Gravitational pull of Earth and escape velocity

[Zynoakib]

I know once the escape velocity is reached, the object will continuous to move away from the Earth. But the Earth's gravity can still act on the object no matter how far it goes, so what keeps the object from stopping or even returning back to Earth?

Thanks in advance!

 

[phinds]

I know once the escape velocity is reached, the object will continuous to move away from the Earth. But the Earth's gravity can still act on the object no matter how far it goes, so what keeps the object from stopping or even returning back to Earth?

Thanks in advance!

It is inherent in the equations of motion. The object does slow down some but not down to zero. That's really the definition of escape velocity; giving an object sufficient velocity that gravity never quite overcomes it. Mathematically, when it gets to infinity it has zero velocity relative to the Earth (assuming it left with exactly the escape velocity), but of course in reality it will be more affected by celestial bodies other than the Earth WAY long before then (and the infinite "then" never actually occurs in reality)

 

[Zynoakib]

It is inherent in the equations of motion. The object does slow down some but not down to zero. That's really the definition of escape velocity; giving an object sufficient velocity that gravity never quite overcomes it. Mathematically, when it gets to infinity it has zero velocity relative to the Earth (assuming it left with exactly the escape velocity), but of course in reality it will be more affected by celestial bodies other than the Earth WAY long before then (and the infinite "then" never actually occurs in reality)

Just want to explain it in my own wording

Although the Earth's gravity can still attract the object to slow it down no matter how far it goes, it will take forever for the object to be slowed down just by a slight degree.

 

[phinds]

Just want to explain it in my own wording

Although the Earth's gravity can still attract the object to slow it down no matter how far it goes, it will take forever for the object to be slowed down just by a slight degree.

No, that's not a good way to say it. It will take forever for it to be slowed to zero.

 

[russ_watters]

No, that's not a good way to say it. It will take forever for it to be slowed to zero.

So, note that escape velocity is not a single/constant value. It decreases with distance. So an object that is launched exactly at escape velocity will always be slowing down, and will always be at the escape velocity of whatever distance it is at.

 

[phinds]

So, note that escape velocity is not a single/constant value. It decreases with distance. So an object that is launched exactly at escape velocity will always be slowing down, and will always be at the escape velocity of whatever distance it is at.

Agreed for sure.

 

[tfr000]

"Hyperbolic excess velocity" is what you're looking for here.

 

[Zynoakib]

Thanks guys, now I understand