According To Kepler’S Second Law, Pluto Will Be Traveling Fastest Around The Sun When At?
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According to Kepler’s second law, Pluto will be traveling fastest around the Sun when at perihelion.
How does Pluto follow Kepler’s second law?
Does Pluto follow Kepler’s Second Law? – A: Yes! All objects in orbit follow Kepler’s Second Law, and all of Kepler’s other laws too. L ike any other object in our solar system, Pluto moves faster when its closer to the sun and slower when its farther away. Posted on April 14, 2015 at 7:47 pm Categories: Gravity & Air Check out other Questions and Answers
What does Kepler’s second law say about a planet’s speed as it moves around the Sun?
Kepler’s Second Law characterizes the the velocity of a planet along its elliptical path. The planet’s speed varies – but it does so in a completely regular way, a way that can be expressed in a simple mathematical formula.
Kepler’s Second Law says says that a line running from the sun to the planet sweeps out equal areas of the ellipse in equal times. This means that the planet speeds up as it approaches the sun and slows down as it departs from it. Let’s use the diagram above to think through how this is so. Suppose it takes a certain time T for the planet to travel from Position 1 to Position 2. The line from the sun to the position of the planet during this journey covers the area bordered by SunP1/P1P2/P2Sun. This is the same area as found in the region bordered by SunP3/P3P4/P4Sun. So the time it takes for the planet to travel from Position 3 to Position 4 will be the same time, T. The path along the ellipse from P1 to P2 (while the planet is closest to the sun) is longer than the path along the ellipse from P3 to P4 (when the planet is farthest from the sun). In other words, the planet is travelling fastest while it is close to the sun and slowest when it is furthest away from the sun. For the areas to be the same, P3P4 has to be shorter than P1P2, because SP3 and SP4 are longer; conversely, P1P2 has to be longer (if the same area is to be swept out), in order to compensate for the shortness of SP1 and SP2. But if a body covers a shorter distance in a given stretch of time than some other body covers in the same stretch of time, it’s going slower. The planet will be traveling fastest at the point on the ellipse midway between P1 and P2, after which it begins to decelerate. And it will be traveling slowest at the point on the orbit midway between P3 and P4, after which it begins to pick up speed. 
Kepler’s law describes the motion not only of planets around the sun but of moons around planets. If your browser is equipped with Shockwave, check out Raman’s orbit simulator to look at a moon traveling in an ellipse around a planet traveling in an ellipse around the sun! (And then think of how much paper and ink Kepler must have gone through in the eleven years it took him to figure out that the way Mars seems to us to travel across the background of the fixed stars how Mars would be produced for an observer on a planet traveling in an elliptical orbit arount the sun by a planet traveling on a different elliptical orbit around the sun (more distant from the former, and out of phase with it) – provided we imagine the right average distances from the sun for the respective orbits, and pick the right point on each orbit corresponding for an initial observation of the more distant planet from the one closer to the sun.
Whew!) The designer of this clever orbit simulator is ahead of Kepler, because he’s working from Newton’s laws, which are a later part of our story. You can nevertheless have some informative fun here by seeing what happens when you tinker with the various variables. For simplicity’s sake, set the velocity of the sun itself at zero.
You might also want to click on the grid. Now experiment with different values for the mass of the sun and for the gravitational constant. If you set these high enough, you’ll get some interesting results. Sometimes the moon gets so accelerated as it passes the sun that it escapes the planet’s gravitational field and travels on out into space.
(Maximize the mass of the star and set the value for the gravitational constant as high as you can on this program, and you’ll get this.) Sometimes it comes so close to the sun that the sun captures it away from its planet, and turns it into another planet, whipping around on a different ellipse. (If you set the mass of the star at 90000 and pretend that the gravitational constant is about 1.64 times what it is in our world, you’ll witness this happening after about 3 planetary revolutions.) Sometimes it ends up plunging into the sun.
Fiddling with the variables gives you a more intuitive feel for what the unchanging formula in which the variables are imbedded means.
At which position is the planet traveling the fastest?
