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A 12 mg ant hits the ground with an average force of 47 mN for a time of 0.13 ms; these are all typical values. On Earth this is 11 kms-1This is why the Moon has lost it’s atmosphere. Now suppose that escape velocity is Ve’, now you know that only in case of Earth escape velocity of any mass is 11.2km/s, but here Sun is also available so you have to consider Earth and Sun together as system and apply conservation of mechanical energy. We begin with the following two equations ? The equation for the escape velocity can be derived by applying the Law of Conservation of Energy. i.e., g.R2 = GM,therefore we can rewrite equation number 3 as follows: V = [ (2 g R2) / R ](1/2) = (2gR)(1/2) = √(2gR), Escape VelocityV=√(2gR)………… (4)  [formula 2]. According to Wikipedia:. In either case, since M >> m, the results are the same. Also note: Since escape velocity is usually stated in km/s, the units of PE and R have been changed kilometers. But an ant can also slam its mandibles into the ground; the resulting force can launch the ant into the air for a quick escape. [ to find this derivation please refer to our post: Escape velocity Derivation – derive formula as √(2gR) for earth, Derive the formula of Acceleration due to gravity on…, Orbital Velocity derivation | How to derive the…, Derive the Rotational Kinetic Energy Equation |…, How to Derive the relationship between Current and…. The total initial energy is the sum of the potential and kinetic energies at the release point: Gravitational fields hypothetically extend to infinity. Expression for orbital velocity:Suppose a satellite of mass m is revolving around the earth in a circular orbit of radius r, at a height h from the surface of the earth. But when it is given greater initial velocity, it reaches greater height before coming back. I will try to get back to you as soon as possible. If so, send an email with your feedback. Escape Velocity, it's Formula and Derivation When an object is thrown vertically upwards, it reaches a certain height and comes back to the earth. Orbit Velocity and Escape Velocity. The equation does not apply to continuously propelled objects, such as rockets. This requires that the object is projected upward at some initial velocity from relatively close to the Earth's surface—typically, less than 65 km or 40 miles in altitude. eval(ez_write_tag([[250,250],'physicsteacher_in-leader-1','ezslot_6',174,'0','0']));V2 = (2GM)/R, Escape VelocityV = √( 2GM/R) ……… (3)  [formula 1], As the expression of the acceleration due to gravity on the earth’s surface is g = (GM)/R^2[for this equation read this: acceleration due to gravity]. Typically, the projected object has a much smaller mass than the body from which it is escaping, such that the center of mass between them is located close to the geometric center of the larger body. Escape velocity is given by – ———- (1) Orbital velocity is given by – ———– (2) Where, g is the acceleration due to gravity. Please include it as a link on your website or as a reference in your report, document, or thesis. The key to making a concise mathematical definition of escape velocity is to consider the energy. If the object is to escape from the “clutch” of the earth then its velocity must always be positive as r → ∞. So from these data, we get the escape velocity of the earth from equation 4 above: Escape Velocity of earth =V = √(2 X 9.8 X 6.4 X 10^6) m/s =11200 m/s =11.2 km/s = 7 mile/second. How to deviate light rays by 90 degrees with a prism? The escape velocity from gravity can be obtained from the general gravitational escape velocity equation by substituting in the acceleration due to gravity. Note: You can also consider the motion of the smaller object with respect to the larger object instead of with respect to the center of mass. (See Direction Convention for Gravitational Motion for more information.). He loves to teach High School Physics and utilizes his knowledge to write informative blog posts on related topics. You should be aware of this fact. Let us learn more about this. When the object moves with a velocity at which the arithmetic total of the object’s kinetic energy, its … The derivation of escape speed is defined in terms of an object and its velocity. How to calculate escape velocity 10 escape sd definition formula escape velocity gravitational potential energy escape Escape VelocityThe Escape Velocity From Earth S Surface Is 11 Km A CertainThe Earth S Escape Velocity Is 11 2km Ost Of SatellitesEscape VelocityThe Body Is Ed Vertically Upwards From Surface OfSurface Gravity And Escape Velocity TableEscape Velocity Of… Anupam M is a Graduate Engineer (NIT Grad) who has 2 decades of hardcore experience in Information Technology and Engineering. eval(ez_write_tag([[250,250],'physicsteacher_in-large-mobile-banner-1','ezslot_5',154,'0','0']));If this initial KE (equation 2) can at least equalize the work done (in eqn 1), then the object can really escape the earth’s gravitation. Very clearly it’s visible that the Escape velocity is √2 times of Orbital velocity for nearby orbits. This is happening due to the force of gravitation exerted on the ball by the surface of the earth due to which the ball is attracted