Does the Earth's gravitational field have height? If so how high is it?

Question

Objects at a certain velocity can escape the Earth's gravitational field. However, I want to know whether there is a certain height as well. I am trying to find the work done when a rocket escapes Earth's gravitational field, using the formula W=fs.

If it doesnt have height, then why is there an "escape velocity" ?

V=sqrt((2GM)/R)
=sqrt((2*6.67E-11)*(5.97E24))/6378100
=11174.27m/s

where G=newtons gravitational constant
M= Mass of Earth
R= radius of Earth

Answer 1

Earth's gravitational field has no "height".

In fact, Earth doesn't "have" a gravitational field at all. There's really only one gravitational field, and it permeates the entire universe. Objects with mass change the value of that field, such that, generally, gravitational acceleration reduces with the square of the distance from an object with mass.

If you have more than one mass (as we do in the...universe), the value of the gravitational field at any point is the sum of the values caused by the "individual" fields of all the masses at that point.

Answer 2

There's a three-body problem that I think they don't have an analytical solution for -- only numerical solutions -- that I think about sometimes.

Suppose you're floating in space somewhere. Will you fall toward the moon, toward the earth, or toward the sun? Is there a place where the three gravitational fields cancel each other out, even if it's an unstable equilibrium?

The moon is constantly falling toward the earth -- that's why it stays in orbit -- and the earth-moon centroid is constantly falling toward the sun.

But forgetting the moon and Mars for a moment, is there a place in space where you'd escape Earth's gravitational field and start falling, say, toward Jupiter?

I think there is, and it's proportional to m/d^2, where m is the mass of Earth or Jupiter, and d is the distance to either planet. The problem with this, of course, is that the distance between Earth and Jupiter is constantly changing.

Anyway, these are just some thoughts somewhat related to this question.

(BTW, there is something called the "heliopause", I think, which is the practical limit of the sun's gravitational field. It's somewhere beyond Pluto and the Van Allen (?) belt, and some speceship has gone beyond it, effectively leaving the solar system. If it gets beyond the Milky Way, maybe it'll start falling toward Andromeda.))

Answer 3

Here's where you want calculus. Work is the integral of the product of force and the distance over which it is applied. Since the gravitational force is inversely proportional to the square of the distance, it never reaches zero. So, only the integral will give you the answer.

An object travelling at exactly the escape velocity will keep travelling for infinite distance and infinite time. It will never stop, but neither will it reverse its direction.

At least according to Newton, the earth's gravitational field has infinite height.

Answer 4

Gravity is technically an infinite force, but it does decrease with distance. The outermost limit where a local gravitational force maintains it's own identity is the Hill Sphere. In the case of the Earth, our planet's Hill Sphere extends to about 0.01 AU, or about 930,000 miles from our planets center of gravity. Beyond that, the gravitational forces of the sun take over.

The larger the mass of the planet, and the further away from the sun, the larger the Hill Sphere.

Answer 5

Theoretically the range of any gravitational field is infinite, but the strength of the field will decrease as distance from its source increases. On Earth's surface (12,756 km from its center) the gravitational field exerts an acceleration of 9.81 meters sec/sec.

The equation to determine gravitational acceleration --
g = G * m / r^2

'G' is the gravitational constant (6.673^ minus 11)
'm' is mass of object generating gravitational energy
'r' is the distance from the gravity source

Since the range of gravity is infinite, the above equation will never solve for zero.

Answer 6

The field of gravity goes on indefinitely, forever. But is gets so weak that it becomes immeasurable.
Its force diminishes to the square of the distance. At twice the distance, 1/4 the power.
Escape velocity for a projectile is 7 1/2 miles/sec
The moon at an average distance of 382500 km (237725.30 miles) still falls around the earth due to earth's gravity.

Answer 7

there's a gravitational tension and a Magnetic container. For gravity, Jupiters tension of gravity is 23.6N/kg whilst in comparison with Earth's 9.8 N/kg.(in different words, plenty greater desirable than earths as a results of its huge length; Jupiter is approximately 11 situations greater desirable in diameter than earth) Magentic fields repel numerous the risky photograph voltaic radiation that comes from our sunlight (the Northern lights fixtures are rather those magnetic container bouncing the photograph voltaic radiation removed from the planet). whilst in comparison with Earth, Jupiters magnetic container is approximately 10-situations greater desirable, despite the fact that it extremely is a gas super and it extremely is unknown if there's a sturdy floor below, despite the fact that it extremely is nicely assumed that there is none). desire this helps Z

Answer 8

It certainly reaches out well beyond our moon...