Kepler’s Laws
Johannes Kepler was born poor and sickly in what is now Germany. His father left home when Johannes was five and never returned. It is believed he was killed in a war. While Johannes was pursuing higher education his mother was tried as a witch. Johannes hired a legal team which was able to obtain her release, mostly on legal technicalities. Although he had an eventful life, Kepler is most remembered for “cracking the code” that describes the orbits of the planets. Prior to Kepler’s discoveries, the predominate theory of the solar system was an Earthcentered geometry as described by Ptolemy. A Suncentered theory had been proposed by Copernicus, but its predictions were plagued with inaccuracies. Working in Prague at the Royal Observatory of Denmark, Kepler succeeded by using the notes of his predecessor, Tycho Brahe, which recorded the precise position of Mars relative to the Sun and Earth. Kepler developed his laws empirically from observation, as opposed to deriving them from some fundamental theoretical principles. Any ellipse has two geometrical points called the foci (focus for singular). There is no physical significance of the focus without the Sun but it does have mathematical significance. The total distance from a planet to each of the foci added together is always the same regardless of where the planet is in its orbit. In any given amount of time, 30 days for example, the planet sweeps out the same amount of area regardless of which 30 day period you choose. Therefore the planet moves faster when it is nearer the Sun and slower when it is farther from the Sun. A planet moves with constantly changing speed as it moves about its orbit. This law is sometimes referred to as the law of harmonies. It compares the orbital time period and radius of an orbit of any planet, to those of the other planets. The discovery Kepler made is that the ratio of the squares of the revolutionary time periods to the cubes of the average distances from the Sun, is the same for every planet.

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Kepler’s Laws
At what point in revolution do planets move faster?
When a planet is closer to the Sun the Sun’s gravitational pull is stronger, so the planet moves faster.
What is Kepler’s 2nd law formula?
13.5 Kepler’s Laws of Planetary Motion – University Physics Volume 1 By the end of this section, you will be able to:
Describe the conic sections and how they relate to orbital motion Describe how orbital velocity is related to conservation of angular momentum Determine the period of an elliptical orbit from its major axis
Using the precise data collected by Tycho Brahe, Johannes Kepler carefully analyzed the positions in the sky of all the known planets and the Moon, plotting their positions at regular intervals of time. From this analysis, he formulated three laws, which we address in this section.
 The prevailing view during the time of Kepler was that all planetary orbits were circular.
 The data for Mars presented the greatest challenge to this view and that eventually encouraged Kepler to give up the popular idea.
 Epler’s first law states that every planet moves along an ellipse, with the Sun located at a focus of the ellipse.
An ellipse is defined as the set of all points such that the sum of the distance from each point to two foci is a constant. shows an ellipse and describes a simple way to create it. Figure 13.16 (a) An ellipse is a curve in which the sum of the distances from a point on the curve to two foci ( f 1 and f 2 ) ( f 1 and f 2 ) is a constant. From this definition, you can see that an ellipse can be created in the following way. Place a pin at each focus, then place a loop of string around a pencil and the pins.
Keeping the string taught, move the pencil around in a complete circuit. If the two foci occupy the same place, the result is a circle—a special case of an ellipse. (b) For an elliptical orbit, if m ≪ M m ≪ M, then m follows an elliptical path with M at one focus. More exactly, both m and M move in their own ellipse about the common center of mass.
For elliptical orbits, the point of closest approach of a planet to the Sun is called the perihelion, It is labeled point A in, The farthest point is the aphelion and is labeled point B in the figure. For the Moon’s orbit about Earth, those points are called the perigee and apogee, respectively.
 An ellipse has several mathematical forms, but all are a specific case of the more general equation for conic sections.
 There are four different conic sections, all given by the equation α r = 1 + e cos θ,
 Α r = 1 + e cos θ,
 The variables r and θ θ are shown in in the case of an ellipse.
 The constants α α and e are determined by the total energy and angular momentum of the satellite at a given point.
