Escape Velocity and Short-Distance Space Travel: Understanding the Science

[blackcat]

can someone please help:

i know escape velocity is the velocity you need to give an object for it exit the pull of the Earth and travel an infinite distance away from earth.

now let's say you have a space shuttle that you need to take to Mars or the moon or something. why would you need to give it the escape velocity when you're only going a few million kilometres and not anywhere near an "infinite distance" away?

so how does that make sense?

 

[ranger]

ow let's say you have a space shuttle that you need to take to Mars or the moon or something. why would you need to give it the escape velocity when you're only going a few million kilometres and not anywhere near an "infinite distance" away?

It doesn't matter where/how far you are going. You just need that velocity to escape the gravitational attraction so it won't fall back down. From there is up to the space shuttle where to go.

Dont use "infinite distance away from earth", you'll confuse yourself. For simplicity sake, it should be finite distance.

 

[blackcat]

thanks, but i still don't quite understand.

what will happen if you launch with escape velocity (and without propulsion). in wikipedia it says you'll get infinitely far away, but you say it doesn't matter.

 

[Janus]

can someone please help:

i know escape velocity is the velocity you need to give an object for it exit the pull of the Earth and travel an infinite distance away from earth.

now let's say you have a space shuttle that you need to take to Mars or the moon or something. why would you need to give it the escape velocity when you're only going a few million kilometres and not anywhere near an "infinite distance" away?

so how does that make sense?

It turns out that you use up most of the escape velocity while you are still very close to the Earth. For instance, While you don't need to achieve full escape velocity (11.2 km/sec) to reach the distance of the Moon, you do need 9.76 km/sec. If you then also want to match the Moon's orbital velocity it jumps up to 10.76 km/sec. In just getting to the Moon you have to almost achieve escape velocity. Going much past the Moon means having to get even closer to escape velocity. After a point, you are having to come so close to escape velocity that the difference doesn't matter.

 

[turdferguson]

The "infinite distance" comes from the reasoning that the potential energy at an infinity is zero. This becomes useful when you get into the math

 

[blackcat]

ok thanks for your help guys.