Gravity and notes about Kittinger's jump

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Circular Earth orbits

Velocity required for orbit is independent of mass and size. A lead bullet orbits at the same velocity as a feather.

The force of the Moon's gravity is 83.3% (or 5/6) less than Earth's force of g. It is less dense, so difference in size does not correspond to difference in g. So if you weigh 175 pounds on Earth you would weigh about 30 pounds on the Moon.

   The Moon is 1/4 of the diameter of the Earth.
   mass of the Moon = 7.36 * 10^22 kilograms
   mass of Earth    = 5.97 * 10^24 kilograms
   Radius of Earth  = 6378 kilometers, 3963 miles

The force of the Earth's gravity (g) at various places:

   g at San Francisco:  9.800 m / s^2
   g at Denver:         9.796 m / s^2
   g at North Pole:     9.832 m / s^2

Edge of space -- “Karman Line”

This is the point where air is so thin that aerodynamic control surfaces are not useful. This definition is still rather arbitrary. NASA uses 122 kilometers as their definition of "re-entry" for the Space Shuttle. This is when it's time to start paying attention to aerodynamics and start using aerodynamic control surfaces for maneuvering. In practice air drag will still be significant much higher than this, so it is not practical to orbit a satellite at the Karman Line because air drag will quickly pull it back to Earth.

   Karman Line altitude:            100 kilometers,   62 miles
   radius:                          6478 kilometers, 4025 miles
   g at this altitude:              9.49 m / s^2

The first artificial satellite, Sputnik-1, has a perigee of 215 kilometers. It's orbit lasted only 3 months before it reentered the atmosphere. It had an eccentric orbit with an apogee (highest altitude) of 939 km, so it presumably suffered less air drag than a satellite in a nearly circular orbit close to 215 km. Yuri Gagarin's, the first human to orbit the Earth had an orbit with the perigee (minimum altitude) of 169 km.

Edge of space -- gravitational influence of the Earth

If going by nearest gravitational source then you have to go about 21 million kilometers away from the Earth for it to no longer be the most significant gravitational body. This is the distance where the strongest gravitational source is no longer the Earth. For reference, the average distance from the Earth to the Sun is 150 million kilometers (also called 1 Astronomical Unit).

Lowest practical orbit

A practical minimum altitude is depends on your definition of practical. At 180 kilometers a satellite can orbit only a few hours before atmospheric drag will bring it back to Earth. The International Space Station (ISS) orbits at a minimum of 340 kilometers. At this altitude its orbit decays about 2 km/month. The ISS has about one of the lowest altitudes of any orbiting artificial body. If you want a satellite to stay in orbit more than a few days without the need for boosts to counteract orbital decay then 200 kilometers is a good start.

   altitude:           200 kilometers, 124 miles
   radius:             6578 kilometers, 4087 miles
   g at this altitude: 9.20677898 m / s^2

Other interesting orbits and the force of g

About half the satellites in orbit are under 1000 kilometers in altitude.

   altitude:           1000 milometers, 621 miles
   radius:             7378 kilometesr, 4585 miles
   g at this altitude: 7.31843389 m / s^2
                       about 75% of Earth at sea level

GPS Satellite orbital altitude: 20200 km, 12551 miles

                       radius: 26560 km, 14018 miles
           g at this altitude: 0.01 m/s^2

Geostationary orbit (orbital velocity in sync with revolution of the Earth):

   geostationary altitude: 42300 km, 26284 miles
   g at this altitude:     0.0025 m/s^2

Moon orbit:

   384403 kilometres, 238857 miles
   g at this altitude:  not fair because the Moon's gravity comes into play.

Gravity and the force it causes

The Gravitational constant, G, is the same throughout the entire universe.

   G = 6.673 × 10^-11 m^3/kg*s^2
   G = 6.673 × 10^-11 m^3 kg^-1 s^-2

Note that g, force of Earth's Gravity, is calculated from your Altitude, A, as follows:

   g = G * MassEarth / RadiusOrbit^2
     = 6.673 * 10^-11 m^3 kg^-1 s^-2 *  5.97 * 10^24 kg / (6378 km + ALTITUDE km) ^ 2
     = (ALTITUDE km + 6378 km) ^-2 * 6.673 * 10^-11 m^3 kg^-1 s^-2 *  5.97 * 10^24 kg

Also note that you can copy that formula directly into Google search and it will calculate the force of g for you. Replace ALTITUDE with the altitude you want to find. You MUST NOT forget the units; in this case "100 km", not just "100":

     (100 km + 6378 km) ^-2 * 6.673 * 10^-11 m^3 kg^-1 s^-2 *  5.97 * 10^24 kg

Google will give you:

       = 9.49322051 m / s^2

Joseph Kittinger

On August 16, 1960, Captain Joseph Kittinger made a jump from the Excelsior III at 31.3 kilometers, 19.4 miles, 102800 feet.

   g at this altitude: 9.7 m / s^2

The force of gravity at 31 km is about 97% of what you feel at sea level. Kittinger was about 3% lighter than on the ground. So if he was 180 pounds on the ground he would be about 175 pounds at 31 kilometers.