Justin A. Parr - Technologist

I was recently asked these questions:

• What’s the difference  between ‘outer space’ and ‘orbit’?
• Does gravity stop in outer space?
• Why do spacecraft heat up when they come out of orbit?
• What’s the difference between a spaceship heating up on re-entry, and a meteor that burns up?

Read on, for an explanation.

 

 

Outer Space

First let’s define “outer space”.

Empty space starts where the Earth’s atmosphere no longer has any influence.

The Earth’s atmosphere consists of five layers, stacked like a cake above the Earth’s surface, where each successive layer has a much lower density of gas particles.

Troposphere 0 to 7 miles	The troposphere is the lowest layer of Earth’s atmosphere. We live in the troposphere, and most activities on Earth take place here.
Stratosphere 7 to 31 miles	The stratosphere is located above the troposphere. The stratosphere is the highest layer of the atmosphere that’s accessible to jet-powered aircraft, and also contains the ozone layer.
Mesosphere 31 to 50 miles	Above the stratosphere, the mesosphere is too high to allow aerodynamic flight, but too low to allow for a stable orbit.
Thermosphere 50 to 440 miles	The thermosphere, located above the mesosphere, constantly varies in height by almost 300 miles due to solar influence. The lower part of the thermosphere contains the ionosphere. Both the International Space Station (ISS) at 200 to 240 miles, and the Hubble Telescope at 340 miles orbit Earth within the thermosphere.
Exosphere 440 to 6,200 miles	The exosphere is the last part of Earth’s atmosphere, beyond which, there is only “empty space”. Most satellites orbit the Earth within the exosphere.

“Space” starts inside the thermosphere, at about 60 miles above the Earth’s surface, and extends through the exosphere, to empty space, where gas particles from Earth’s atmosphere are no longer present.

The Hubble Telescope and International Space Station have what is known as a Low Earth Orbit (LEO), and LEO satellites can range from about 100 miles above the surface, up to about 1,200 miles above Earth’s surface, or well in to the exosphere.

Intermediate or Medium Earth Orbit (MEO) extends from about 1,200 miles above the surface, up to geosynchronous orbit at 22,236 miles.  Satellites in MEO are used mostly for navigation and communication, and MEO extends from the early part of the exosphere well in to empty space.

Geosynchronous orbit (22,236 miles) is the point where an object in stable orbit revolves around the Earth once in 24 hours, meaning that the object is directly over the same spot on Earth at all times.

Above geosynchronous orbit is High Earth Orbit (HEO), which is less commonly used.

The moon orbits Earth at a distance of about 239,000 miles.

When we talk about “outer space”, there are several definitions.  For treaty purposes, the Kármán Line, at 100 km (62 miles) above the Earth’s surface is considered to be “outer” space.

From a practical standpoint, we can consider “outer” space to begin somewhere in the exosphere, and extend in to empty space.

 

 

Where Does (the Earth’s) Gravity Stop?

The simple answer is that it doesn’t!

At the Earth’s surface, the acceleration due to gravity is about 32 feet per second per second.

An object dropped from some arbitrary height will be falling at 32 feet per second (about 22 miles per hour) after the first second, but will gain an additional 32 feet per second for each additional second that it falls!  Assuming no wind drag, after 10 seconds of falling to Earth, an object would be traveling at 10 * 32 or about 320 feet per second.  This constant change in velocity is called acceleration.

Newton’s second law states that:

F = m * a

Force = mass * acceleration.

The acceleration due to gravity is a constant, which means that more massive objects are attracted to Earth with a greater force.

Acceleration is a function of the Earth’s gravitational field, which can be calculated from its mass, and the distance from its center.

Newton’s universal law of gravitation:

F = G * (m1 * m2) / r^2

The force of gravity is equal to G, which is the universal gravitational constant, times the product of the two masses, divided by the square of the distance between them.

The gravitational (acceleration) field of any mass can be calculated by simply dividing by m2:

F / m2 = G * m1 / r^2

We know that F = m2 * a, and therefore a = F / m2.

