### Does the Same Weight On Another Planet Mean the Same Escape Velocity?

Astronomers tell us we have to travel 7 miles per second to escape the gravitational pull of our planet Earth. Does that mean if we weigh the same on another planet, the escape velocity would be the same as well?

First of all, let's investigate the possibilities our weighing the same on the surfaces (assuming we could stand on the surfaces) of other planets...

On a planet that's sixteen times as massive as Earth but sporting a radius four times as great, we'd weigh the same. This is because of the inverse square law. We'd be four times further from the center of gravity, which causes the pull of gravity to decrease by sixteen times (4 x 4 = 16). Dividing the mass by the square of the radius gives us one (16 divided by 16 = 1). An answer of one means the same weight. (Incidentally, the seventh and eight planets from the Sun, Uranus and Neptune, almost match the mass and dimensions of this hypothetical planet.)*

In a different scenario, suppose a planet is one hundred times as massive as Earth but with a radius that's ten times greater. Again, we divide the mass by the square of the radius (100 divided by 100 = 1) to find that we'd weigh the same. The sixth planet from the Sun, Saturn, has a mass and size not much different from this hypothetical planet.**

Astronomers claim the escape velocity on these planets would be different, in spite of our weighing the same. Escape velocity is found by taking the planet's mass and dividing it by the planet's radius. The square root of that number reveals the planet's escape velocity.

For the sample planet in paragraph three, the mass (16) divided by the radius (4) equals to 4. The square root of 4 equals 2, so consequently, the escape velocity is twice as great: 14 miles per second.

For the sample planet in paragraph four, 100 divided by 10 equals 10. The square root of 10 equals 3.16, giving an escape velocity of 22.12 miles per second.

Next month, the escape velocity on the Moon...

* According to the World Almanac, Uranus' mass is 14.54 times greater than Earth's and its radius is 3.98 times greater. The numbers for Neptune are 17.15 and 3.86.
** According to the World Almanac, Saturn's mass is 95.16 and its radius is 9.14.