What speed must a rocket maintain to escape the Earth's gravitational field and why?

Question

science homework..

Answer 1

I don't think there would be any minimum speed.  There would be a minimum force, dependent on the mass of the rocket (The force would have to counteract gravity, and hence be greater than mg).  But unless you assumed the rocket would run out of fuel at some point and go off it's inertia after that, it wouldn't matter how slow the rocket moved as long as it kept moving upwards.

You would also need to define what you mean by escaping the Earth's gravitational field, since technically you never escape it, it just becomes insignificant.

Answer 2

http://en.wikipedia.org/wiki/Escape_velo...

Answer 3

Usually, one solves this problem by integrating the force*distance function (work) to calculate the initial velocity needed to escape the earth's pull.  (it involves calculus).  The answer works out to about 11.4 km/sec (if memory serves).

EDIT: Sorry, 11.2 km/sec

The velocity (solved below) is...v = SQRT(2GMe/R)

G=univeral gravity constant; R=earth's radius; Me=mass earth

Assuming you are using calculus to solve this...

Integrate Fdx from R to infinity (where R  radius of earth)

F = GMe*m/x^2 * dx  (G = universal gravity constant and Me is the mass of earth)

The integral evaluates to -GMe*m/x and the limits are infinity and R

So the work needed is 0--GMe*m/R = GMe*m/R

Set thids equal to the energy of the rocked at launch = 1/2 m*v^2 and solve for velocity (escape)

v = SQRT(2GMe/R)  Now that the "heavy lifting" is done, just plug and chug.  Look up G amd Me and R and use your trusty ol' calculator.

-Fred

You can also solve this using energy considerations without calculus.  An excellent source for physics without calculus is Beiser's (Arthur) "Physics".

G = 6.670 E-11 N m^2/kg^2

R=6.38 E6 meters

Me=5.98 E24 kg

Plug these in and find that 11.2 km/s is iondeed the correct value of velocity needed to "throw" something out of earth's gravity field.

EDIT: "Doctor" below me is "all wet".  The initial velocity needed by a rocket to escape earth's gravity field is correctly outlined above.  There is no need to consider fuel of any other nonsense.