Surface Gravity on Different Planets
How much would you weigh on other planets? Let's calculate surface gravity using planetary masses and radii.
The Physics
Surface gravity is given by Newton's law: g = GM/R^2
Earth (baseline)
g_earth = G * M_earth / R_earth^29.820 [9.790, 9.851] N / kg {acceleration}
Earth's surface gravity: 9.820 [9.790, 9.851] N / kg {acceleration}
Mars
Mars is smaller and less massive:
g_mars = G * M_mars / R_mars^2
mars_weight_ratio = g_mars / g_earth0.3796 [0.3784, 0.3808]
On Mars, you'd weigh 0.3796 [0.3784, 0.3808] of your Earth weight.
Jupiter
The gas giant is massive but also very large:
g_jupiter = G * M_jupiter / R_jupiter^2
jupiter_weight_ratio = g_jupiter / g_earth2.639 [2.631, 2.648]
On Jupiter's "surface" (cloud tops), you'd weigh 2.639 [2.631, 2.648] of your Earth weight.
The Moon
g_moon = G * M_moon / R_moon^2
moon_weight_ratio = g_moon / g_earth0.1653 [0.1648, 0.1658]
On the Moon, you'd weigh only 0.1653 [0.1648, 0.1658] of your Earth weight - that's why astronauts could hop around!
Summary
| Body | Surface Gravity | Weight Ratio |
|---|---|---|
| Earth | 9.820 [9.790, 9.851] N / kg {acceleration} | 1.0 |
| Mars | 3.7279 [3.7274, 3.7283] N / kg {acceleration} | 0.3796 [0.3784, 0.3808] |
| Moon | 1.6234 [1.6232, 1.6236] N / kg {acceleration} | 0.1653 [0.1648, 0.1658] |
| Jupiter | 25.920 [25.916, 25.925] N / kg {acceleration} | 2.639 [2.631, 2.648] |
Escape Velocity Bonus
How fast do you need to go to escape each body?
v_escape_earth = sqrt(2 * G * M_earth / R_earth) as km/s
v_escape_mars = sqrt(2 * G * M_mars / R_mars) as km/s
v_escape_moon = sqrt(2 * G * M_moon / R_moon) as km/s2.3751 [2.3750, 2.3751] km / s {velocity}
- Earth: 11.186 [11.177, 11.195] km / s {velocity}
- Mars: 5.0270 [5.0269, 5.0272] km / s {velocity}
- Moon: 2.3751 [2.3750, 2.3751] km / s {velocity}