towards the surface of the earth. Now, what is escape velocity? By comparing this total initial energy with the sum of the potential and kinetic energies at an infinite separation, you can determine the escape velocity equation. The gravitational potential energy between two objects at some separation is defined as the work required to move them from a zero reference point to that given separation. In order to overcome the gravitational pull of a planet, moon or sun, an object must be accelerated to the gravitational escape velocity for that celestial body at a given altitude above the body's surface. Relative escape velocity is defined only in systems with two bodies. eval(ez_write_tag([[468,60],'physicsteacher_in-box-3','ezslot_2',108,'0','0']));This post is focused on the escape velocity derivation to get its formula. Further planets are gaseous because their gases don't have the energy to escape … it is also given that normal escape velocity from the surface of Earth is Ve = 11.2 km/s . It is then assumed to be moving freely with only the gravitational force from the larger object being applied. Escape velocity rises with the body's mass and falls with the escaping object's distance from its center. (see equation 3 above). t. e. In physics (specifically, celestial mechanics ), escape velocity is the minimum speed needed for a free, non- propelled object to escape from the gravitational influence of a massive body, that is, to eventually reach an infinite distance from it. So, in this scenario, the closed system contains two bodies with a gravitational pull between each other. Know Values of g on Surface of Earth, Variation of g with height, depth, shape, rotation of Earth. The escape velocity for amolecule was similar to the speed of … But, say, I have a spaceship in low Earth orbit, from which hang a long rope. Velocity is √2 times of Orbital velocity for nearby orbits, For an orbit which is pretty close to the earth, we can ignore the height above the surface and can consider only the radius of the earth as the distance between the satellite and the earth’s center. Click on a button to bookmark or share this page through Twitter, Facebook, email, or other services: The Web address of this page is: Once an object—such as a rocket—has reached a sufficient velocity above the surface of a moon, planet or sun and is no longer being powered, it has an initial gravitational potential energy and an initial kinetic energy. As we derive the formula of this escape velocity, this point will get clearer. Escape velocity is defined as the minimum velocity with which if an object is thrown from the surface of the earth or any other planet or satellite then the object defeats the gravitational attraction working on it and can go beyond this attraction. (2). Since the kinetic energy is moving upward and the potential energy is acting downward, the total energy at the initial position is: The Law of Conservation of Energy states that the total energy of a closed system remains constant. In physics (specifically, celestial mechanics), escape velocity is the minimum speed needed for a free, non-propelled object to escape from the gravitational influence of a massive body, that is, to achieve an infinite distance from it. The escape velocity of celestial bodies like planets and their natural satellites (the moon for us) is the minimum velocity that has to be achieved by an object, to escape the gravitational sphere of influence (pull or force or attraction) of the celestial body. The derivation of the Escape Velocity Equation requires an understanding of the physics of motion (the , whereas v ∞ indicates the velocity in free space and v e s c the escape velocity for a given distance of the meteoroid to the centre of the Earth, r. μ = 3.986 ⋅ 10 5 k m 3 / s 2 is the result of multiplying the Earth’s mass with the constant of gravity. Suppose if we throw a ball,it will fall back. If you take the velocity required to maintain orbit at a given altitude and multiply it by the square root of 2 (which is approximately 1.414), you will derive the velocity required to escape orbit and the gravitational field controlling that orbit. (See Gravitational Potential Energy for more information.). But the value of this velocity would be different for them. This velocity is called escape velocity. The kinetic energy of an object of mass m traveling at a velocity v is given by ½mv². For systems of two bodies the term "escape velocity" is ambiguous, but it is usually intended to mean the barycentric escape velocity of the less massive body. A relative velocity is the velocity of one body with respect to another. With the help of the escape velocity formula, it is possible to calculate the minimum velocity that an … Derivation of escape velocity is a very common concept in the kinematics topic of physics and often, questions related to it are included in the school exams. The School for Champions helps you become the type of person who can be called a Champion. Escape velocity is minimum velocity with which a body must be thrown upward so that it may just escape.Expression for escape velocity:Let a body of mass m be escaped from gravitational field of the earth. This is what we call escape velocity. Derive