Therefore, we can substitute “a” (acceleration) for F/ m2:

a = G * m1 / r^2

M1, the mass of the Earth is about 5.972 × 10^24 kg.

G, the universal gravitational constant, is about 6.67 x 10^-11 (in metric units).

If we substitute r for the radius of the Earth in meters, or 6.371 x 10^6 meters:

a = 6.67 x 10^-11 * 5.972 x 10^24 / (6.371 x 10^6)^2

a = 6.67 x 10^-11 * 5.972 x 10^24 / 4.059 x 10^13

a = 9.81 m / s^2

To go from meters to feet, multiply by 3.3:

a = 9.81 m / s^2 * 3.3

a = 32 feet / s^2

As we can see, we get 32 fps^2, or the standard acceleration due to gravity.

To calculate the gravitational field at any arbitrary height above Earth:

1. Convert Miles to meters (multiply by 1600)
2. Add meters to the radius of the Earth:  m + 6.371 x 10^6
3. Execute Newton’s formula:
   a = 6.67 x 10^-11 * 5.972 x 10^24 / (m + 6.371 x 10^6)^2
4. Convert meters / s^2 to feet / s^2 by multiplying a * 3.3

Side Note:  I could do the entire calculation in either customary or SI units.  The reason I’m converting back and forth… for better or worse, people in the US think in customary units.  If you say to Americans, “I’m 1.6 meters tall, I weigh 60kg, and it’s 34C outside”, our heads will explode.  If you say, “my living room is about 30 feet long, my dog weighs 50 lb, and room temperature is 72F”, we know exactly what you mean.  Converting “G” to customary units without making some kind of error makes my head spin, so it’s easier to treat the whole thing as a black box, and then convert back and forth.

Here is the acceleration due to Earth’s gravity at various distances from the Earth’s surface:

Height (mi) above sea level	Feet	Meters	a (m/ss)	a (f/ss)	150lb man
0 Earth’s Surface	0	0	9.81	32.39	150.00
0.52 World’s Tallest Building	2722	825	9.81	32.38	149.96
7 Start of Stratosphere	36960	11200	9.78	32.27	149.47
9 Typical commercial jet flight	45000	13636	9.77	32.25	149.36
200 ISS Orbit	1056000	320000	8.90	29.36	136.00
340 Hubble Orbit	1795200	544000	8.33	27.49	127.33
440 Start of Exosphere	2323200	704000	7.96	26.26	121.63
6,200 Start of Empty Space	32736000	9920000	1.50	4.95	22.94
22,236 Geosynchronous orbit	117406080	35577600	0.23	0.75	3.46
239,000 Moon orbit	1261920000	382400000	0.00	0.01	0.04

As you can see, even standing on top of the world’s tallest building, the Earth’s gravity would only affect you 1/100 less than at sea level, and you would only weigh a mere 1/25 of 1 pound less than normal.

The highest altitude that most of us will travel to, is about 45,000 feet – the typical altitude of a commercial jet airliner.  Airplanes are constantly under acceleration, and thus you probably won’t notice that you weigh about 1/2 pound less than normal.

Even at the orbit of the ISS, you’d still weigh 136 pounds.

At the start of empty space, you’d still weigh 23 pounds.

Even at geosynchronous orbit, you’d weigh 3.5 pounds, which is not “weightless”.

Even at the moon’s orbit from Earth (not IN orbit of the moon), you’d weigh SOMETHING…. even though your weight of 1/25 of  a pound would mean that it takes 22 seconds for the Earth to pull you a mere 10 feet… you would STILL WEIGH SOMETHING.

 

 

So How Does Weightlessness Work?

The sensation of weightlessness is a result of every force being in balance, and thus there are no unbalanced forces acting on you.

This is where Orbit comes in to play.

Although it’s quite an incredible technical achievement to reach space, we’ve shown that gravity would still pull you right back down.  You’d have a few microseconds of weightlessness, as the force pushing you “up” slowly runs out, and is momentarily balanced by the force of gravity (resulting in no net force, or weightlessness), to be immediately replaced by the sensation of Earth beginning to pull you back down.

