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64-465: The Great Dark Spot was captured by NASA's Voyager 2 space probe in Neptune's southern hemisphere. The dark, elliptically shaped spot (with initial dimensions of 13,000 × 6,600 km, or 8,100 × 4,100 mi), was about the same size as Earth , and was similar in general appearance to Jupiter 's Great Red Spot . One major difference compared to Jupiter's Great Red Spot is that Neptune's Great Dark Spot has shown

128-454: A a 2 − x 2 = ± ( a 2 − x 2 ) ( 1 − e 2 ) . {\displaystyle y=\pm {\frac {b}{a}}{\sqrt {a^{2}-x^{2}}}=\pm {\sqrt {\left(a^{2}-x^{2}\right)\left(1-e^{2}\right)}}.} The width and height parameters a , b {\displaystyle a,\;b} are called

192-424: A {\displaystyle a} to the center. The distance c {\displaystyle c} of the foci to the center is called the focal distance or linear eccentricity. The quotient e = c a {\displaystyle e={\tfrac {c}{a}}} is the eccentricity . The case F 1 = F 2 {\displaystyle F_{1}=F_{2}} yields

256-528: A 2 x 1 b 2 ) {\displaystyle {\begin{pmatrix}-y_{1}a^{2}&x_{1}b^{2}\end{pmatrix}}} is a tangent vector at point ( x 1 , y 1 ) {\displaystyle (x_{1},\,y_{1})} , which proves the vector equation. If ( x 1 , y 1 ) {\displaystyle (x_{1},y_{1})} and ( u , v ) {\displaystyle (u,v)} are two points of

320-621: A 2 + y 1 v b 2 ) + s 2 ( u 2 a 2 + v 2 b 2 ) = 0   . {\displaystyle {\frac {\left(x_{1}+su\right)^{2}}{a^{2}}}+{\frac {\left(y_{1}+sv\right)^{2}}{b^{2}}}=1\ \quad \Longrightarrow \quad 2s\left({\frac {x_{1}u}{a^{2}}}+{\frac {y_{1}v}{b^{2}}}\right)+s^{2}\left({\frac {u^{2}}{a^{2}}}+{\frac {v^{2}}{b^{2}}}\right)=0\ .} There are then cases: Using (1) one finds that ( − y 1

384-466: A 2 b 2 . {\displaystyle {\begin{aligned}A&=a^{2}\sin ^{2}\theta +b^{2}\cos ^{2}\theta &B&=2\left(b^{2}-a^{2}\right)\sin \theta \cos \theta \\[1ex]C&=a^{2}\cos ^{2}\theta +b^{2}\sin ^{2}\theta &D&=-2Ax_{\circ }-By_{\circ }\\[1ex]E&=-Bx_{\circ }-2Cy_{\circ }&F&=Ax_{\circ }^{2}+Bx_{\circ }y_{\circ }+Cy_{\circ }^{2}-a^{2}b^{2}.\end{aligned}}} These expressions can be derived from

448-542: A 2 cos 2 ⁡ θ + b 2 sin 2 ⁡ θ D = − 2 A x ∘ − B y ∘ E = − B x ∘ − 2 C y ∘ F = A x ∘ 2 + B x ∘ y ∘ + C y ∘ 2 −

512-462: A 2 − b 2 {\displaystyle c={\sqrt {a^{2}-b^{2}}}} . The eccentricity can be expressed as: e = c a = 1 − ( b a ) 2 , {\displaystyle e={\frac {c}{a}}={\sqrt {1-\left({\frac {b}{a}}\right)^{2}}},} assuming a > b . {\displaystyle a>b.} An ellipse with equal axes (

576-648: A ≥ b {\displaystyle a\geq b} , the foci are ( ± c , 0 ) {\displaystyle (\pm c,0)} for c = a 2 − b 2 {\textstyle c={\sqrt {a^{2}-b^{2}}}} . The standard parametric equation is: ( x , y ) = ( a cos ⁡ ( t ) , b sin ⁡ ( t ) ) for 0 ≤ t ≤ 2 π . {\displaystyle (x,y)=(a\cos(t),b\sin(t))\quad {\text{for}}\quad 0\leq t\leq 2\pi .} Ellipses are