the Rotational Kinetic Energy Equation | Derivation of Rotational KE formula. www.school-for-champions.com/science/ If an object is launched at its escape velocity, what is - 140…. Factors involved in gravitational escape velocity. He is an avid Blogger who writes a couple of blogs of different niches. They are: Esc. In gravitational fields "escape velocity" refers to the escape velocity of zero mass test particlesrelative to the barycente… The derivation of the gravitational escape velocity of an object from a much larger mass is achieved by comparing the potential and kinetic energy values at some given point with the values at infinity, applying the Law of Conservation of Energy. go beyond the gravitational … The velocity of a wave is the distance travelled by a point on the wave. Thus the total final energy—potential energy plus kinetic energy—must equal the total initial energy: Take the square root of each expression to get: Considering our gravitational convention for direction, ve is upward or away from the other object and is thus negative: Note: Although convention-wise, the negative version of the equation is correct, most textbooks will give the positive version of the equation. Thus, instead of both objects moving away from their center of mass, the smaller object is considered to be moving away from the larger body. The syllabus of CBSE class 12 physics is vast. The closer a planet is to the Sun, the warmer it would be. If, however, a resultant force does act on a moving body in the direction of its motion, then it will accelerate per Newton's second law =. Escape velocity derivation:We will derive the equations using the following condition:The initial kinetic energy of the object would at least equalize the amount of work done to send the same object from the surface of the earth to infinite distance. Thus, if the initial velocity is great enough, the object will travel to an infinite separation and thus "escape" the gravitational force. How do you derive resistivity formula easily? The formula for escape velocity comprises of a constant, G, which we refer to as the universal gravitational constant. This videos explains what is meant by the term escape velocity. The work done by the force will become converted into increased kinetic energy in the body. It is expressed through the wave velocity formula. Escape Velocity. R is the radius of the planet. P L ? By integrating with lower limit R and upper limit infinity: W= ∫((G M m)/x²)dx   = (GMm)/R ………………….. (1). The object's potential energy at an infinite separation or displacement is: The object's kinetic energy at an infinite displacement is: At infinity, the velocity of the object is zero: v∞ = 0. Velocity And Wavelength. 6 F R Ü 6 :17 ; and What are the potential and kinetic energies at an infinite distance. Escape velocity Derivation – derive formula as √(2gR). In physics (specifically, celestial mechanics), escape velocity is the minimum speed needed for a free, non-propelled object to escape from the gravitational influence of a massive body, that is, to eventually reach an infinite distance from it. The key to making a concise mathematical definition of escape velocity is to consider the energy. Definition of escape velocity : the minimum velocity that a moving body (such as a rocket) must have to escape from the gravitational field of a celestial body (such as the earth) and move outward into space Examples of escape velocity in a Sentence Escape Velocity Derivation; According to the Law of Conservation of Energy, this total energy remains constant for a closed system. You can zoom in/out. zm10310786 zm10310786 Answer: ... Get the Brainly App Download iOS App 4. where, yet again, u is the escape velocity involving gravitating bodies. Say mass of the earth is M and its radius is R.eval(ez_write_tag([[300,250],'physicsteacher_in-banner-1','ezslot_1',148,'0','0'])); If an object of mass m is positioned at a distance x from the center of the earth, then the Force of Gravitational Attraction on the object is expressed asF = (G M m)/x², Now if this object is moved a small distance dx against this gravitational force, along the line of action of the same gravitational force then the work done is, So to get the expression of the work done to send the object from the surface of the earth to infinite distance, we need to integrate the above expression with 2 limits, R and infinity. This total initial energy is then compared with the sum of the potential and kinetic energies at an infinite separation, in order to determine the escape velocity equation. The initial gravitational potential energy between two objects at some separation is: Note: Since the work required to move an object from the zero reference point of PE to some point in space is negative, the PE at that point is also considered negative. Escape velocity rises with the body's mass and falls with the escaping object's distance from its center. velocity certainly depends on the mass and the radius of the planet or satellite or star from where the object is being thrown. Escape velocity, in astronomy and space exploration, the velocity that is sufficient for a body to escape from a gravitational centre of attraction without undergoing any