###### Asked in Astronomy

Astronomy

# What is the distance from one of the foci of the ellipse from its center?

## Answer

###### Wiki User

###### July 11, 2009 8:09AM

The length of the semi-major axis multiplied by the eccentricity.

## Related Questions

###### Asked in Astronomy

### What is the shape of planets orbit?

The planets orbit in an ellipse. An ellipse is described as a
geometric shape where the sum of the distance from the foci at any
point is the same. An ellipse has three main points. Two foci and a
center like a circle. While a true circle has all its external
points equidistant from its center, an ellipse measures its points
from the foci, which are equidistant to the center point at on both
sides.
The planets ellipse is closer to a circle than an all out
ellipse, however, the orbit is still a true ellipse.
It is also true that the shape of a planet's orbit (an ellipse)
is a conic section, i.e. the intersection of a right circular cone
where the intersecting plane is not perpendicular to the cone's
axis, but less than being parallel to one of the cone's nappes.

###### Asked in Astronomy, Planetary Science, The Moon

### How many foci in circular orbit?

Most orbits are elliptical; all NATURAL orbits are. There are
two foci, or focuses, to an ellipse. The distance between the foci
determines how eccentric, or non-circular, they are.
If the two foci are in the same place, then the ellipse becomes
a circle. So a circular orbit would have only one focus.

###### Asked in Astronomy, Planetary Science

### What planets has the least distance between the two foci of its elliptical orbit?

Planets don't have circular orbits; all orbits are ellipses. A
circle has one center, but an ellipse has two focuses, or "foci".
The further apart the foci, the greater the eccentricity, which is
a measure of how far off circular the ellipse is.
Venus has the lowest eccentricity, at 0.007. Neptune is next
with an eccentricity of 0.011. (Earth's orbit has an eccentricity
of 0.017.)
So, Venus has the shortest focus-to-focus distance.

###### Asked in Astronomy

### What factors affect the perihelion and aphelion distance?

The orbit of a planet is not a circle with the sun at the
center. It's an ellipse with
the sun at one focus.
An ellipse is an 'egg shape', or 'oval', or 'squashed circle'.
It has two foci (focuses)
and neither one is in the center.
So you can easily see that as the planet moves along the
ellipse, its distance from the sun
changes, and there is a minimum distance (perihelion) and a
maximum distance (aphelion).
Those don't change unless the shape of the ellipse changes, and
the only way
that happens is through the gravitational influence of the other
planets, which
is relatively tiny over the course of many millennia.

###### Asked in Math and Arithmetic, Algebra, Calculus

### What is the equation of an ellipse with vertices 2 0 2 4 and foci 2 1 2 3?

Vertices and the foci lie on the line x =2
Major axis is parellel to the y-axis b > a
Center of the ellipse is the midpoint (h,k) of the vertices
(2,2)
Equation of the ellipse is (x - (2) )^2 / a^2 + (y - (2) )^2 /
b^2
Equation of the ellipse is (x-2)^2 / a^2 + (y-2)^2 / b^2
The distance between the center and one of the vertices is b
The distance between(2,2) and (2,4) is 2, so b = 2
The distance between the center and one of the foci is c
The distance between(2,2) and (2,1) is 1, so c = 1
Now that we know b and c, we can find a^2
c^2=b^2-a^2
(1)^2=(2)^2-a^2
a^2 = 3
The equation of the ellipse is
Equation of the ellipse is (x-2)^2 / 3 + (y-2)^2 / 4 =1

###### Asked in Health, Definitions, Calculus, Biodiversity

### What is foci?

Foci, (the plural of focus), are a pair of points used in
determining conic sections. They always fall on the major axis of
symmetry of a conic. For example, in a circle, there is only one
focus, the centerpoint. Every distance from the focus to any other
point on the circle will be the same. In a parabola, the distance
from any point of the parabola to the focus equals the distance
from the centerpoint to the directrix. In a hyperbola, the
difference of the distances between a point on the hyperbola and
the focus points will be constant, and in an ellipse, the sum of
the distances from any point on the ellipse to one of the foci is
constant.

###### Asked in Astronomy, Geometry

### Define the focus and the eccentricity of an ellipse?

A circle is perfectly round, and has one center. An ellipse is
like a circle with TWO "centers", and each "center" is called a
"focus". The plural of "focus" is "foci".
Take a piece of string and tie a loop in each end. Put a pin
through the loops, and hold it still in the center of the circle.
Place the tip of your pencil at the center of the string, and you
can draw a circle by keeping the string taut.
Now take TWO pins, and put one pin at each end of the string;
place the pins at some short distance apart, and hold them there.
Place your pencil and draw, and the shape you draw will be an
ellipse. The two pinpoints are the focuses, or foci, of the
ellipse.
Eccentricity is a measure of how far the ellipse varies from a
circle. An ellipse with an eccentricity of zero _IS_ a circle,
while an eccentricity of 1.0 is a straight line, with that string
stretched out straight.
In astronomy, every natural orbit is an ellipse.