The constant e is called the eccentricity. The values of α α and e determine which of the four conic sections represents the path of the satellite. Figure 13.17 As before, the distance between the planet and the Sun is r, and the angle measured from the x axis, which is along the major axis of the ellipse, is θ θ, One of the real triumphs of Newton’s law of universal gravitation, with the force proportional to the inverse of the distance squared, is that when it is combined with his second law, the solution for the path of any satellite is a conic section. Figure 13.18 All motion caused by an inverse square force is one of the four conic sections and is determined by the energy and direction of the moving body. If the total energy is negative, then 0 ≤ e < 1 0 ≤ e < 1, and represents a bound or closed orbit of either an ellipse or a circle, where e = 0 e = 0, For ellipses, the eccentricity is related to how oblong the ellipse appears. A circle has zero eccentricity, whereas a very long, drawnout ellipse has an eccentricity near one. If the total energy is exactly zero, then e = 1 e = 1 and the path is a parabola. Recall that a satellite with zero total energy has exactly the escape velocity. (The parabola is formed only by slicing the cone parallel to the tangent line along the surface.) Finally, if the total energy is positive, then e > 1 e > 1 and the path is a hyperbola. These last two paths represent unbounded orbits, where m passes by M once and only once. This situation has been observed for several comets that approach the Sun and then travel away, never to return. We have confined ourselves to the case in which the smaller mass (planet) orbits a much larger, and hence stationary, mass (Sun), but also applies to any two gravitationally interacting masses. Each mass traces out the exact sameshaped conic section as the other. That shape is determined by the total energy and angular momentum of the system, with the center of mass of the system located at the focus. The ratio of the dimensions of the two paths is the inverse of the ratio of their masses. You can see an animation of two interacting objects at the My Solar System page at, Choose the Sun and Planet preset option. You can also view the more complicated multiple body problems as well. You may find the actual path of the Moon quite surprising, yet is obeying Newton’s simple laws of motion. People have imagined traveling to the other planets of our solar system since they were discovered. But how can we best do this? The most efficient method was discovered in 1925 by Walter Hohmann, inspired by a popular science fiction novel of that time. The method is now called a Hohmann transfer, For the case of traveling between two circular orbits, the transfer is along a “transfer” ellipse that perfectly intercepts those orbits at the aphelion and perihelion of the ellipse. shows the case for a trip from Earth’s orbit to that of Mars. As before, the Sun is at the focus of the ellipse. For any ellipse, the semimajor axis is defined as onehalf the sum of the perihelion and the aphelion. In, the semimajor axis is the distance from the origin to either side of the ellipse along the x axis, or just onehalf the longest axis (called the major axis). Hence, to travel from one circular orbit of radius r 1 r 1 to another circular orbit of radius r 2 r 2, the aphelion of the transfer ellipse will be equal to the value of the larger orbit, while the perihelion will be the smaller orbit. The semimajor axis, denoted a, is therefore given by a = 1 2 ( r 1 + r 2 ) a = 1 2 ( r 1 + r 2 ), Figure 13.19 The transfer ellipse has its perihelion at Earth’s orbit and aphelion at Mars’ orbit. Let’s take the case of traveling from Earth to Mars. For the moment, we ignore the planets and assume we are alone in Earth’s orbit and wish to move to Mars’ orbit.
 From, the expression for total energy, we can see that the total energy for a spacecraft in the larger orbit (Mars) is greater (less negative) than that for the smaller orbit (Earth).
 To move onto the transfer ellipse from Earth’s orbit, we will need to increase our kinetic energy, that is, we need a velocity boost.
The most efficient method is a very quick acceleration along the circular orbital path, which is also along the path of the ellipse at that point. (In fact, the acceleration should be instantaneous, such that the circular and elliptical orbits are congruent during the acceleration.
In practice, the finite acceleration is short enough that the difference is not a significant consideration.) Once you have arrived at Mars orbit, you will need another velocity boost to move into that orbit, or you will stay on the elliptical orbit and simply fall back to perihelion where you started.
For the return trip, you simply reverse the process with a retroboost at each transfer point. To make the move onto the transfer ellipse and then off again, we need to know each circular orbit velocity and the transfer orbit velocities at perihelion and aphelion.
The velocity boost required is simply the difference between the circular orbit velocity and the elliptical orbit velocity at each point. We can find the circular orbital velocities from, To determine the velocities for the ellipse, we state without proof (as it is beyond the scope of this course) that total energy for an elliptical orbit is where M S M S is the mass of the Sun and a is the semimajor axis.