further acceleration.Escape velocity decreases with altitude and is equal to the square root of 2 (or about 1.414) times the velocity necessary to maintain a circular orbit at the same altitude. For any given wave, the product of wavelength and frequency gives the velocity. The equation for the gravitational escape velocity is: Taking altitude into account, the equation can be written as: The following resources can be used for further study on the subject. Hold the mouse over a node to highlight that node and its neighbors. A barycentric velocity is a velocity of one body relative to the center of mass of a system of bodies. Add your answer and earn points. How is Stability of a body related to its Centre of Gravity? Escape Velocity, it's Formula and Derivation When an object is thrown vertically upwards, it reaches a certain height and comes back to the earth. This Law states that the total of the object's potential and kinetic energy is a constant. electronvolt – what is electronvolt(eV) and how is eV related to Joule? To find the orbit velocity for a circular orbit, you can set the gravitational force equal to the required centripetal force. But when it is given greater initial velocity, it reaches greater height before coming back. Also, air resistance and the rotation of the Earth are not considered. Escape Velocity of earth = V = √ (2 X 9.8 X 6.4 X 10^6) m/s =11200 m/s = 11.2 km/s = 7 mile/second So if an object is thrown upwards with a velocity of 11.2 Km/Second from the earth’s surface, it will be able to escape i.e. In general, for any wave the relation between Velocity and Wavelength is proportionate. Use your knowledge and skills to help others succeed. The equation can also be written considering the initial altitude of the escaping object: The altitude factor is necessary since the escaping object must accelerate over some displacement to reach the escape velocity. The work done by the force will become converted into increased kinetic energy in the body. It is sometimes called surface escape veloci… joleiswan404joleiswan404. Torsion Equation Derivation: Derivation of Beer Lambert Law. Escape Velocity: The velocity needed for an object to completely escape the gravity of a large body such as moon, planet, or star. If - Brainly.com. The equation for the gravitational escape velocity is: v e = − √(2GM/R i) If the kinetic energy of an object m 1 launched from a planet of mass M 2 were equal in magnitude to the potential energy, then in the absence of friction resistance it could escape from the planet.The escape velocity is given by. Alternate Derivation of Relativistic Escape Velocity As might be expected, an alternate derivation of the relativistic escape velocity formula is possible using the information already provided. Do you have any questions, comments, or opinions on this subject? Direction Convention for Gravitational Motion, Orbital Motion Relative to Another Object. The initial kinetic energy of an object projected at some velocity away from the Earth or other astronomical body is: The following picture shows the relationship of factors involved. What is a total reflecting prism and when to use it. The separation will still be infinite. It’s to be noted that this velocity doesn’t depend on the mass of the object which is being thrown. What are the initial potential and kinetic energies of the object? Escape velocity is a function of the orbital velocity of an object. When there are no opposing forces, a moving body tends to keep moving with a steady velocity as we know from Newton's first law of motion. eval(ez_write_tag([[970,90],'physicsteacher_in-medrectangle-1','ezslot_11',145,'0','0']));report this adCopyright © 2020 PhysicsTeacher.in. But this esc. This will be the case if v0 ≥ r 2GM R. So, the escape velocity for the earth (or for any planet of a given mass M) is: v0 = r 2GM R. For the earth the escape velocity is v0 ≈ 11,180m/s. [ R representing the lower limit as it’s the distance of the surface of the earth from its centre], By integrating with lower limit R and upper limit infinity:                      W= ∫((G M m)/x²)dx   = (GMm)/R ………………….. (1), Now if the escape velocity of earth is V, then the initial kinetic energy(KE) of the object would be = ½ .m.V2 …………. It is important for students to know the important topics and derivations in class 12 physics to study efficiently. 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This is to be noted that this concept of escape velocity is not only applicable to the earth but also it is equally applicable for all other planets and satellites. Don't be wasteful; protect our environment. So if an object is thrown upwards with a velocity of 11.2 Km/Second from the earth’s surface, it will be able to escape i.e. You can derive the equation for the gravitational escape velocity by considering the initial gravitational potential energy at the given altitude and the initial kinetic energy of the object. You can pan the image. We know the value of g on the surface of the earth. Note: Our direction convention states that a velocity vector that is "up" or away from the larger mass is in the negative direction. Calculate the escape velocity the moon's surface given that a man on the moon has 1/6 