Time the Earth requires to go towards Pluto?

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SUMMARY

The discussion centers on calculating the time it would take for Earth to reach Pluto's orbital distance if the gravitational attraction from the Sun suddenly ceased. The current distance from the Sun to Earth is approximately 150 million kilometers, while the distance to Pluto is about 5.9 billion kilometers. Participants emphasize that Earth would not move directly away from the Sun but rather follow a tangential path due to its orbital velocity. Utilizing Pythagorean theorem to analyze the trajectory is recommended for accurate calculations.

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  • Familiarity with basic physics concepts such as velocity and acceleration
  • Ability to apply Pythagorean theorem in two-dimensional motion analysis
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  • Calculate the tangential velocity of Earth in its orbit around the Sun
  • Explore the implications of gravitational forces on orbital mechanics
  • Learn about escape velocity and its significance in celestial dynamics
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Students studying physics, particularly those interested in celestial mechanics and orbital dynamics, as well as educators looking for practical examples of gravitational effects in space.

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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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