Remarkably, this is the same as for circular orbits, but with the value of the semimajor axis replacing the orbital radius. Since we know the potential energy from, we can find the kinetic energy and hence the velocity needed for each point on the ellipse.
We leave it as a challenge problem to find those transfer velocities for an EarthtoMars trip. We end this discussion by pointing out a few important details. First, we have not accounted for the gravitational potential energy due to Earth and Mars, or the mechanics of landing on Mars. In practice, that must be part of the calculations.
Second, timing is everything. You do not want to arrive at the orbit of Mars to find out it isn’t there. We must leave Earth at precisely the correct time such that Mars will be at the aphelion of our transfer ellipse just as we arrive. That opportunity comes about every 2 years.
 And returning requires correct timing as well.
 The total trip would take just under 3 years! There are other options that provide for a faster transit, including a gravity assist flyby of Venus.
 But these other options come with an additional cost in energy and danger to the astronauts.
 Visit this for more details about planning a trip to Mars.
Kepler’s second law states that a planet sweeps out equal areas in equal times, that is, the area divided by time, called the areal velocity, is constant. Consider, The time it takes a planet to move from position A to B, sweeping out area A 1 A 1, is exactly the time taken to move from position C to D, sweeping area A 2 A 2, and to move from E to F, sweeping out area A 3 A 3, Figure 13.20 The shaded regions shown have equal areas and represent the same time interval. Comparing the areas in the figure and the distance traveled along the ellipse in each case, we can see that in order for the areas to be equal, the planet must speed up as it gets closer to the Sun and slow down as it moves away.
This behavior is completely consistent with our conservation equation,, But we will show that Kepler’s second law is actually a consequence of the conservation of angular momentum, which holds for any system with only radial forces. Recall the definition of angular momentum from, L → = r → × p → L → = r → × p →,
For the case of orbiting motion, L → L → is the angular momentum of the planet about the Sun, r → r → is the position vector of the planet measured from the Sun, and p → = m v → p → = m v → is the instantaneous linear momentum at any point in the orbit.
Since the planet moves along the ellipse, p → p → is always tangent to the ellipse. We can resolve the linear momentum into two components: a radial component p → rad p → rad along the line to the Sun, and a component p → perp p → perp perpendicular to r → r →, The cross product for angular momentum can then be written as L → = r → × p → = r → × ( p → rad + p → perp ) = r → × p → rad + r → × p → perp L → = r → × p → = r → × ( p → rad + p → perp ) = r → × p → rad + r → × p → perp,
The first term on the right is zero because r → r → is parallel to p → rad p → rad, and in the second term r → r → is perpendicular to p → perp p → perp, so the magnitude of the cross product reduces to L = r p perp = r m v perp L = r p perp = r m v perp,
Note that the angular momentum does not depend upon p rad p rad, Since the gravitational force is only in the radial direction, it can change only p rad p rad and not p perp p perp ; hence, the angular momentum must remain constant. Now consider, A small triangular area Δ A Δ A is swept out in time Δ t Δ t,
The velocity is along the path and it makes an angle θ θ with the radial direction. Hence, the perpendicular velocity is given by v perp = v sin θ v perp = v sin θ, The planet moves a distance Δ s = v Δ t sin θ Δ s = v Δ t sin θ projected along the direction perpendicular to r,
 Since the area of a triangle is onehalf the base ( r ) times the height ( Δ s ) ( Δ s ), for a small displacement, the area is given by Δ A = 1 2 r Δ s Δ A = 1 2 r Δ s,
 Substituting for Δ s Δ s, multiplying by m in the numerator and denominator, and rearranging, we obtain Δ A = 1 2 r Δ s = 1 2 r ( v Δ t sin θ ) = 1 2 m r ( m v sin θ Δ t ) = 1 2 m r ( m v perp Δ t ) = L 2 m Δ t,
Δ A = 1 2 r Δ s = 1 2 r ( v Δ t sin θ ) = 1 2 m r ( m v sin θ Δ t ) = 1 2 m r ( m v perp Δ t ) = L 2 m Δ t, Figure 13.21 The element of area Δ A Δ A swept out in time Δ t Δ t as the planet moves through angle Δ ϕ Δ ϕ, The angle between the radial direction and v → v → is θ θ, The areal velocity is simply the rate of change of area with time, so we have areal velocity = Δ A Δ t = L 2 m,
areal velocity = Δ A Δ t = L 2 m, Since the angular momentum is constant, the areal velocity must also be constant. This is exactly Kepler’s second law. As with Kepler’s first law, Newton showed it was a natural consequence of his law of gravitation. You can view an of, and many other interesting animations as well, at the School of Physics (University of New South Wales) site.
