What you are missing is that as the satellite moves farther away from the Earth, it slows down because of work done by the gravitational field.
Since you have given the satellite more total energy (kinetic plus potential) and because the total energy of a bound orbit is $-GMm/2a$, where $a$ is the semi-major axis, then to increase the energy (make it less negative), $a$ must increase.
For a tangential $\Delta v$, the resulting orbit is an ellipse with a perigee at the point where the velocity was added to the satellite. This is because both energy and angular momentum are conserved - when the satellite returns to the same radius it must have the same tangential velocity (to conserve angular momentum), but then cannot have an extra radial velocity component because that would change the total energy. This is a Hohmann transfer orbit.
On the other hand, a radial impulse adds energy but does not change the angular momentum. The result is an elliptical orbit with a larger $a$, but with a perigee closer to the Earth. The satellite moves outwards first but then falls back. When the satellite returns to the same radius then the tangential part of its velocity must be the same as before the impulse, but to conserve energy there must be an inward radial velocity taking it closer to the Earth. i.e. a more eccentric ellipse is produced than if the same impulse is given tangentially.
As we know, the velocity of the planet changes as it orbits around the sun, both in its magnitude and direction. The centripetal acceleration causes the change in the direction of velocity but I want to know what is the tangential force that acts on the planet to change the velocity by its $magnitude$.
The answer normally as to why the speed changes is:
If the force that the Sun exerts on the planet increases (as the planet moves closer), then the acceleration of the planet must increase, resulting in a higher orbital speed, and vice versa.
But this force is not along the body but towards the sun. So such a force should only change its direction.
Kepler’s laws show the effects of gravity on orbits. They apply to any object that orbits another: planets orbiting the Sun, moons orbiting a planet, spacecraft orbiting Earth.
The orbit of a planet around the Sun (or of a satellite around a planet) is not a perfect circle. It is an ellipse—a “flattened” circle. The Sun (or the center of the planet) occupies one focus of the ellipse. A focus is one of the two internal points that help determine the shape of an ellipse. The distance from one focus to any point on the ellipse and then back to the second focus is always the same.
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.
Kepler’s Third Law Compares the Motion of Objects in Orbits of Different Sizes
A planet farther from the Sun not only has a longer path than a closer planet, but it also travels slower, since the Sun’s gravitational pull on it is weaker. Therefore, the larger a planet’s orbit, the longer the planet takes to complete it.
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