# Is projectile trajectory on Earth affected by the fact that it isn't a singular point?

So in high school physics, we were told that projectiles traveled in a parabola, but Google searches have said that it's more like an ellipse, since the Earth isn't flat. However, I was thinking that since most projectiles stay so close to Earth, you can't really assume that gravity acts only towards the center, since gravity dictates that all particles are attracted to each other, so the core isn't the only thing on earth pulling the object "down". Is this logic valid?

High School: $$d = v_{0}t + \frac{1}{2}at^2$$

For a perfect spherical and homogenous Earth, the gravity at any point would act towards the center. This is because the added pull of each earthly particle on you (or whatever object you fancy) resolves to a single force towards the center. Regardless of where you are, (on the surface, above the surface, below the surface, wherever), you effectively have just the one force pulling you straight into the center.

However, the Earth is not exactly a sphere, and is definitely not homogenous. This causes the gravity to vary at different points on the surface of the Earth to vary. Due to these variations, the pull doesn't exactly add into a force directed straight at the center - it is oh so slightly eccentric. Not enough to change where that football you just kicked is going to land, though.

• That does not alter the fact that any planet, including the earth; has in the Newtonian limit, a single point center of mass, towards which, the gravitational force on ANY other external body points. With that center of mass point as the reference for the co-ordinate system, the trajectory of the second body is an ellipse; not a parabola. Yes if you want to get nit picky, you can say both travel in orbits about their common center of mass. For very small orbiting objects, the earth center of mass is one focus of the ellipse.
– user26165
Oct 22, 2013 at 5:38
• True. In this case, the center of mass is NOT at the geometric center of the Earth because of said non-homogeneity. The gravity force points to that center of mass, not the geometric center. What point are you trying to make? Oct 23, 2013 at 3:53
• The OP's question relates to projectile trajectories. He was told the're parabolas. They aren't parabolas; they are ellipses, referenced to the center of mass of the earth. The earth center is irrelevant; it is the CM that matters to the projectile. The homogeneity of the planet matters not a jot. Why are you introducing extraneous matters, that are quite unrelated to OP's question ?? And for the nitpicker trolls; yes if you launch the projectile at exactly the right direction and instantaneous velocity, it can have a parabolic trajectory. No such launch vehicle exists on earth.
– user26165
Oct 23, 2013 at 23:13
• "you can't really assume that gravity acts only towards the center" This is what my answer addresses. The CM is all that matters - agreed - however, it doesn't coincide with the geometric center, which is what I'm saying in my answer Oct 23, 2013 at 23:24
• """"".....Is projectile trajectory on Earth affected by the fact that it isn't a singular point?.....""""" That is the OP's question. The answer is very simple.... NO !!
– user26165
Oct 24, 2013 at 1:05