Kepler’s third law states that the square of the period is proportional to the cube of the semimajor axis of the orbit. In, we derived Kepler’s third law for the special case of a circular orbit. gives us the period of a circular orbit of radius r about Earth: For an ellipse, recall that the semimajor axis is onehalf the sum of the perihelion and the aphelion.
We have changed the mass of Earth to the more general M, since this equation applies to satellites orbiting any large mass.
Why do planets move faster when they are closer to the Sun?
Kepler’s Second Law Describes the Way an Object’s Speed Varies along Its Orbit – A planet’s orbital speed changes, depending on how far it is from the Sun. The closer a planet is to the Sun, the stronger the Sun’s gravitational pull on it, and the faster the planet moves. The farther it is from the Sun, the weaker the Sun’s gravitational pull, and the slower it moves in its orbit.
Which state that a planet moves fastest when it is nearest to the Sun?
Transcript – The planets orbit the Sun in a counterclockwise direction as viewed from above the Sun’s north pole, and the planets’ orbits all are aligned to what astronomers call the ecliptic plane. The story of our greater understanding of planetary motion could not be told if it were not for the work of a German mathematician named Johannes Kepler.
Kepler lived in Graz, Austria during the tumultuous early 17th century. Due to religious and political difficulties common during that era, Kepler was banished from Graz on August 2nd, 1600. Fortunately, an opportunity to work as an assistant for the famous astronomer Tycho Brahe presented itself and the young Kepler moved his family from Graz 300 miles across the Danube River to Brahe’s home in Prague.
Tycho Brahe is credited with the most accurate astronomical observations of his time and was impressed with the studies of Kepler during an earlier meeting. However, Brahe mistrusted Kepler, fearing that his bright young intern might eclipse him as the premier astronomer of his day.
 He, therefore, led Kepler to see only part of his voluminous planetary data.
 He set Kepler, the task of understanding the orbit of the planet Mars, the movement of which fit problematically into the universe as described by Aristotle and Ptolemy.
 It is believed that part of the motivation for giving the Mars problem to Kepler was Brahe’s hope that its difficulty would occupy Kepler while Brahe worked to perfect his own theory of the solar system, which was based on a geocentric model, where the earth is the center of the solar system.
Based on this model, the planets Mercury, Venus, Mars, Jupiter, and Saturn all orbit the Sun, which in turn orbits the earth. As it turned out, Kepler, unlike Brahe, believed firmly in the Copernican model of the solar system known as heliocentric, which correctly placed the Sun at its center.
 But the reason Mars’ orbit was problematic was because the Copernican system incorrectly assumed the orbits of the planets to be circular.
 After much struggling, Kepler was forced to an eventual realization that the orbits of the planets are not circles, but were instead the elongated or flattened circles that geometers call ellipses, and the particular difficulties Brahe hand with the movement of Mars were due to the fact that its orbit was the most elliptical of the planets for which Brahe had extensive data.
Thus, in a twist of irony, Brahe unwittingly gave Kepler the very part of his data that would enable Kepler to formulate the correct theory of the solar system, banishing Brahe’s own theory. Since the orbits of the planets are ellipses, let us review three basic properties of ellipses.
The first property of an ellipse: an ellipse is defined by two points, each called a focus, and together called foci. The sum of the distances to the foci from any point on the ellipse is always a constant. The second property of an ellipse: the amount of flattening of the ellipse is called the eccentricity.
The flatter the ellipse, the more eccentric it is. Each ellipse has an eccentricity with a value between zero, a circle, and one, essentially a flat line, technically called a parabola. The third property of an ellipse: the longest axis of the ellipse is called the major axis, while the shortest axis is called the minor axis.
