Given mass of an object as M, what is the velocity needed for that object to beat earth's gravitational pull

Question

Given mass of an object as M, what is the velocity needed for that object to beat earth's gravitational pull. I am looking for the formula

Answer 1

i think that if u imagine a sky-rocket that we launch it so here: F=Ma that "a"must be >9.8 because it must beat earth's gravity.so here we don't need to calculate the velocity. :)

Answer 2

Escape velocity is derived from the formula of escape enregy, that is the energy needed for an object to escape earths gravity. It is calcualted with this formula:

Wf= G* ((Mm)/r0)

Where M is the mass of earth, m is the mass of the object, r0 is the distance to earths center and G is the gravitational constant.
This is the kinetic energy which is calulated from the formula:

(m*v^2)/2

We can use this formula to get the velocity needed. We know the escapeenergy formula and so they have to be equal.

(m*v^2)/2 = G*((Mm)/r0)

So there is v for velocity. Lets drag it out. But first we simplify. Note that m is on both sides of the equalsign. Away it goes!

vf= scrrt((2GM)/r0) (sorry. Can´t write the squareroot sign here..)
So since we took out the mass of the object from the equation it isn´t needed any more. So let´s see what we get.
r0 = 6.378*10^6 meter
M = 5.974*10^24 kg
G = 6.668*10^-11 N m^1 kg^-2

I got 11176 meter/second or 11 km/s.

Answer 3

In physics, escape velocity is the speed where the kinetic energy of an object is equal in magnitude to its potential energy in a gravitational field.

Objects which have velocity v = √ [2gr=11201m/s on the earth's surface will escape from the gravitational pull.

Due to the atmosphere it is not possible to give an object near the surface of the Earth a speed of 11.2 km/s, and would cause most objects to burn up due to atmospheric friction.
For an actual escape orbit a spacecraft is first placed in low Earth orbit and then accelerated to the escape velocity at that altitude, which is a little less, 10.9 km/s. The required acceleration, however, is generally even less because from that sort of an orbit the spacecraft already has a speed of 8 km/s.

Answer 4

The velocity of escape at the surface of the Earh is calculated as the Square root of the gravitational potential.
The gravitational energy beween two masses is as follows;
E =2 G M x m/ R

Gravitational potential = E/m =2Gm/R

The escape velocity = (2 GM/R)^1/2 =Ve

The Gravity power to escape the earth gravity power is equal to the gravity force times the escape velocity.

Gravity force between mass m & mass M,F= G x Mxm/R^2

Escape power =F x Ve

Where G is Newton Universal Gravitational constant
and Where M is the Mass of the Earth
R is the Radius of the Earth
m is the escaping mass.
F =Gravity force between mass of the earth and the escaping mass.
Ve = escape velocity of mass m.

Therefore it takes a cerain amount of Power applied on mass "m" to overcome the Gravity power which is holding mass m on the surface of the Earth. And the escape power must be applied within an escape time equal to The escape velocity divided by the acceleration at the surface of the Earth.

So we have the Equations of escape Power ,escape Time and escape Velocity for a mass to escape the Earth's Gravity field.

Answer 5

In order that an object of mass M at rest may beat earth's gravitational pull, it should be given K.E. equal in magnitude to its negative P.E. on earth
=> (1/2) Mv^2 = GMM' / R,
where M' = mass of earth and R = radius of earth.

=> v = √(2GM'/R) = √(2GM'R/R^2) = √(2gR)
=> v = √(2 * 9.8 * 6400 * 10^3) = 14 x 8 x 100 m/s
= 11.2 km/s
[Note that the velocity is independent of mass.]

Answer 6

w=mg (weight force = mass * gravity)
N = kg * m.s^-2

it is not a velocity that causes an object to beat the earth's gravity, it is a force.

so the force required would be at least 9.8 * M. This formula does not take into account air resistance.

However Wikipedia says that the escape velocity is 40270 km/h (11186ms^-1), in case that's what you're looking for.

Answer 7

ANS :- (2GM/R)^1/2
where G---->Gravitational constant = 6.67*10^-11
M----> Mass of body to be projected
R -----> Radius of earth

Answer 8

its' called escape velocity and is independent of mass

for the earth i think its about 11km/s but the atmosphere would mess it up a lot


this isnt what shuttles or rockets do, its just the initial speed that'll get you into deep space

Answer 9

regarless of mass the escape velocity from Earth is 6.9 miles per second.