PDA

View Full Version : Gradient of Earth's gravity well?



redshifter
2010-Feb-23, 07:23 PM
Hi folks, I was thinking about this last night & figured someone here probably has the answer to this: At what altitude above the Earth does one start to experience noticably reduced gravity? I assume this is a gradual thing and not a situation where one would be say 30 miles above the Earth's surface and experience a full 1g, and at 31 miles experience say .01g. I was wondering how fast the gravitational pull drops off as one gains altitude.

Tensor
2010-Feb-23, 07:47 PM
Hi folks, I was thinking about this last night & figured someone here probably has the answer to this: At what altitude above the Earth does one start to experience noticably reduced gravity? I assume this is a gradual thing and not a situation where one would be say 30 miles above the Earth's surface and experience a full 1g, and at 31 miles experience say .01g. I was wondering how fast the gravitational pull drops off as one gains altitude.

You can do a quick and dirty estimate using the following formula:

ga = 9.81 m/sec2(6370000 m/6370000 m+h)2 where 9.81 is the standard gravitational acceleration, or 1g, the 63700 is the Earth's radius in meters and h is the height, in meters, above the surface. ga would be your gravitational acceleration at height h.

George
2010-Feb-23, 07:52 PM
Hi folks, I was thinking about this last night & figured someone here probably has the answer to this: At what altitude above the Earth does one start to experience noticably reduced gravity? I assume this is a gradual thing and not a situation where one would be say 30 miles above the Earth's surface and experience a full 1g, and at 31 miles experience say .01g. I was wondering how fast the gravitational pull drops off as one gains altitude.
Gravity as an inverse square phenomena.

The equation for the value of gravity for changing altitudes is:

g' = g0 * (Re/(Re + h))2

Re ~ Radius of the Earth
g0 ~ Std. gravity at sea level

I don't know at what point it would be noticeable, but here are some values.

g' at 50 km...... 98% of g
g' at 500 km.... 86% of g
g' at 1000 km... 75% of g
g' at 1500 km... 66% of g
g' at 2000 km... 58% of g

a1call
2010-Feb-23, 08:13 PM
In the off chance someone might puzzle over the reduced gravity in orbit such as in the ISS. You could experience it at any altitude given you are in a free fall or even in a fast descent.

korjik
2010-Feb-23, 08:43 PM
You can do a quick and dirty estimate using the following formula:

ga = 9.81 m/sec2(63700 m/63700 m+h)2 where 9.81 is the standard gravitational acceleration, or 1g, the 63700 is the Earth's radius in meters and h is the height, in meters, above the surface. ga would be your gravitational acceleration at height h.

63.7 km radius? Are you missing a few zeros? :)

grant hutchison
2010-Feb-23, 09:01 PM
63.7 km radius? Are you missing a few zeros? :)I was just going to say that. It's a small world ...

Grant Hutchison

Tensor
2010-Feb-23, 10:20 PM
63.7 km radius? Are you missing a few zeros? :)

Yep, I hit preview, saw that, went to change it, got distracted, and then hit post, and went back to the distraction. Thanks. And thanks to you too Grant.

grant hutchison
2010-Feb-23, 11:21 PM
And thanks to you too Grant.I only did it for the "small world" pun.

Grant Hutchison

George
2010-Feb-23, 11:45 PM
I only did it for the "small world" pun. Nice. :) I got it. Often your posts get me a little disney.

undidly
2010-Feb-24, 10:55 AM
Gradient of Earth's gravity well?


Hi folks, I was thinking about this last night & figured someone here probably has the answer to this: At what altitude above the Earth does one start to experience noticably reduced gravity? I assume this is a gradual thing and not a situation where one would be say 30 miles above the Earth's surface and experience a full 1g, and at 31 miles experience say .01g. I was wondering how fast the gravitational pull drops off as one gains altitude.

What is this GRADIENT of which you speak?.

Tensor
2010-Feb-24, 12:12 PM
I only did it for the "small world" pun.

Grant Hutchison

That's what the thanks were for.:lol: