Time the Earth requires to go towards Pluto?

[Theivax]

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?

 

[Borek]

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.

 

[Curious3141]

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.