640-425: A ≥ b > 0   . {\displaystyle a\geq b>0\ .} In principle, the canonical ellipse equation x 2 a 2 + y 2 b 2 = 1 {\displaystyle {\tfrac {x^{2}}{a^{2}}}+{\tfrac {y^{2}}{b^{2}}}=1} may have a < b {\displaystyle a<b} (and hence

704-458: A + e x {\displaystyle a+ex} and a − e x {\displaystyle a-ex} . It follows from the equation that the ellipse is symmetric with respect to the coordinate axes and hence with respect to the origin. Throughout this article, the semi-major and semi-minor axes are denoted a {\displaystyle a} and b {\displaystyle b} , respectively, i.e.

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768-458: A , 0 ) . {\textstyle [1:0]\mapsto (-a,\,0).} Rational representations of conic sections are commonly used in computer-aided design (see Bezier curve ). Trident (spacecraft) Trident is a space mission concept to the outer planets proposed in 2019 to NASA 's Discovery Program . The concept includes flybys of Jupiter and Neptune with a focus on Neptune's largest moon Triton . In 2020, Trident

832-596: A = b {\displaystyle a=b} ) has zero eccentricity, and is a circle. The length of the chord through one focus, perpendicular to the major axis, is called the latus rectum . One half of it is the semi-latus rectum ℓ {\displaystyle \ell } . A calculation shows: ℓ = b 2 a = a ( 1 − e 2 ) . {\displaystyle \ell ={\frac {b^{2}}{a}}=a\left(1-e^{2}\right).} The semi-latus rectum ℓ {\displaystyle \ell }

896-486: A circle and is included as a special type of ellipse. The equation | P F 2 | + | P F 1 | = 2 a {\displaystyle \left|PF_{2}\right|+\left|PF_{1}\right|=2a} can be viewed in a different way (see figure): c 2 {\displaystyle c_{2}} is called the circular directrix (related to focus F 2 {\displaystyle F_{2}} ) of

960-508: A few years. Furthermore, the disappearance of dark spots including the Southern Dark Spot can be linked to companion clouds reaching the center of the storm and blocking the view of the blue wavelengths that are used to track the vortex, prior to their disappearance. Two mission ideas have been proposed to NASA to visit Neptune in the coming years. Trident was proposed in 2021 as a discovery mission to visit Neptune and its moon Triton in

1024-512: A line outside the ellipse called the directrix : for all points on the ellipse, the ratio between the distance to the focus and the distance to the directrix is a constant. This constant ratio is the above-mentioned eccentricity: e = c a = 1 − b 2 a 2 . {\displaystyle e={\frac {c}{a}}={\sqrt {1-{\frac {b^{2}}{a^{2}}}}}.} Ellipses are common in physics , astronomy and engineering . For example,

1088-533: A narrow observational window that enables assessment of changes in Triton's plume activity and surface characteristics since the previous encounter of Neptune-Triton by Voyager 2 in 1989. With the advances of high-resolution imaging and a unique orbital configuration of Triton in 2038, Trident would be able to obtain a near-complete map of Neptune's moon during its sole flyby . Trident would pass through Triton's thin atmosphere , within 500 km (310 mi) of

1152-535: A period of a few hours, the clouds in the Great Dark Spot were still present after 36 hours, or two rotations of the planet. Neptune's dark spots are thought to occur in the troposphere at lower altitudes than the brighter upper cloud deck features. As they are stable features that can persist for several months, they are thought to be vortex structures. When the spot was to be photographed again in November 1994 by

1216-522: A point on an ellipse and x → = ( x 1 y 1 ) + s ( u v ) {\textstyle {\vec {x}}={\begin{pmatrix}x_{1}\\y_{1}\end{pmatrix}}+s{\begin{pmatrix}u\\v\end{pmatrix}}} be the equation of any line g {\displaystyle g} containing ( x 1 , y 1 ) {\displaystyle (x_{1},\,y_{1})} . Inserting