###### Asked in Math and Arithmetic, Algebra, Geometry

### The eccentricity of the ellipse if minor axis is equal to the distance between the foci is Answer is 1 radical 2 how?

The standard equation for an ellipse centered at the origin is
[x2/a2] + [y2/b2] = 1
We also have the relationship, b2 = a2 - c2 where c is the
distance of the foci from the centre and a & b are the half
lengths of the major and minor axes respectively.
When the length of the minor axis equals the distance between
the two foci then 2b = 2c : b = c.
Thus, a2 =b2 + c2 = 2b2
One of the formulae for the eccentricity of an ellipse is, e =
√[(a2 - b2)/a2]
Thus, e = √[(2b2 - b2) / 2b2] = √½ = 1/√2.

###### Asked in Astronomy, Geometry

### What is also known as the semimajor axis?

The major axis of an ellipse is its longest diameter, a line
that runs through the center and both foci, its ends being at the
widest points of the shape.
The semi-major axis is one half of the major axis, and
thus runs from the centre, through a focus, and to the edge of the
ellipse. It represents a "long radius" of the ellipse, and is the
"average" distance of an orbiting planet or moon from its parent
body.

###### Asked in Astronomy, Planetary Science

### How far away from the Sun is the other focus of Earth's orbit?

What a great question !
The earth's orbit is elliptical, the ellipse has two foci
(focuses), and the center
of the sun is at one of them. All true.
But the earth's orbit is so close to being circular that the
distance between the
two foci isn't that great, and the other focus is inside the sun
!
I'm not sure about Pluto, but I think that's true for all the
other planets.

###### Asked in Astronomy, Planetary Science, The Moon

### Is the sun directly in the center of Earth as Earth revolves around it?

The Earth's orbital path around the Sun isn't a circle; it is an
ellipse, a sort of oval shape. Some orbits are ALMOST circular,
like the Earth's; some are more oval, like Pluto's. A comet has an
elliptical orbit which is VERY stretched out.
An ellipse doesn't have a center, exactly; it has a "focus".
Actually, it has TWO "foci", which define the ovalness of the
ellipse. The Sun is at one focus of the Earth's elliptical orbit.
(There is no physical object at the other focus of the
ellipse.)
The Moon's orbit is elliptical, too, with the Earth at one focus of
the ellipse.

###### Asked in The Moon, Astronomy, Planetary Science

### If an asteroid is in an elliptical orbit about the Sun with the Sun almost at the center of the ellipse what would the eccentricity of the ellipse be?

All natural orbits are ellipses. We can force an artificial
satellite into a spherical orbit, but it won't STAY there without
occasional adjustments.
The "primary body" - in this case, the Sun - is at one of the
two focuses (foci) of the orbit. If the focus is very close to the
"center" of the ellipse, then the eccentricity of the orbit (how
much it varies from a perfect circle) is close to zero.

###### Asked in Astronomy, Dwarf Planet Pluto, Stars

### Is the sun in the center of the orbit?

Not quite. The orbits of planets are not circles, but
ellipses.
A circle has a center; you can tie a piece of string to the
center of the circle and swing the other end of the string around
and get the circle. If the orbit were a circle, the Sun would be at
the center. But it isn't.
An ellipse has a "focus"; actually, it has two, and the plural
is "foci". Put one end of the string at one "focus" and the other
end of the string at the other focus, and see where the string
goes; that's an ellipse.
With elliptical orbits, the Sun is at one focus of the
orbit.

###### Asked in The Solar System

### What happens to the shape of an obit as eccentricity gets smaller?

As the eccentricity reaches zero the two foci merge together and
the ellipse becomes a circle.
If a is half the major axis of the ellipse, and e is the
eccentricity, the distance between the foci is 2ae. For a planet
the Sun occupies one focus and the other is vacant, so the Sun is a
distance of ae from the centre of the ellipse.
The minor axis is sqrt(1-e^2) times the minor axis, so for all
the planets except Mercury the minor axis is more than 99½% of the
major axis. The best way to draw an orbit is to ignore this small
difference and draw a circle, and then place the Sun at the right
distance off-centre.