Gravity of a Planet

Drag the observer to different positions. We assume the test mass (the observer above) to have a mass of $m=1kg$ for simplicity.

• Drag the observer.
• The solid curves take into account the finite size of the planet, the dotted lines do not.
• $g = \frac{GM}{r^2}$ (outside the planet)
• $F_g = mg = \frac{GMm}{r^2}$ (outside the planet)
• $PE = U = -\frac{GMm}{r}$ (outside the planet)
• Mass of earth: $M_e = 5.972\times 10^{24}kg$
• Radius of earth: $R_e = 6371km$
• Acceleration due to gravity on earth's surface: $g_e = \frac{GM_e}{R_e^2} = 9.8m/s$
• Magnitude of the PE of a $1kg$ mass on earth's surface: $U_e = |-\frac{GM_e m}{R_e}| = 62.6\times 10^6 J$

Artwork from Spriters Resource, uploaded by Arima, IsaacDavid.

Launching Projectiles

We assume the test mass (the observer above) to have a mass of $m=1kg$ for simplicity. Small discrepancies from the theoretical predictions may arise when the simulation runs over a long period of time.

• Drag the observer.
• $g = \frac{GM}{r^2}$
• $F_g = mg = \frac{GMm}{r^2}$
• $PE = U = -\frac{GMm}{r}$
• $E_{total} = KE + PE = \frac{1}{2}mv^2 -\frac{GMm}{r}$
• $KE = E_{total} - PE$, so the gap between $E_{total}$ and $PE$ in the graph is the $KE$ of the projectile.
• Mass of earth: $M_e = 5.972\times 10^{24}kg$
• Radius of earth: $R_e = 6371km$
• Acceleration due to gravity on earth's surface: $g_e = \frac{GM_e}{R_e^2} = 9.8m/s$
• Magnitude of the PE of a $1kg$ mass on earth's surface: $U_e = |-\frac{GM_e m}{R_e}| = 62.6\times 10^6 J$

Artwork from Spriters Resource, uploaded by Arima, IsaacDavid, FattyMcGee.