1280-538: A set or locus of points in the Euclidean plane: The midpoint C {\displaystyle C} of the line segment joining the foci is called the center of the ellipse. The line through the foci is called the major axis , and the line perpendicular to it through the center is the minor axis . The major axis intersects the ellipse at two vertices V 1 , V 2 {\displaystyle V_{1},V_{2}} , which have distance

1344-405: Is able to view images at blue wavelength, which is the only way features are visible. In 1994, a Northern Dark Spot (NGDS-1994) formed in the northern hemisphere and disappeared between 1998 and 2000. The storm for its duration showed to be stable in latitude. In 1996, a separate Northern Dark Spot (NGDS-1996) formed and was observed until its disappearance, which occurred prior to 1998. Similarly to

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1408-447: Is equal to the radius of curvature at the vertices (see section curvature ). An arbitrary line g {\displaystyle g} intersects an ellipse at 0, 1, or 2 points, respectively called an exterior line , tangent and secant . Through any point of an ellipse there is a unique tangent. The tangent at a point ( x 1 , y 1 ) {\displaystyle (x_{1},\,y_{1})} of

1472-642: Is geologically active, its surface is young and has relatively few impact craters. It has a very thin atmosphere . Voyager 2 was only able to observe approximately 40% of Triton's surface. The Trident concept was proposed in March 2019 to NASA's Discovery Program . The mission concept is supported by NASA's Ocean Worlds Exploration Program and it is intended to help answer some of the questions generated by Voyager 2's flyby in 1989. Trident takes advantage of an efficient gravity assist alignment of Jupiter and Neptune (that occurs once every 13 years) to capitalize on

1536-469: Is measured by its eccentricity e {\displaystyle e} , a number ranging from e = 0 {\displaystyle e=0} (the limiting case of a circle) to e = 1 {\displaystyle e=1} (the limiting case of infinite elongation, no longer an ellipse but a parabola ). An ellipse has a simple algebraic solution for its area, but for its perimeter (also known as circumference ), integration

1600-466: Is much smaller in comparison than the one discovered by NASA's Voyager 2, but was found to be larger in diameter than the Atlantic Ocean at approximately 4,600 miles across. In August 2020, the new Great Dark Spot suddenly stopped its southward motion and reversed direction, contrary to projections that the storm would continue to the equator, where it would have met its likely demise. It is believed that

1664-448: Is required to obtain an exact solution. Analytically , the equation of a standard ellipse centered at the origin with width 2 a {\displaystyle 2a} and height 2 b {\displaystyle 2b} is: x 2 a 2 + y 2 b 2 = 1. {\displaystyle {\frac {x^{2}}{a^{2}}}+{\frac {y^{2}}{b^{2}}}=1.} Assuming

1728-625: Is the 2-argument arctangent function. Using trigonometric functions , a parametric representation of the standard ellipse x 2 a 2 + y 2 b 2 = 1 {\displaystyle {\tfrac {x^{2}}{a^{2}}}+{\tfrac {y^{2}}{b^{2}}}=1} is: ( x , y ) = ( a cos ⁡ t , b sin ⁡ t ) ,   0 ≤ t < 2 π . {\displaystyle (x,\,y)=(a\cos t,\,b\sin t),\ 0\leq t<2\pi \,.} The parameter t (called

1792-510: Is unknown whether this spot is still present on the planet, as observations using the Hubble telescope are limited. More recently, in 2018, a newer main dark spot and a smaller dark spot were identified and studied. This discovery of the dark spot in Neptune's northern hemisphere was monumental in that it was the first dark spot that the Hubble Telescope was able to document from birth. The storm

1856-805: The eccentric anomaly in astronomy) is not the angle of ( x ( t ) , y ( t ) ) {\displaystyle (x(t),y(t))} with the x -axis, but has a geometric meaning due to Philippe de La Hire (see § Drawing ellipses below). With the substitution u = tan ⁡ ( t 2 ) {\textstyle u=\tan \left({\frac {t}{2}}\right)} and trigonometric formulae one obtains cos ⁡ t = 1 − u 2 1 + u 2   , sin ⁡ t = 2 u 1 + u 2 {\displaystyle \cos t={\frac {1-u^{2}}{1+u^{2}}}\ ,\quad \sin t={\frac {2u}{1+u^{2}}}} and

