10) State how the eccentricity of the ellipse above compares to the eccentricity of the orbit of Uranus.
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