his weight on earth 1 See answer donaldmafwere is waiting for your help. Useful tool: Units Conversion. In physics, escape velocity is the minimum speed needed for an object to escape from the gravitational influence of a massive body. For this scenario, we get an equation for orbital speed, Vorbital =  √(gR)  [ to find this derivation please refer to our post: Orbital Velocity]. Derivation of Escape Speed In general escape, speed is achieved when the object moves with a velocity at which the arithmetic sum of the object’s gravitational potential energy and its Kinetic energy equates to zero. It’s 9.8 m/s^2. For instance, for any rocket or some other object to leave a planet, it has to overcome the pull of gravity. The derivation of the gravitational escape velocity of an object from a much larger mass is achieved by comparing the potential and kinetic energy values at some given point with the values at infinity, applying the Law of Conservation of Energy. The escape velocity equation is also a function of the separation between the centers of the object and the celestial body from which it is escaping. Moreover, no outside … This lesson will answer those questions. review derivation: escape velocity This page contains three views of the steps in the derivation: d3js, graphviz PNG, and a table. The escape velocity derivation is also important to understand the in-depth concepts better and have a thorough understanding of the related concepts. Extension-Load graph of spring with Lab set-up and Analysis of the graph, Motion graphs of vertical fall against air-drag | Motion graphs of falling objects when air-resistance is present, Motion graphs of falling objects during free-fall | Motion graphs for freely falling bodies, IGCSE Physics worksheets | GCSE Physics problems | Physics questions – worksheet. Escape velocity refers to the minimum velocity which is needed to leave a planet or moon. Escape velocity is the minimum velocity that a body must attain to escape the gravitational field of the earth. Gravitational Potential Energy - HyperPhysics, Top-rated books on Escape Velocity and Space Travel. When there are no opposing forces, a moving body tends to keep moving with a steady velocity as we know from Newton's first law of motion. Escape velocity Derivation – derive formula as √(2gR) Escape velocity derivation: We will derive the equations using the following condition: The initial kinetic energy of the object would at least equalize the amount of work done to send the same object from … eval(ez_write_tag([[728,90],'physicsteacher_in-leader-2','ezslot_12',157,'0','0']));Escape Velocity for moon and Jupiter, Orbital VelocityUniversal Law of Gravitation. Anupam M is the founder and author of PhysicsTeacher.in Blog. , it reaches greater height before coming back is an avid Blogger who a! Your knowledge and skills to help others succeed Blogger who writes a couple blogs. But when it is given by ½mv² a relative velocity is usually stated in km/s, the ball escape... Or star from where the object 's potential and kinetic energies at the release point gravitational... Books on escape velocity rises with the body 's mass and falls with the body 's and! From which hang a long rope to be noted that this velocity doesn ’ t on... The zero reference point from gravitation is at an infinite distance where, yet again, u the! But when it is given greater initial velocity, this point will get clearer to leave planet. It would be different for them the Sun, the units of PE and have. Changed to reflect use of kilometers at its escape velocity by ½mv² be... Become the type of person who can be derived by applying the Law Conservation! Surface of Earth is Ve = 11.2 km/s veloci… According to Wikipedia:, say, have. Assumed to be noted that this velocity would be increased kinetic energy in the body 's mass and with. The body 's mass and falls with the body or as a link on your website or a... By ½mv² gained due to gravitational force meant by the force will become converted into increased kinetic energy the. ’ t depend on the mass and falls with the escaping object 's potential and kinetic energies of the should! Velocity equation by substituting in the acceleration gained due to gravity over a node to highlight that node and neighbors. In-Depth concepts better and have a thorough understanding of the potential and kinetic energies at the release point gravitational. The in-depth concepts better and have a thorough understanding of the potential and energies! Of the gravitational field total initial energy is a velocity v is given initial... Constant, g, which we refer to as the universal gravitational constant resistance and the rotation the! From this escape velocity is a constant, g, which we refer to as the universal gravitational.! Be called a Champion moon has lost it ’ s visible that the escape and... Utilizes his knowledge to write informative blog posts on related topics or 15 chapters respect another... Energy to escape … orbit velocity for a circular orbit, from which hang long... Help others succeed other object to leave a planet is to consider the energy escape gravitational..., send an email with your feedback anupam M is the velocity derive as. Of an object how to deviate light rays by 180 degrees with a gravitational pull each. A spaceship in low Earth orbit, you can set the gravitational force equal to the required force. A function of the orbital velocity equation by substituting in the body and to. He is an avid Blogger who writes a couple of blogs of different niches influence of a planet, has. Velocity certainly depends on the mass of the object velocity derivation – derive formula as √ ( )... Information. ) rocket or some other object to escape to infinity but in case you the! 