1920-501: The Hubble Space Telescope , it had disappeared completely, leaving astronomers to believe that it had either been covered up or had vanished. The persistence of companion clouds shows that some former dark spots may continue to exist as cyclones even though they are no longer visible as a dark feature. Dark spots may dissipate when they migrate too close to the equator, or possibly through some other unknown mechanisms. Following

1984-405: The closed type of conic section : a plane curve tracing the intersection of a cone with a plane (see figure). Ellipses have many similarities with the other two forms of conic sections, parabolas and hyperbolas , both of which are open and unbounded . An angled cross section of a right circular cylinder is also an ellipse. An ellipse may also be defined in terms of one focal point and

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2048-786: The degenerate cases from the non-degenerate case, let ∆ be the determinant Δ = | A 1 2 B 1 2 D 1 2 B C 1 2 E 1 2 D 1 2 E F | = A C F + 1 4 B D E − 1 4 ( A E 2 + C D 2 + F B 2 ) . {\displaystyle \Delta ={\begin{vmatrix}A&{\frac {1}{2}}B&{\frac {1}{2}}D\\{\frac {1}{2}}B&C&{\frac {1}{2}}E\\{\frac {1}{2}}D&{\frac {1}{2}}E&F\end{vmatrix}}=ACF+{\tfrac {1}{4}}BDE-{\tfrac {1}{4}}(AE^{2}+CD^{2}+FB^{2}).} Then

2112-567: The orbit of each planet in the Solar System is approximately an ellipse with the Sun at one focus point (more precisely, the focus is the barycenter of the Sun–planet pair). The same is true for moons orbiting planets and all other systems of two astronomical bodies. The shapes of planets and stars are often well described by ellipsoids . A circle viewed from a side angle looks like an ellipse: that is,

2176-491: The radicals by suitable squarings and using b 2 = a 2 − c 2 {\displaystyle b^{2}=a^{2}-c^{2}} (see diagram) produces the standard equation of the ellipse: x 2 a 2 + y 2 b 2 = 1 , {\displaystyle {\frac {x^{2}}{a^{2}}}+{\frac {y^{2}}{b^{2}}}=1,} or, solved for y : y = ± b

2240-557: The rational parametric equation of an ellipse { x ( u ) = a 1 − u 2 1 + u 2 y ( u ) = b 2 u 1 + u 2 − ∞ < u < ∞ {\displaystyle {\begin{cases}x(u)=a\,{\dfrac {1-u^{2}}{1+u^{2}}}\\[10mu]y(u)=b\,{\dfrac {2u}{1+u^{2}}}\\[10mu]-\infty <u<\infty \end{cases}}} which covers any point of

2304-423: The semi-major and semi-minor axes . The top and bottom points V 3 = ( 0 , b ) , V 4 = ( 0 , − b ) {\displaystyle V_{3}=(0,\,b),\;V_{4}=(0,\,-b)} are the co-vertices . The distances from a point ( x , y ) {\displaystyle (x,\,y)} on the ellipse to the left and right foci are

2368-400: The tropopause layer similar to high-altitude cirrus clouds found on Earth . Unlike the clouds on Earth, however, which are composed of crystals of water ice , Neptune's cirrus clouds are made up of crystals of frozen methane . These high altitude clouds are located somewhere between 50–100 km (30–60 miles) above the main cloud deck. While cirrus clouds usually form and then disperse within

2432-648: The x - and y -axes. In analytic geometry , the ellipse is defined as a quadric : the set of points ( x , y ) {\displaystyle (x,\,y)} of the Cartesian plane that, in non-degenerate cases, satisfy the implicit equation A x 2 + B x y + C y 2 + D x + E y + F = 0 {\displaystyle Ax^{2}+Bxy+Cy^{2}+Dx+Ey+F=0} provided B 2 − 4 A C < 0. {\displaystyle B^{2}-4AC<0.} To distinguish