 Half of the major axis is termed a semimajor axis.
 Nowing then that the orbits of the planets are elliptical, johannes Kepler formulated three laws of planetary motion, which accurately described the motion of comets as well.
 Epler’s First Law: each planet’s orbit about the Sun is an ellipse.
 The Sun’s center is always located at one focus of the orbital ellipse.
The Sun is at one focus. The planet follows the ellipse in its orbit, meaning that the planet to Sun distance is constantly changing as the planet goes around its orbit. Kepler’s Second Law: the imaginary line joining a planet and the Sun sweeps equal areas of space during equal time intervals as the planet orbits.
 Basically, that planets do not move with constant speed along their orbits.
 Rather, their speed varies so that the line joining the centers of the Sun and the planet sweeps out equal parts of an area in equal times.
 The point of nearest approach of the planet to the Sun is termed perihelion.
 The point of greatest separation is aphelion, hence by Kepler’s Second Law, a planet is moving fastest when it is at perihelion and slowest at aphelion.
Kepler’s Third Law: the squares of the orbital periods of the planets are directly proportional to the cubes of the semimajor axes of their orbits. Kepler’s Third Law implies that the period for a planet to orbit the Sun increases rapidly with the radius of its orbit.
 Thus we find that Mercury, the innermost planet, takes only 88 days to orbit the Sun.
 The earth takes 365 days, while Saturn requires 10,759 days to do the same.
 Though Kepler hadn’t known about gravitation when he came up with his three laws, they were instrumental in Isaac Newton deriving his theory of universal gravitation, which explains the unknown force behind Kepler’s Third Law.
Kepler and his theories were crucial in the better understanding of our solar system dynamics and as a springboard to newer theories that more accurately approximate our planetary orbits.
Which planet moves the fastest around the Sun?
It only takes 88 days for Mercury to orbit around the sun. No other planet travels around the sun faster.
Which planet is the fastest around the Sun?
In Depth  Mercury – NASA Solar System Exploration Introduction The smallest planet in our solar system and nearest to the Sun, Mercury is only slightly larger than Earth’s Moon. From the surface of Mercury, the Sun would appear more than three times as large as it does when viewed from Earth, and the sunlight would be as much as seven times brighter.
 Mercury’s surface temperatures are both extremely hot and cold.
 Because the planet is so close to the Sun, day temperatures can reach highs of 800°F (430°C).
 Without an atmosphere to retain that heat at night, temperatures can dip as low as 290°F (180°C).
 Despite its proximity to the Sun, Mercury is not the hottest planet in our solar system – that title belongs to nearby Venus, thanks to its dense atmosphere.
But Mercury is the fastest planet, zipping around the Sun every 88 Earth days. Namesake
Which planet moves the fastest and why?
Eight extremes: The fastest thing in the universe By Whizzing around our solar system (Image: Johns Hopkins University Applied Physics Laboratory/Arizona State University/Carnegie Institution of Washington/NASA) See gallery: “” Speed is relative. There is no absolute standard for “stationary” in the universe.
 Perhaps the nearest thing is the allpervasive cosmic microwave background radiation.
 Its Doppler shift across the sky – blue in one direction, red in the other – reveals that, relative to the CMB, the solar system is rattling along at 600 kilometres per second.
 Microwaves are rather insubstantial, though, so we don’t feel the wind in our hair.
Distant galaxies are also moving at quite a rate. Space is expanding everywhere: the more space you are looking through the faster the galaxies you see are moving away from us. Far enough off, galaxies are effectively retreating faster than light speed, which means we can never see them because their radiation can’t reach us.
While such inaccessible extremes may have abstract appeal, speed becomes much more interesting if you are moving fast relative to some large object nearby – something you can see whoosh past your windows, or something you might just crash into. Within our solar system, Mercury, the messenger of the gods, is the fastestmoving planet, with an orbital speed of about 48 kilometres per second; Earth manages only about 30 km/s.
In 1976, Mercury was outpaced for the first time by a human artefact, the Helios 2 solar probe, which reached more than 70 km/s as it whizzed by the sun. Sungrazing comets that swoop in from the outer solar system trump both, skimming past the solar surface at up to 600 km/s.