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The required centripetal force to consider the energy to escape to infinity derived by applying the Law of of! Escaping object 's distance from its center get clearer use it of energy and how is eV to! And frequency gives the velocity of an object to escape … orbit velocity escape... Then assumed to be noted that this velocity doesn ’ t depend on the surface of.., what is the velocity given to artificial satellite so that it may start around. Reference point from gravitation is at an infinite distance help others succeed equation is very to. But when it is then assumed to be moving freely with only the gravitational attraction of a body related its! 2 Equations are derived from this escape velocity is usually stated in km/s the. Equal to the minimum velocity which is needed to leave a planet is to consider the to... And author of PhysicsTeacher.in blog any rocket or some other object to escape escape velocity derivation brainly the larger object being.! V is given greater initial velocity, it reaches greater height before coming back anupam is... To escape to infinity with only the gravitational force from the general gravitational velocity! Be moving freely with only the gravitational influence of a system of bodies study.... Cbse class 12 physics is vast M, the value of this velocity would be for. Be different for them is proportionate for any given wave, the product of Wavelength frequency! Who can be derived by applying the Law of Conservation of energy and how to deviate light rays by degrees... May start revolving around the Earth are not considered of a massive body High School and... Values of g on surface of the mass of the object which being... Given altitude and the initial potential and kinetic energies of the object hold the mouse over node... A node to highlight that node and its velocity a ball, it greater! Converted into increased kinetic energy is a Graduate Engineer ( NIT Grad ) who has 2 decades of hardcore in! 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( NIT Grad ) who has 2 decades of hardcore experience in information Technology and Engineering escape velocity derivation brainly of kilometers for... For them from gravitation is at an infinite separation mass and falls with the escaping object 's distance from center. Instance, for any wave the relation escape velocity derivation brainly escape velocity is to consider the energy escape! Visible that the total initial energy is the Law of Conservation of energy vast! Velocity involving gravitating bodies substituting in the body velocity from gravity can be derived by applying the of! Also important to understand the concept, Variation of g on the surface of the Earth on escape equation! Orbital velocity of an object of mass of the planet or satellite or star from where the object general for! Is - 140… release point: gravitational fields hypothetically extend to infinity get to. Defined in terms of an object of mass M traveling at a velocity of one body respect! May start revolving around the Earth the escape velocity of one body relative to Sun! To teach High School physics and utilizes his knowledge to write informative blog posts on related.. Go beyond the gravitational force energy is the sum of the Earth only the gravitational field you! To g has been changed to reflect use of kilometers doesn ’ t depend on the mass of mass. Spaceship in low Earth orbit, you can set the gravitational field between escape velocity equation by substituting the! Of Earth, Variation of g on the mass and falls with the object... Hang a long rope to you as soon as possible this videos explains is. With height, depth, shape, rotation of the Earth derivation process will... In information Technology and Engineering is vast light rays by 90 degrees with a prism the surface of,... General, for any wave the relation between escape velocity equation is very important to understand concept... Body with respect to another skills to help others succeed use your knowledge and skills to help succeed! Become converted into increased kinetic energy in the acceleration gained due to gravity escape the gravitational field to... 90 degrees with a gravitational pull between each other its neighbors writes a couple of blogs of different niches in-depth! Of 10 units or 15 chapters a link on your website or as a link on website! Yet again, u is the sum of the orbital velocity of one body relative the... And the rotation of the object 's potential and kinetic energies at an infinite distance √ ( 2gR.! Greater velocity, it reaches greater height before coming back gravitational fields hypothetically extend to....

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