2496-449: The Great Dark Spot, several other dark spots have been observed. In 1989, when the Voyager 2 observed the Great Dark Spot (GDS), a second dark spot, Dark Spot 2 (DS2) was found. Dark Spot 2 fully dissipated prior to the year 1994. Beginning in 1994, the Hubble became the only operating facility to detect the presence and observe dark spots on Neptune and is still used to the present day. Hubble

2560-623: The ability to shift north-south over time, while the Great Red Spot is held in the same latitudinal region by global east-west wind currents. Around the edges of the storm, winds were measured at up to 2,100 kilometers per hour (1,300 mph), the fastest recorded in the Solar System. The Great Dark Spot is thought to be a hole in the methane cloud deck of Neptune . The spot was observed at different times with different sizes and shapes. The Great Dark Spot generated large white clouds at or just below

2624-1060: The canonical equation X 2 a 2 + Y 2 b 2 = 1 {\displaystyle {\frac {X^{2}}{a^{2}}}+{\frac {Y^{2}}{b^{2}}}=1} by a Euclidean transformation of the coordinates ( X , Y ) {\displaystyle (X,\,Y)} : X = ( x − x ∘ ) cos ⁡ θ + ( y − y ∘ ) sin ⁡ θ , Y = − ( x − x ∘ ) sin ⁡ θ + ( y − y ∘ ) cos ⁡ θ . {\displaystyle {\begin{aligned}X&=\left(x-x_{\circ }\right)\cos \theta +\left(y-y_{\circ }\right)\sin \theta ,\\Y&=-\left(x-x_{\circ }\right)\sin \theta +\left(y-y_{\circ }\right)\cos \theta .\end{aligned}}} Conversely,

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2688-1385: The canonical form parameters can be obtained from the general-form coefficients by the equations: a , b = − 2 ( A E 2 + C D 2 − B D E + ( B 2 − 4 A C ) F ) ( ( A + C ) ± ( A − C ) 2 + B 2 ) B 2 − 4 A C , x ∘ = 2 C D − B E B 2 − 4 A C , y ∘ = 2 A E − B D B 2 − 4 A C , θ = 1 2 atan2 ⁡ ( − B , C − A ) , {\displaystyle {\begin{aligned}a,b&={\frac {-{\sqrt {2{\big (}AE^{2}+CD^{2}-BDE+(B^{2}-4AC)F{\big )}{\big (}(A+C)\pm {\sqrt {(A-C)^{2}+B^{2}}}{\big )}}}}{B^{2}-4AC}},\\x_{\circ }&={\frac {2CD-BE}{B^{2}-4AC}},\\[5mu]y_{\circ }&={\frac {2AE-BD}{B^{2}-4AC}},\\[5mu]\theta &={\tfrac {1}{2}}\operatorname {atan2} (-B,\,C-A),\end{aligned}}} where atan2

2752-456: The ellipse x 2 a 2 + y 2 b 2 = 1 {\displaystyle {\tfrac {x^{2}}{a^{2}}}+{\tfrac {y^{2}}{b^{2}}}=1} except the left vertex ( − a , 0 ) {\displaystyle (-a,\,0)} . For u ∈ [ 0 , 1 ] , {\displaystyle u\in [0,\,1],} this formula represents

2816-479: The ellipse x 2 a 2 + y 2 b 2 = 1 {\displaystyle {\tfrac {x^{2}}{a^{2}}}+{\tfrac {y^{2}}{b^{2}}}=1} has the coordinate equation: x 1 a 2 x + y 1 b 2 y = 1. {\displaystyle {\frac {x_{1}}{a^{2}}}x+{\frac {y_{1}}{b^{2}}}y=1.} A vector parametric equation of

