This morning, July 20, 2021, Blue Origin’s New Shepard rocket launched in to space for its first 11-minute passenger flight.
Congrats to Bezos and team!
HOWEVER, the commentator on one of the science channels made this statement: “The rocket needs to go high enough to reach orbit, even briefly”
A popular misconception is that orbit and outer space are the same thing – actually, I’ve written about this previously. However, I would expect a science commentator on a science-related channel to know the difference!
Just to recap:
- The Kármán Line, at 100Km (about 62 miles) above the Earth’s surface is considered for treaty purposes to be the delineator between the Earth and “outer space”. From what I can tell, New Shepard will briefly surpass this, making all of its passengers “official” astronauts.
- For reference, the International Space Station’s orbit fluctuates, but the average is about 240 miles above Earth’s surface.
- Reaching outer space doesn’t automatically mean that you are in orbit, nor that you somehow magically become weightless.
Even hundreds of thousands of miles away from the surface, any object is still within the Earth’s gravitational influence. So, if you fire a rocket straight up (perpendicular to the Earth’s surface), even hundreds or even thousands of miles in to space, eventually, the rocket will run out of fuel, and the Earth’s gravity will pull it back down.
In orbit, however, an object’s velocity parallel to the Earth’s surface creates centrifugal force which balances the pull gravity.
My understanding of New Shepard is that it will basically travel straight up, give the passengers a few minutes of weightlessness, and then return to Earth.
Although gravity will be acting on the spaceship and its passengers during the descent, the passengers will experience weightlessness (which is different than outer space and also different than orbit) because gravity acts on both nearly-equally. The state or sensation of weightlessness occurs when there are no net forces acting on the passengers, which is only true inside the ship, and only relative to the ship itself.
Although the exact height of the New Shepard’s mission isn’t listed, it is expected to go “well above” the Kármán Line. So if we were to guess 65 miles, we would be in the right ball park.
This means that New Shepard’s velocity at 65 miles above the Earth’s surface will be zero, after its rockets turn off, and gravity bleeds away all of its upward velocity. At that exact point, with gravity acting constantly, it will begin to accelerate back down to Earth. Until the ship hits turbulence in the atmosphere, or they fire their re-entry rocket, the passengers will continue to fall at an ever faster rate toward Earth, pulled by gravity, yet experiencing weightlessness within the ship.
In contrast, to attain orbit at 65 miles above the Earth’s surface, the ship would have to be travelling almost 17,780 miles per hour parallel to the Earth’s surface in order to have enough centrifugal force to exactly counter the force of gravity.
How do we go about calculating this? Glad you asked…
Force of gravity:
F = m * g
- m = mass of the object
- g = acceleration due to gravity
Centrifugal force (same as centripetal force, but in the opposite direction):
F = m * v^2 / r
- m = mass of the object
- v = linear velocity
- r = radius of the orbit (from the center of the Earth)
In orbit, the net force is zero, so:
m * g = m * v^2 / r
We quickly see that mass is irrelevant, and we can solve for v:
v = sqrt( g * r )
- sqrt = square root function
If we measure gravity and orbital radius in feet, we get orbital velocity in feet per second. To simplify things, we can use 78,545 miles per hour^2 as the acceleration due to gravity:
v = sqrt( 78545 * r )
The radius of the Earth is about 3960 miles. To find orbital velocity, we have to have the radius from the center of the Earth, which include’s the Earth’s radius plus the height above the surface:
v = sqrt( 78545 * ( 3960 + r ) )
If we plug in 65 miles, we get about 17,780 miles per hour required for orbit.
So again, good luck to Bezos and team – although you won’t be “in orbit”, you will definitely be in outer space.