Why our satellite need escape velocity as much at 28,080km/h, when Earth gravity are less outside atmosphere and Earth rotating at 1656km/h?

Question

Hi guys, i want to know how much actual Earth gravity at outside Earth atmosphere. We all knows that Earth normal gravity inside Earth atmosphere is 9.8 meters/second^(2*time). but if we talk about gravity outside Earth atmosphere, it should be less than that, am i right?

when we go up until there's no air, it means that gravity outside there should be are so weak. even gases out there is nothing left because less gravity, isn't it?

back to my previous question, if my satellite successfully going up with drone until there's no air left on edge of Earth atmosphere, don't you think that my satellite should be already have escape velocity at 1656km/h due to Earth rotation, and if i moving my satellite with additional rocket made by fireworks stuff like i mention before to the reverse of direction of Earth rotation, don't you think that it's enough to make my satellite doesn't falls to Earth with let say 1800km/h escape velocity (Earth rotation + my rocket velocity) and keep it rotating on Earth orbit up there?

Thanks in advance..

Paula · Accepted Answer

First question
Gravity decreases with distance from Earth's center.
Earth's radius is 6,200 km
At a height of 6200k (12,400 from Earth's center) gravity will be 1/4 of surface gravity = 9.8 / 4 = 2.9 m/sec/sec
200 km above the grond, gravity will not be very much reduced from surface gravity.

Second question
No.
Your drone will just lift itself vertically.
To go into earth orbit it must increase its speed (relative to earth's surface) to about 28,000 kph. Otherwise it will just fall back down when drone motor cuts off.

This article may explain it.
https://en.wikipedia.org/wiki/Geocentric_orbit#Tangential_velocities_at_altitude
Note that the first line gives details for a point on earth's equator.
The 2nd line gives details for a satellite orbiting at sea level.
the 3rd line gives details for a low earth orbit 200 km above the ground.
Below 200 km, air resistance quickly causes a satellite's orbit to decay.

Ronald 7 · Answer

Earth's gravity stays constant
Like so does the Sun
That is why Probes exiting our Solar System like the Pioneers, Voyagers and New horizons exceed a velocity relative to Earth of over 33, 000 mph

Jeffrey K · Answer

Gravitational force has nothing to do with the atmosphere. The air mostly ends at an altitude of 100 miles, but the earth's gravity up there is still 99 % of what it is on the surface. 
The ISS is about 200 miles up and its orbital speed is 17000 mi/hr. The speed of earth's rotation at the equator is 1000 mi/hr. Using that rotation helps, but you still need to accelerate the satellite another 16000 mi/hr to put it in orbit. 
If you want it to move only at earth's rotation speed, it must be 22,000 miles high, not just a couple hundred. This is a geosynchronous orbit. But to get it up that far, fighting against gravity, takes a lot of fuel and a huge rocket.

Robert J · Answer

Escape velocity and orbital velocity are two very different things.

The strength of gravity reduces with distance, but it's not because of the atmosphere.

It's strength is proportional to the inverse square of the distance ratio.
eg. The surface of the Earth is about 4000 miles from the earths centre of gravity. You need to be 4000 miles above the surface (2x the distance) for gravity to reduce to a quarter the surface strength (divided by two squared).

40,000 miles from the centre of the earth, 10 x distance, it would be 1/100th the strength at the surface, etc.

Escape velocity is the speed that something in a ballistic path needs to travel at away from a planet or star etc. so that it never falls back; although it's slowing, it's not slowing as fast as gravity is weakening.

On the other hand, to get a satellite into orbit, as well as getting to a suitable altitude, it must also be given enough "sideways" velocity to achieve a stable orbit.

A low orbit at has a period of eg. about 90 minutes; that means over 25,000 miles (the circumference of the Earth) plus the extra distance due to altitude, in 90 mins; over 16,000 miles per hour "sideways" at release.

For a high, geostationary orbit, it needs 25,000 miles altitude and roughly (2 * 25,000 * pi) = 157,000 miles in 24 hours = roughly 6500 miles per hour lateral speed.

billrussell42 · Answer

9.8 meters/second^(2*time). ?? I suspect this is 9.8 m/s²

that value has nothing to do with atmosphere. That is the value at the surface of earth, and it decreases with height.  The table below illustrates that. it does NOT go to zero outside the atmosphere, but decreases slowly, never going to zero.

The rest of your question doesn't make sense. Yes, escape velocity goes down with height, but not as much as you think.  here is the formula:
Escape speed
V₀ = √(2GM/r)
V₀ = √(2gr) (alternate)
G = 6.673e-11 Nm²/kg²
where M is mass of earth and r is distance 
   from center of earth
g is gravity at the surface

Earth's escape velocity is 11.2 km/s or 40320 km/hr
but that is not orbital speed, which is less, as low as 7900 m/s or 28440 km/hr.

g = (3.98e8)/(h+6371)²
0 km, g = 9.80 m/s²
10 km, g = 9.78 m/s²
20 km, g = 9.75
50 km, g = 9.66
100 km, g = 9.51
200 km, g = 9.23
500 km, g = 8.44
1000 km, g = 7.33
2000 km, g = 5.69
2650 km, g = 4.9 (g/2)
5000 km, g = 3.08
10000 km, g = 1.49
400000 km (moon) g = 0.002

Anonymous · Answer

You say 'dont you think' a lot. But at the end of the day, the few thousand satellites orbiting earth are evidence that we think you are wrong.

To maintain an orbit, the satellite is in a constant state of falling to earth but moving just fast enough that it's orbit path doesn't collide with the planet and not too fast so that it escapes orbit and flies off.

This speed os relative to the altitude.

Gravity doesn't just fall off suddenly outside the atmosphere, it slowly and linearly decreases with range/altitude. But the key thing here is lack of drag. Inside the atmosphere thrust must be constant to maintain a constant speed as a satellite has to push against atmospheric drag. As soon you are clear of (most of) the atmosphere you can establish an orbital velocity thst is appropriate for your altitude without any further thrust. This velocity, again is relative to the altitude of the orbit.

Gravity has infinite range, but linearly decreases in strength dependent on altitude.

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Why our satellite need escape velocity as much at 28,080km/h, when Earth gravity are less outside atmosphere and Earth rotating at 1656km/h?

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