GreyOwl40 Loc: Quebec City

It has nothing to do with fuel consumption or rockets. Escape velocity is the velocity required to propel an object away from, in our case, the earth so that it never returns. Think of throwing a ball straight up into the air. At what speed would the ball have to leave your hand so as to never to come back down.

Fotoartist Loc: Detroit, Michigan

I see there are a lot of rocket scientists on the UHH after all.

johngault007 Loc: Florida Panhandle

Or played too many hours of Kerbal Space Program.

Which is basically a rocket science simulator with fun graphics.

Longshadow Loc: Audubon, PA, United States

A ball has a single initial velocity. It would require an immense initial velocity because there would be no continued propulsion to escape (go into space, and how far). Depending on how far it went (its stopping point), if insufficient, it would eventually return to earth because of the gravitational pull, even so minuscule. It might take a long time though.

A rocket can maintain a velocity as long as its fuel exists.
An object can escape gravity, straight up, traveling at any speed, it just depends on having sufficient fuel for the distance and time required to do so.

Now to put something in orbit, whether stationery or moving, is different. It requires a certain speed to do so, depending on the altitude of the orbit. Geostationary orbits require the matching of the earth's rotational speed (which would be higher for higher altitudes) , geocentric, faster.

It's a lot more complicated that just shooting something out there.

skyscapes Loc: Portland, Ore

In physics, Force = Mass * Acceleration, or for your question, Acceleration = Force/Mass. Force is provided by your rocket's engines, Mass is the total weight of the rocket structure (propellant tanks, engines, etc.), remaining fuel, and the payload at any point in time.

To leave the earth's surface, you need to:
a) overcome earth's gravity just to leave the launch pad, then
b) get beyond the atmosphere (source of drag) and gaining sufficient velocity to stay up (either into orbit or escape velocity.)

The more time you spend gaining velocity to get to orbital velocity (slow acceleration) the more fuel you burn doing nothing but holding off earth's gravity, which means you need more fuel, which means you have more mass, which means you need still more fuel to lift the additional mass, which means...

The 2018 SpaceX Falcon Heavy Rocket weighed 13,000 pounds to launch a 2,900 pound Tesla into solar orbit. That is 78% rocket and 22% payload. The Apollo moon mission were 99% rocket / 1% payload.

Additionally, you also need to take into consideration air resistance as the rocket leaves the atmosphere (go slow where the air is thickest at sea level, and faster as the air thins higher up.) Some rockets have to reduce their thrust as their speed increases to minimize the maximum aerodynamic drag (saves weight by not having to make the rocket as strong), then increase thrust again as the atmosphere continues to thin. See "Max Q."

Interesting note on the slow-but-steady acceleration front: they are running experiments using a solar sail for propulsion. The net acceleration observed is comparable to the weight of a paper clip, but you don't have to carry any fuel (pressure from sunlight provides the push.) Once you are in orbit, the small acceleration strategy becomes possible. Check out the Solar Sail project: http://www.planetary.org/explore/projects/lightsail-solar-sailing/lightsail-mission-control.html

skyscapes Loc: Portland, Ore

Universal law of gravitation: F = Gm1m2/r^2, where F is the force due to gravity, between two masses (m1 and m2), which are a distance r apart; G is the gravitational constant.

Gravitational pull is inversely proportional to the square of the distance between two bodies. If your ball goes far enough, the pull from earth continues to exist, but is negligible to other forces (planets, suns, et al) acting on the ball. So the ball does not return.

Longshadow Loc: Audubon, PA, United States

Key operator: "if the ball goes far enough".

GreyOwl40 Loc: Quebec City

To find escape velocity, neglecting air resistance and the gravitational pull of other celestial bodies, one solves a separable differential equation. This turns out to be about 11,186 m/sec.

skyscapes Loc: Portland, Ore

The immense initial velocity required is about 25,000 mph (7 miles every second.)

My photography is better than my rocketry.

SteveR Loc: Michigan

Escape velocity? Depends on how fast the dog can run.

Longshadow Loc: Audubon, PA, United States

I was tempted...
Thanks for figuring that out!

jeep_daddy Loc: Prescott AZ

It has something to do with the speed at which the earth turns. And, it's closer to 26,000 mph not 25,000.

sb Loc: Florida's East Coast

"Space" means different heights for different uses. The ISS is in a low orbit at about 125 miles or so. It is going fast enough to stay at that low altitude and not fall back into the atmosphere of earth. Communications and weather satellites can be launched up to 22,500 miles where the speed required to orbit the earth puts them rotating the earth at the same speed that the earth rotates, so they stay over the same spot on land continuously - tis is called "geosynchronous orbit". A rocket could go straight up to escape earth's gravity, but it is easier to get up and get positioned in orbit and then fire booster rockets at the right time to escape orbit.

HOHIMER

Careful! Escape velocity is a function of earth’s gravity not earth’s rotational speed.
It is true earth’s rotational speed (about 1000 mph) is used to add this amount of velocity to an object being propelled into orbit or space (saves on fuel).

Wes Loc: Dallas

Calculate the escape velocity of earth if its mass is 5.972 \times 1024 kg and has radius of 6371 km.
Solution:

Given: Mass of earth M = 5.972 \times 1024 kg, radius of earth R = 6371 km, W.k.t the gravitational constant G = 6.67 \times 10-11 m3 /kg/s2

The Escape velocity formula is given by,

Ve = 2GMR‾‾‾‾√


Ve
= 2×6.67×10−11×5.972×10246371×103m‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√
2
×
6.67
×
10
−
11
×
5.972
×
10
24
6371
×
10
3
m


Ve
e
= 11.18 km/s