Time the Earth requires to go towards Pluto?

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If the gravitational attraction between the Earth and the Sun suddenly ceased, the Earth would escape its orbit and travel away at its current orbital speed. To determine the time it would take for Earth to reach Pluto's orbital distance, one must calculate the escape velocity and the trajectory, which is tangential rather than radial. A diagram can help visualize the scenario, applying Pythagorean theorem to find the necessary distances. The discussion emphasizes understanding orbital mechanics and the implications of losing gravitational pull. Ultimately, the Earth would take a significant amount of time to reach Pluto's distance, depending on the calculations made.
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Homework Statement


Suppose that, suddendly, the gravitational attraction between the Earht and the Sun goes away.
How many time will the Earth require to reach an orbital distance from the Sun equal to the actual orbital radius of Pluto?
(Sun-Earth: 150*10^6 km; Sun-Pluto: 5900*10^6 km approximatively)

The Attempt at a Solution


I know that the Earth run in an circular orbit around the sun, then once the attraction goes away, it should "escape" form it. But I can't figure out at what speed it would go away. How can I find it?
 
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Just at its orbital [STRIKE]speed[/STRIKE] velocity.

Technically it is not different from what happens when you rotate a puck on the string, and the string breaks.
 
Last edited:
Theivax said:

Homework Statement


Suppose that, suddendly, the gravitational attraction between the Earht and the Sun goes away.
How many time will the Earth require to reach an orbital distance from the Sun equal to the actual orbital radius of Pluto?
(Sun-Earth: 150*10^6 km; Sun-Pluto: 5900*10^6 km approximatively)

The Attempt at a Solution


I know that the Earth run in an circular orbit around the sun, then once the attraction goes away, it should "escape" form it. But I can't figure out at what speed it would go away. How can I find it?

It wouldn't go "straight" away (i.e. radially). Remember that orbital velocity is tangential.

Draw a diagram. You'll find a right triangle to which you can apply Pythagoras' theorem.
 
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