Projectile motion without air resistance [closed]

Does the mass of projectile affect its trajectory when it is projected in no air resistance environment and why?

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closed as off-topic by tpg2114, Qmechanic♦Nov 3 '13 at 2:29

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check here for more explanation physicstutorials.org/home/mechanics/1d-kinematics/… – Smith Apr 9 '11 at 16:42

No, the mass affects nothing; only the initial velocity, angle of projection and acceleration due to gravity determine the trajectory the projectile takes.

This is because the inertial mass $m_i$ which appears in $F=m_ia$ is equal to the gravitational mass $m_g$ which appears in $F=m_gGM/R^2$ of Newton's gravitational law. These two cancel in all your equations. This property of masses is one way of stating Einstein's Equivalence Principle.

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I see, so more force will be required to attain the same velocity. – user2363 Mar 2 '11 at 23:00

It will only significantly affect the trajectory if the mass of the projectile is significant compared to the mass of the planet or other body providing the gravity.

For example, Earth's mass is $6 \times 10^{24}$ kg, so even a large aircraft or spacecraft of $10^6$ or $10^7$ kg will not have a measurably different trajectory because of its mass. However, the Moon is $7 \times 10^{22}$ kg, so its trajectory is measurably different from what it would be if it were massless.

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At least in the usage I'm familiar with, "projectile motion" is defined as motion in 2 dimensions with acceleration of constant magnitude and direction. This approximation is not exactly true for a real projectile for the reason you've identified. So for a real projectile, this is correct (albeit usually completely negligible); however, it doesn't apply to the way projectile motion is typically dealt with in intro physics classes. – David Z Mar 2 '11 at 23:49