In “A”, we see that the force of the rocket (red arrow) exceeds the force of gravity (black arrow), resulting in upward movement.

In “B”, as the rocket begins to run out of fuel, the two forces are momentarily equal, providing a few microseconds of weightlessness.

In “C”, the force of gravity begins to take over, as you fall back to Earth

In “D”, the rocket is completely expended, and only the force of gravity acts on your spaceship.

In order to be truly weightless, you need a force that exactly counterbalances gravity, caused by being in a stable orbit.

In orbit, your spacecraft’s momentum perpendicular to the Earth’s surface (green) causes centrifugal acceleration (red) equal to the centripetal acceleration created by Earth’s gravitational force (black).

In other words, you have to be going sideways, REALLY FAST, to be in orbit around the Earth, and the momentum of your spacecraft tends to travel in a straight line.  Gravity exactly counteracts that momentum, resulting in a perfectly-balanced force, or zero net force.

You are constantly accelerating toward Earth due to Earth’s gravity, but your spacecraft’s momentum perpendicular to Earth’s surface causes you to continually miss, as you pass by it.

When you’re in a car that takes a left turn, you feel centrifugal acceleration forcing you to the right, as the car turns.  This is really your body’s momentum trying to keep moving “forward” in the original direction it was traveling.

Likewise, in orbit, your spaceship is constantly turning left (or right), and this force is exactly balancing the force of gravity that is trying to pull you back to Earth.

Momentum is a measurement of Newton’s first law – the tendency of an object in motion to remain in motion (in the same direction) unless acted upon by an outside force.

Momentum is the energy your spaceship has built up, in the form of velocity.  The faster your ship is moving, the more momentum your ship has.

If your ship has too little energy, the resulting centrifugal force is less than gravity, and your ship will slowly start to spiral toward Earth, and you would perceive an unbalanced force pulling you toward Earth.

If your ship has too much energy, the resulting centrifugal force is stronger than gravity, and your ship will slowly start to spiral outward, toward space, and you would perceive an unbalanced force pushing you away from Earth.

When the two forces are exactly balanced, you feel no force, which you perceive as being weightless.

 

The Effect of Acceleration

Any unbalanced acceleration, such as firing your ship’s rockets, will disrupt the “weightlessness”, just as turning left in a moving car causes you to perceive a force pulling you to the right – the unbalanced force appears to “pull” you in the direction opposite of the rocket’s thrust.

 

 

Reaching Orbit vs. Reaching Space

As you can see, it takes a WHOLE LOT more energy to reach orbit, as compared to touching outer space.

We’ve seen that if your spaceship simply takes you “up to space”, you’ll eventually lose momentum, experience a few microseconds of weightlessness, and then fall back to Earth.

In order to stay up in space, and experience weightlessness, you must enter orbit.

In “E”, we see your rocket travel straight up.  As we’ve seen, it will eventually lose momentum, and fall back to Earth.  The amount of energy your spaceship is capable of expending must provide enough force (red arrow) to counteract the gravitational force for sufficient time for the spaceship to reach space.

In “F”, to reach orbit, not only must your spaceship counteract gravity for sufficient time to reach space, but it must also build momentum perpendicular to the force of gravity.  The path along the red arrow is significantly longer in “F” versus “E”.

 

 

Why Do Spaceships Heat Up When Coming Out of Orbit?

As we discussed, beyond simply reaching space, being in orbit means that your spaceship has momentum perpendicular to Earth’s surface, that creates centrifugal force and counteracts Earth’s gravity.

Although higher orbits require less momentum, they require significantly more energy (in the form of fuel) to counteract gravity.

Lower orbits are more economical, because, even though they require more momentum, less fuel is required to counteract gravity.

Even the ISS, at a very low orbit of 200 to 240 miles, must be traveling at a linear velocity (perpendicular to Earth’s surface) of over 17,000 miles per hour, in order to counteract gravity.

