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AbhiFromXtraZ
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Can you please explain why the paths of objects are hyperbolic, parabolic and elliptic for energies positive, zero and negative respectively?
AbhiFromXtraZ said:Can you please explain why the paths of objects are hyperbolic, parabolic and elliptic for energies positive, zero and negative respectively?
tiny-tim said:By "energy", you mean total mechanical energy, = kinetic energy plus gravitational potential energy.
Potential energy has to be measured relative to an arbitrary zero-level.
In this case, we choose "at infinity" to be the zero-level of potential energy.
Consider a parabolic orbit.
As it "approaches infinity", its speed becomes smaller and smaller, and tends to zero ¡ ie, its speed (and KE) is zero "at infinity".
So, anywhere along its trajectory, its KE is minus its PE, ie its total energy is 0 (and its speed is always equal to the local escape velocity).
AbhiFromXtraZ said:The total energy in an attractive field is given by,
E = 1/2mv^2 + 1/2Iw^2 - k/r
According to your answer, if the total energy is zero, then the path will be parabolic...but why? It could be hyperbolic...as it also an unbounded path and ends at infinity just like a parabola.
now if the total energy is positive such that 1/2mv^2 term is greater than the sum of other two terms (negative)...Then??...if the centre of force is earth, it will attack earth...then where will be the turning point??
tiny-tim said:negative total energy tells you that the trajectory is an ellipse, but it does not tell you the eccentricity of the ellipse
The trajectory of space objects is primarily determined by the object's mass, velocity, and the gravitational forces acting upon it. Other factors such as atmospheric drag and the influence of nearby objects can also affect the trajectory.
Scientists use mathematical models and equations, such as Newton's laws of motion and the law of universal gravitation, to calculate the trajectory of space objects. They also use data from observations and simulations to refine their predictions.
Yes, the trajectory of space objects can be changed through various methods such as thrust from rockets, gravitational slingshot maneuvers, and aerobraking. However, the feasibility and effectiveness of these methods depend on the specific characteristics of the object and its surroundings.
Yes, there are potential dangers associated with the trajectory of space objects. If an object's trajectory intersects with Earth, it could potentially cause damage or harm. Additionally, the increasing amount of space debris in orbit poses a risk for collisions that could alter the trajectory of objects.
Scientists use various methods to track the trajectory of space objects, including radar, telescopes, and satellites. They also collaborate with international organizations, such as NASA and ESA, to share data and track objects in orbit.