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e semi-major axis found if perihelion and aphelion distance are known? | Socratic
For example, if an asteroid has a perihelion distance of 2.0 and an aphelion distance of 4.0 AU, what is the semi-major axis?
The semi major axis distance is half the sum of the perihelion and aphelion distances.
Given that the orbit is an ellipse with semi major axis a and eccentricity e, then the aphelion distance is
Therefor the semi major axis distance is half the sum of the perihelion and aphelion distances.
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How is the semi-major axis located?
The semi-major axis is half the length of the major axis, and its length can be calculated using the formula: b>Length of the semi-major axis = (AF + AG) / 2/b>, where A is any point on the ellipse and F and G are its foci.
If you know the perihelion and aphelion, how do you find the major axis?
The semi-major axis is half of the major axis, or half of (0.5 + 3.5) = half of 4 = 2 AU, and the major axis is the product of the perihelion and aphelion distances.
How can I determine the AU’s semi-major axis?
In the special case of the solar system, we can use Kepler’s third law in its original form: b>(P/yr)2 = (a/au)3/b>. Plugging in the period of 76 yr gives a semi-major axis of a = 17.9AU=2.68 1012 m. For any general system, the period and eccentricity are insufficient to calculate the semi-major axis.
Are aphelion and semi-major axis the same thing?
The semi-major axis is the average of the aphelion and perihelion distances because the aphelion is the point on a planet’s orbit that is furthest from the Sun and is located on the major axis directly opposite the perihelion point.
Given a perihelion, how do you find the semi-major axis?
The semi-major axis of an ellipse is equal to half the sum of its perihelion and aphelion.
How can I determine the aphelion’s semi-major axis?
The semi major axis distance is half the sum of the perihelion and aphelion distances because the orbit is an ellipse with a semi major axis of a and an eccentricity of e. As a result, the aphelion distance is equal to a(1?e) and the aphelion distance is equal to a(1+e), which when added together gives 2a.
How is the semi-minor axis located?
The semi-minor axis of an ellipse is half of the minor axis and extends from the center of the ellipse (a point halfway between and on the line connecting the foci) to the edge of the ellipse.
What is the Sun’s semi-major axis?
The semi-major axis, also known as the distance from the Sun (106 km or 106 miles), is the average distance between the planet and the Sun in millions of kilometers or millions of miles.
How does the third law of kepler help in the calculation of semi-major axes?
The equation for Kepler’s Third Law is P2 = a3, which means that when expressed in astronomical units, the period of a planet’s orbit (P) squared is equal to the size of the semi-major axis of the orbit (a) cubed.
What does Kepler’s law mean by a semi-major axis?
In fact, (Figure) gives us Kepler’s third law if we simply replace r with a and square both sides. T2=4?2GMa3. Recall that for an ellipse, the semi-major axis is one-half the sum of the perihelion and the aphelion. For a circular orbit, the semi-major axis (a) is the same as the radius for the orbit.