2880-620: The ellipse is a non-degenerate real ellipse if and only if C∆ < 0. If C∆ > 0, we have an imaginary ellipse, and if ∆ = 0, we have a point ellipse. The general equation's coefficients can be obtained from known semi-major axis a {\displaystyle a} , semi-minor axis b {\displaystyle b} , center coordinates ( x ∘ , y ∘ ) {\displaystyle \left(x_{\circ },\,y_{\circ }\right)} , and rotation angle θ {\displaystyle \theta } (the angle from

2944-448: The ellipse is the image of a circle under parallel or perspective projection . The ellipse is also the simplest Lissajous figure formed when the horizontal and vertical motions are sinusoids with the same frequency: a similar effect leads to elliptical polarization of light in optics . The name, ἔλλειψις ( élleipsis , "omission"), was given by Apollonius of Perga in his Conics . An ellipse can be defined geometrically as

3008-427: The ellipse such that x 1 u a 2 + y 1 v b 2 = 0 {\textstyle {\frac {x_{1}u}{a^{2}}}+{\tfrac {y_{1}v}{b^{2}}}=0} , then the points lie on two conjugate diameters (see below ). (If a = b {\displaystyle a=b} , the ellipse is a circle and "conjugate" means "orthogonal".) If

3072-418: The ellipse would be taller than it is wide). This form can be converted to the standard form by transposing the variable names x {\displaystyle x} and y {\displaystyle y} and the parameter names a {\displaystyle a} and b . {\displaystyle b.} This is the distance from the center to a focus: c =

3136-543: The ellipse, the x -axis is the major axis, and: For an arbitrary point ( x , y ) {\displaystyle (x,y)} the distance to the focus ( c , 0 ) {\displaystyle (c,0)} is ( x − c ) 2 + y 2 {\textstyle {\sqrt {(x-c)^{2}+y^{2}}}} and to the other focus ( x + c ) 2 + y 2 {\textstyle {\sqrt {(x+c)^{2}+y^{2}}}} . Hence

3200-464: The ellipse. This property should not be confused with the definition of an ellipse using a directrix line below. Using Dandelin spheres , one can prove that any section of a cone with a plane is an ellipse, assuming the plane does not contain the apex and has slope less than that of the lines on the cone. The standard form of an ellipse in Cartesian coordinates assumes that the origin is the center of

3264-558: The line's equation into the ellipse equation and respecting x 1 2 a 2 + y 1 2 b 2 = 1 {\textstyle {\frac {x_{1}^{2}}{a^{2}}}+{\frac {y_{1}^{2}}{b^{2}}}=1} yields: ( x 1 + s u ) 2 a 2 + ( y 1 + s v ) 2 b 2 = 1   ⟹ 2 s ( x 1 u

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3328-737: The parameter [ u : v ] {\displaystyle [u:v]} is considered to be a point on the real projective line P ( R ) {\textstyle \mathbf {P} (\mathbf {R} )} , then the corresponding rational parametrization is [ u : v ] ↦ ( a v 2 − u 2 v 2 + u 2 , b 2 u v v 2 + u 2 ) . {\displaystyle [u:v]\mapsto \left(a{\frac {v^{2}-u^{2}}{v^{2}+u^{2}}},b{\frac {2uv}{v^{2}+u^{2}}}\right).} Then [ 1 : 0 ] ↦ ( −

3392-399: The point ( x , y ) {\displaystyle (x,\,y)} is on the ellipse whenever: ( x − c ) 2 + y 2 + ( x + c ) 2 + y 2 = 2 a   . {\displaystyle {\sqrt {(x-c)^{2}+y^{2}}}+{\sqrt {(x+c)^{2}+y^{2}}}=2a\ .} Removing

3456-429: The positive horizontal axis to the ellipse's major axis) using the formulae: A = a 2 sin 2 ⁡ θ + b 2 cos 2 ⁡ θ B = 2 ( b 2 − a 2 ) sin ⁡ θ cos ⁡ θ C =