Which planet revolves around the Sun the fastest quizlet?
Venus orbits the Sun faster than Earth orbits the Sun. Inner planets orbit the Sun at higher speed than outer planets. Venus orbits the Sun faster than Earth orbits the Sun.
Why is Kepler’s 2nd law important?
Orbital Motion: Kepler’s 2nd Law – This activity involves taking the code at the end of the Slingshot with Gravity exercise and doing some experiments with that code to learn more about the special properties of objects that are experiencing the gravitational pull from a central object.
 This central object can be a star or a black hole or a neutron star, etc.
 And the object in orbit can be a comet or an asteroid or a space capsule or even a whole planet.
 Usually this topic is connected to discussions of the motion of planets around a star.
 Epler made a number of important discoveries about the motion of the planets in the solar system.
In the Slingshot with Gravity activity we created a code that demonstrated that $1/r^2$ forces like gravity naturally produce elliptical orbits. Hopefully you played around with that code to try to see if you could make orbits other than an ellipse. It turns out that as long as the object does not have enough kinetic energy to totally escape the gravitational field of the star it will produce some kind of elliptical orbit.
 Not only will the trajectory be an ellipse, the object will follow this same path every time it moves around the star.
 This result is often referred to as Kepler’s first law.
 Epler was an astronomer who looked closely at the orbits of planets like Venus and Mars.
 In this activity we will consider Kepler’s second law.
Kepler’s second law has to do with how quickly the planet moves in its elliptical orbit. Kepler showed that the area that the planet “sweeps out” over some interval of time is the same regardless what part of the orbit the planet is in. If you’ve never heard of Kepler’s laws the sentence you just read about planets sweeping things out will probably not make much sense.
What is the significance of Kepler’s 2nd law?
Kepler’s laws of planetary motion Laws describing the motion of planets For a more precise historical approach, see in particular the articles and, Figure 1: Illustration of Kepler’s three laws with two planetary orbits.
 The orbits are ellipses, with focal points F 1 and F 2 for the first planet and F 1 and F 3 for the second planet. The Sun is placed at focal point F 1,
 The two shaded sectors A 1 and A 2 have the same surface area and the time for planet 1 to cover segment A 1 is equal to the time to cover segment A 2,
 The total orbit times for planet 1 and planet 2 have a ratio ( a 1 a 2 ) 3 2 } }}\right)^ }},
Part of a series on 
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In, Kepler’s laws of planetary motion, published by between 1609 and 1619, describe the of around the, The modified the of, replacing its and with trajectories, and explaining how planetary vary. The three laws state that:
 The of a planet is an with the Sun at one of the two,
 A joining a planet and the Sun sweeps out equal areas during equal intervals of time.
 The square of a planet’s is proportional to the cube of the length of the of its orbit.
The elliptical orbits of planets were indicated by calculations of the orbit of, From this, Kepler inferred that other bodies in the, including those farther away from the Sun, also have elliptical orbits. The second law helps to establish that when a planet is closer to the Sun, it travels faster.
How does this planet obey Kepler’s second law?
Transcript – The planets orbit the Sun in a counterclockwise direction as viewed from above the Sun’s north pole, and the planets’ orbits all are aligned to what astronomers call the ecliptic plane. The story of our greater understanding of planetary motion could not be told if it were not for the work of a German mathematician named Johannes Kepler.
Kepler lived in Graz, Austria during the tumultuous early 17th century. Due to religious and political difficulties common during that era, Kepler was banished from Graz on August 2nd, 1600. Fortunately, an opportunity to work as an assistant for the famous astronomer Tycho Brahe presented itself and the young Kepler moved his family from Graz 300 miles across the Danube River to Brahe’s home in Prague.
Tycho Brahe is credited with the most accurate astronomical observations of his time and was impressed with the studies of Kepler during an earlier meeting. However, Brahe mistrusted Kepler, fearing that his bright young intern might eclipse him as the premier astronomer of his day.
