How high does a rocket have to go above Earth's surface before its weight is half of what it is on Earth?

Question

How high does a rocket have to go above Earth's surface before its weight is half of what it is on Earth?

Answer 1

The weight loss not only depend on height but also on the exhaust velocity. This factor is also required for proper answer

Answer 2

Do you mean how high does it get before it loses half it's weight in fuel?

In terms of the Space Shuttle, the main external fuel tank weights over 7 times the shuttle, and the solid rocket boosters weigh almost 6 times the shuttle.  Since the shuttle is burning fuel from the external tank immediately on take off, the total weight of shuttle, external tank plus boosters will be down by 50% long before the solid rocket boosters detatch at 45.7 km, and fly off to be recovered.

For exact data, you will probably get a better answer on NASA's website. (it has a blog)

http://www.nasa.gov/home/index.html

Answer 3

Using newton's stuff about force and gravity:

F = force

m = mass of something

M = mass of the Earth

G = gravitational constant

r = distance between the earth and the something

F = ma = GMm/r^2

a = GM/r^2

Using R as the radius of the earth and g the acceleration of gravity at R:

At the surface of the earth: g = GM/R^2

We want a = g/2 which will be at some separation r. So:

a = GM/r^2 = g/2 = GM/(2R^2)

1/r^2 = 1/(2R^2)

r = SQRT(2) R

The altitude for the rocket will then be SQRT(2)R - R

Altitude = [SQRT(2) - 1](6378.137) km

Altitude = 2642 km

Answer 4

An altitude of one thousand miles, this is one quarter of the radius of Earth, gravity will be reduced by a factor of one half.