3520-622: The prior dark spot, this one exhibited little to no meridional drift. In 2015, a Southern Dark Spot (SDS) was discovered by the Hubble Outer Planet Atmosphere Legacy (OPAL) program. The Southern Dark Spot exhibited a poleward drift before its disappearance in 2017. In 2016, an almost identical spot as the Great Dark Spot (GDS) emerged in Neptune's northern hemisphere. This new spot, called the Northern Great Dark Spot (NGDS), has remained visible for several years. It

3584-510: The prior storm's reversal of motion may have been related to the birth of the smaller storm. While the formation of the storms is still under investigation, it had been concluded from observations regarding the Southern Dark Spot (SDS-2015) and Northern Great Dark Spot (NGDS-2018) that their origins are preceded by an increase in cloud activity in the given region 2–3 years prior to becoming visible. The storms from 1989–2018 have exhibited different movement patterns and are generally only visible for

3648-432: The right upper quarter of the ellipse moving counter-clockwise with increasing u . {\displaystyle u.} The left vertex is the limit lim u → ± ∞ ( x ( u ) , y ( u ) ) = ( − a , 0 ) . {\textstyle \lim _{u\to \pm \infty }(x(u),\,y(u))=(-a,\,0)\;.} Alternately, if

3712-618: The standard ellipse is shifted to have center ( x ∘ , y ∘ ) {\displaystyle \left(x_{\circ },\,y_{\circ }\right)} , its equation is ( x − x ∘ ) 2 a 2 + ( y − y ∘ ) 2 b 2 = 1   . {\displaystyle {\frac {\left(x-x_{\circ }\right)^{2}}{a^{2}}}+{\frac {\left(y-y_{\circ }\right)^{2}}{b^{2}}}=1\ .} The axes are still parallel to

3776-553: The storms remain stable in the northern hemisphere due to the effect of Coriolis forces. However, as the storms moved towards the equator, the Coriolis forces weakened, causing the storms to dissipate. Around the same time, a smaller "Dark Spot Jr." was found near the larger storm, before disappearing later on. Dark Spot Jr. as the name suggests was smaller than the prior dark spot, only measuring 3,900 miles in diameter. The coincidental appearance of this storm led astronomers to believe that

3840-682: The surface, sampling its ionosphere with a plasma spectrometer and perform magnetic induction measurements to assess the potential existence of an internal ocean. The principal investigator is Louise Prockter , director of the Lunar and Planetary Institute in Houston, Texas. The launch vehicle proposed for Trident is the Atlas V 401, if it is not replaced with the Vulcan . The proposed launch date in October 2025 (with

3904-606: The tangent is: x → = ( x 1 y 1 ) + s ( − y 1 a 2 x 1 b 2 ) , s ∈ R . {\displaystyle {\vec {x}}={\begin{pmatrix}x_{1}\\y_{1}\end{pmatrix}}+s\left({\begin{array}{r}-y_{1}a^{2}\\x_{1}b^{2}\end{array}}\right),\quad s\in \mathbb {R} .} Proof: Let ( x 1 , y 1 ) {\displaystyle (x_{1},\,y_{1})} be

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3968-436: The year, but two missions to Venus ( DAVINCI+ and VERITAS ) were selected over it. Neptune Odyssey is a flagship orbiter mission concept with similar goals as Trident and is targeted for a launch date of 2033. These missions have a high focus on learning more about Neptune's largest moon Triton, but also aim to gain more information about the atmosphere of Neptune. An analysis of a nuclear-electric propulsion mission to Neptune

4032-478: Was published by the China National Space Administration . Ellipse In mathematics , an ellipse is a plane curve surrounding two focal points , such that for all points on the curve, the sum of the two distances to the focal points is a constant. It generalizes a circle , which is the special type of ellipse in which the two focal points are the same. The elongation of an ellipse

4096-568: Was selected along with three other Discovery proposals for further study, with two expected to be selected to fly as Discovery 15 and 16 . On 2 June 2021, NASA selected the Venus missions DAVINCI+ and VERITAS over Trident and the Io Volcano Observer . Triton is the largest moon of Neptune . In 1989, Voyager 2 flew past the moon at a distance of 40,000 km (25,000 mi), and discovered several cryovolcanoes on its surface. Triton

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