- The projectile
is as aforesaid a test particle: i.e.,
an object of
negligible mass
compared to the Earth,
and so it does
**NOT**affect the Earth's motion at all. - As the image implies,
as launch velocity increases
(v↑),
the projectile
orbit is as follows:
- A: a parabolic trajectory crashing into the Earth.
- B: like A, but with a longer trajectory.
- C: a circular orbit,
- D: an elliptical orbit,
- E: an escape orbit which may be just at escape velocity leading to a parabolic orbit or may be above escape velocity leading to a hyperbolic orbit.

See the mathematical description of Newton's cannonball thought experiment (or Gedanken experiment) below.

- The image shows that being in orbit
is actually being perpetually in
free fall, but always
**NOT**hitting the orbited astro-body. The literal truth.You keep missing because you have velocity component

**NOT**aimed at the center of force or, in physics jargon, you have an angular momentum about the center of force. The central force by itself has**NO**way of removing this angular momentum: i.e., there is conservation of angular momentum in a central force system. - Note gravity is
**NOT**turned off in space. It's often quite strong: e.g., in low Earth orbit, it's nearly as strong as on the Earth's surface. But if**NO**forces resist gravity, an astronaut and his spacecraft are in free fall: falling together under gravity and being weightless. - Isaac Newton (1643--1727) himself
thought up
Newton's cannonball
and a diagram of it appeared in his book the
*Principia*(1687) (see Wikipedia: Newton's cannonball: Other appearances).Note that a thought experiment (or Gedanken experiment) is an experiment that can be performed in principle and that illustrates a physical point of interest. The experiment may or may

**NOT**be possible in practice, but usually when one calls something explicitly a thought experiment (or Gedanken experiment), one means an experiment**NOT**or**NOT**easily done in practice.Of course, Newton's cannonball was a pure thought experiment (or Gedanken experiment) in Newton's time, but nowadays it is done all the time with rockets,

*mutatis mutandis*: i.e., no cannon, no cannonball, no mountain. - Newton's cannonball videos
(i.e., Newton's cannonball
videos):

- Projectiles launched horizontally into orbit (Newton's cannonball) | 0:16: With continuous variation of launch speed. Short enough for classroom.
- Newton's Cannon in action | 0:28: Good. Short enough for classroom.
- Newton's cannon animation | 0:30: With background music. Short enough for classroom.

- Mathematical discription of
Newton's cannonball
thought experiment (or Gedanken experiment)
with projectile
launch velocity v:
- For v less than the low-Earth-orbit velocity v_circular ≅ 7.9 km/s, the projectile follows approximately a parabolic trajectory and crashes into Earth.
- For v = v_circular, the projectile goes into a circular low Earth orbit.
- For v_circular < v < v_escape ≅ 11.2 km/s (i.e., the escape velocity) the projectile goes into a elliptical orbit.
- For v = v_escape, the projectile goes into an open orbit (or an escape orbit) and escapes to infinity. It will reach infinite distance with zero velocity in infinite time if nothing else affects it. The open orbit is a parabolic orbit.
- For v > v_escape, the projectile goes into an open orbit (or an escape orbit) and escapes to infinity. It will reach infinite distance with greater than zero velocity in infinite time if nothing else affects it. The open orbit is a hyperbolic orbit.

- For reference, see the insert below (which is omitted if
the Newton's cannonball
figure is repeated):
EOF

Caption: An illustration of Newton's cannonball thought experiment (or Gedanken experiment) for a projectile (e.g., a cannonball) launched from a giant mountain on the Earth. The projectile has negligible mass and size compared to the Earth (i.e., it is a test particle) and we neglect air drag.

Features:

Image link: Wikipedia: File:Newton Cannon.svg.

Local file: local link: newton_cannonball.html.

File: Orbit file: newton_cannonball.html.