He, therefore, led Kepler to see only part of his voluminous planetary data. He set Kepler, the task of understanding the orbit of the planet Mars, the movement of which fit problematically into the universe as described by Aristotle and Ptolemy. It is believed that part of the motivation for giving the Mars problem to Kepler was Brahe’s hope that its difficulty would occupy Kepler while Brahe worked to perfect his own theory of the solar system, which was based on a geocentric model, where the earth is the center of the solar system.
Based on this model, the planets Mercury, Venus, Mars, Jupiter, and Saturn all orbit the Sun, which in turn orbits the earth. As it turned out, Kepler, unlike Brahe, believed firmly in the Copernican model of the solar system known as heliocentric, which correctly placed the Sun at its center.
 But the reason Mars’ orbit was problematic was because the Copernican system incorrectly assumed the orbits of the planets to be circular.
 After much struggling, Kepler was forced to an eventual realization that the orbits of the planets are not circles, but were instead the elongated or flattened circles that geometers call ellipses, and the particular difficulties Brahe hand with the movement of Mars were due to the fact that its orbit was the most elliptical of the planets for which Brahe had extensive data.
Thus, in a twist of irony, Brahe unwittingly gave Kepler the very part of his data that would enable Kepler to formulate the correct theory of the solar system, banishing Brahe’s own theory. Since the orbits of the planets are ellipses, let us review three basic properties of ellipses.
 The first property of an ellipse: an ellipse is defined by two points, each called a focus, and together called foci.
 The sum of the distances to the foci from any point on the ellipse is always a constant.
 The second property of an ellipse: the amount of flattening of the ellipse is called the eccentricity.
The flatter the ellipse, the more eccentric it is. Each ellipse has an eccentricity with a value between zero, a circle, and one, essentially a flat line, technically called a parabola. The third property of an ellipse: the longest axis of the ellipse is called the major axis, while the shortest axis is called the minor axis.
Half of the major axis is termed a semimajor axis. Knowing then that the orbits of the planets are elliptical, johannes Kepler formulated three laws of planetary motion, which accurately described the motion of comets as well. Kepler’s First Law: each planet’s orbit about the Sun is an ellipse. The Sun’s center is always located at one focus of the orbital ellipse.
The Sun is at one focus. The planet follows the ellipse in its orbit, meaning that the planet to Sun distance is constantly changing as the planet goes around its orbit. Kepler’s Second Law: the imaginary line joining a planet and the Sun sweeps equal areas of space during equal time intervals as the planet orbits.
Basically, that planets do not move with constant speed along their orbits. Rather, their speed varies so that the line joining the centers of the Sun and the planet sweeps out equal parts of an area in equal times. The point of nearest approach of the planet to the Sun is termed perihelion. The point of greatest separation is aphelion, hence by Kepler’s Second Law, a planet is moving fastest when it is at perihelion and slowest at aphelion.
Kepler’s Third Law: the squares of the orbital periods of the planets are directly proportional to the cubes of the semimajor axes of their orbits. Kepler’s Third Law implies that the period for a planet to orbit the Sun increases rapidly with the radius of its orbit.
 Thus we find that Mercury, the innermost planet, takes only 88 days to orbit the Sun.
 The earth takes 365 days, while Saturn requires 10,759 days to do the same.
 Though Kepler hadn’t known about gravitation when he came up with his three laws, they were instrumental in Isaac Newton deriving his theory of universal gravitation, which explains the unknown force behind Kepler’s Third Law.
Kepler and his theories were crucial in the better understanding of our solar system dynamics and as a springboard to newer theories that more accurately approximate our planetary orbits.
Why do planets follow Kepler’s second law?
Kepler’s Second Law Describes the Way an Object’s Speed Varies along Its Orbit – A planet’s orbital speed changes, depending on how far it is from the Sun. The closer a planet is to the Sun, the stronger the Sun’s gravitational pull on it, and the faster the planet moves. The farther it is from the Sun, the weaker the Sun’s gravitational pull, and the slower it moves in its orbit.
Does Pluto satisfy Kepler’s third law?
Q: Does Pluto follow Kepler’s third law, which is only applicable for planets in our solar system? First, Kepler’s laws are applicable for all objects in orbits about other objects. Since Pluto is in orbit of the Sun, then it also follows Kepler’s laws, all of them.