Just as reaching a stable orbit is more complicated than “reaching space”, dropping out of orbit and landing on Earth is a much more technically-complicated task, than simply pointing toward the Earth’s surface and firing the rocket engines.

This task is further complicated by the fact that most spaceships, such as the space shuttle, expend the majority of their fuel during takeoff, counteracting gravity while building enough momentum to reach orbit.

When it comes time to “drop out” of orbit, there isn’t enough fuel to fire the rockets, and accelerate for enough time in the opposite direction of motion, and thus “bleed off” enough momentum to land.

In a car, you can apply the brakes, which uses friction to stop the car’s horizontal motion.  In a plane, you can increase pitch and reduce thrust in order to create drag, in order to slow down the aircraft.

In a spaceship, you don’t have the luxury of “brakes” — the only way to slow down is to create an unbalanced force that bleeds off the spaceship’s momentum.

Instead, the pilot (and computer) very carefully select a re-entry vector that’s designed to move the spaceship in to the Earth’s atmosphere, and in to a strategic position such that the atmosphere, through Newton’s third law (every force has an equal and opposite force), pushes back on the spaceship.

As soon as the spaceship hits the mesosphere, the force of air pushing against the spaceship is converted to heat through friction, and bleeds off the spaceship’s momentum, decelerating the spaceship.

In essence, the reason spaceships heat up upon re-entry, is that they need to bleed off the tremendous kinetic energy that was used to remain in orbit, trading it for heat energy.

If the spaceship hits the mesosphere at too shallow of an angle, the atmosphere could actually push back with enough force to cause the spaceship to “skip off” and head away from Earth.

If the spaceship hits the mesosphere at too steep of an angle, the spaceship won’t lose enough momentum, and thus it will retain too high of a velocity, and could hit the ground with enough force to destroy the spaceship and kill the crew.

 

 

What’s the Difference Between Re-Entry and a Meteor Burning Up?

In essence, they are very similar.

A spacecraft starts in a stable orbit, where linear momentum perpendicular to Earth’s surface is used to counteract gravity through centrifugal force.

In the case of a meteor burning up in Earth’s atmosphere, there are quire a few more variables.

A spaceship could be traveling at tens of thousands of miles per hour, while a meteor could be traveling at hundreds of thousands of miles per hour.

A spaceship is primarily negotiating Earth’s gravity, while a meteor could be affected by gravity from the Earth, Moon, Sun, Jupiter, or all four.

A spaceship enters the mesosphere at a carefully-selected angle, but a meteor’s trajectory is a nearly random product of whatever forces brought it in contact with the Earth.

In general, meteors will hit the atmosphere moving much faster, will create much more heat, will decelerate much more quickly, they could break up in to multiple chunks, and each chunk could still hit the ground with the energy of an atomic bomb!

Most of the meteors we see are tiny – they hit the mesosphere with enough force that they burn up completely.

Occasionally, a meteor will be large enough, or hit the atmosphere at just the right angle to survive being vaporized.

In general, meteors hit the atmosphere with millions of times more energy than a spaceship.

 

 

Conclusion

• What’s the difference  between ‘outer space’ and ‘orbit’?
  Answer:  Outer space begins somewhere around 1,200 miles above the Earth.  Orbit occurs when an object’s momentum perpendicular to the Earth’s surface creates sufficient centrifugal force to counteract Earth’s gravity.  The ISS (200 mi) and Hubble Telescope (350 mi) are in orbit within the thermosphere.
• Does gravity stop in outer space?
  Answer:  No.  Weightlessness occurs when all forces are balanced, such as when a spaceship is in a stable orbit.
• Why do spacecraft heat up when they come out of orbit?
  Answer:  This is necessary, and carefully calculated in order to bleed off momentum, in order for the spaceship to land safely.
• What’s the difference between a spaceship heating up on re-entry, and a meteor?
  Answer:  A meteor follows a random trajectory, and could have millions of times more energy than a spaceship.