What factors determine a planet's gravity?

In Science Fiction we often see the protagonists exploring all sorts of strange new worlds with no apparent discomfort to the variations in gravity.

What factors determine how strong the gravity will be on a planet? Is it purely based on the size of the planet in question or are other factors like core density involved?

In short: is it possible for a human to walk on the surface of a planet which is a thousand times the size of the earth without being crushed?

Only two factors impact gravity: mass and size. Alternatively, density and size (since density is mass divided by volume, a measurement of size).

The bigger the mass, the stronger the gravity. This is direct and unavoidable.

The bigger the size for a given mass, the smaller the gravity, since you are farther from the center of mass (the center of the planet). But this is not so important since habitable plantes (those with a solid rocky surface) have quite a reduced span of available densities.

Besides, you can think on external effects. Since your question do not have tags about "hard science" or "fantasy", you can say that there are no external factors (hard science), some natural factors like a dense atmosphere that causes some floating like in water or the rapid spinning Tim B. has proposed in his answer (sci-fi, but note these does not truly changes gravity) or there are magic minerals with antigravity capabilities like Cavorite (fantasy).

Also, gravity pulling from an external body causes variations on gravity (tides), but you can see here on Earth how much you notice them.

• If you're allowing parallel universes with different physical constants then the value of G, the gravitational constant, also has an effect. But as far as we know G is fixed and unchangeable in our universe. Commented Mar 27, 2019 at 10:55

Envite covered most things, but to answer the specific question:

In short is it possible a human could walk on the surface of a planet which is a thousand times the size of the earth without being crushed?

Not with any known natural planetary body. The density of the planet would need to be far lower than any known material for this to be possible.

An artificial structure might be able to do this (for example a hollow sphere you walk around on). Alternatively the use of technology would allow this if anti-gravity fields of some kind were available.

One last option might be a planet with an extremely rapid spin. You could land on the equator and centripetal effect (the spin of the planet throwing you off) would counteract some of the gravity. Get the balance right and it would be survivable, the planet would be an odd shape though (very flattened) and have some wicked weather systems. There's an old-school hard sci-fi novel called "Mission of Gravity" set on just such a world although from what I remember even there it wasn't as extreme in size as you are suggesting.

Three more effects to compliment the previous answers:

1. Shape - If a planet somehow obtained a non-spherical shape during its formation, gravity would undoubtedly vary over its surface. This is even true for earth. You can imagine that if a planet was even more oblong than earth variations in gravity at different points on the surface would increase. This would also have a great effect on the different species which could inhabit different parts of the planet if it supported life. Also note that for an oblong planet, the direction of the gravity vector will not always be perpendicular the surface of the planet.
2. Terrain Elevation must also be considered, whose effects are similar to variations in the planet's shape.
3. Density Variation - There will also be gravitational variations if there is a non-uniform density distribution (I'm talking about variations over the azimuthal or polar angles, not just radial variations). Remember that for free body diagram style analyses the gravity vector will always point towards the center of mass (COM) of the planet, which is likely not the centroid of the shape if there is a non-uniform density distribution. Also keep in mind that the center of mass is also the center of rotation for the planet, so if you have a spherical planet where the COM and the centroid are not co-incident there will be a noticeable eccentricity in any rotation it has.

The Space Trilogy by CS Lewis (Author of The Chronicles of Narnia) describes an interplanetary adventure where some gravitational effects are discussed. It's also a good read :).

Answers: 1 & 2: (previously answered) the Planet's mass and your distance from the center of that mass (usually also known as the planet's radius - but it isn't in all cases).

3: NO A person could not walk around on any planet 1000x the size of Earth given what we know about planets.

The very special circumstances would be a world rotating so fast, it is almost ready to break apart. It would generate a huge equatorial bulge. The addition of that bulge placing you further from the center of mass and the centripetal acceleration would enable a person to walk on a planet up to about Jupiter's mass ($1000 \times$ that of Earth's).

The density that goes with this number indicates that such a planet would need to be almost entirely made of water or lighter elements - so you might not find a surface.

Of course, specifying smaller planets makes it easier to find a combination that would enable humans to walk around.

Here is an easy formula to determine surface gravity of a planet relative to the Earth. All you need is to know your "planet" in Earth masses and Earth radii. Then the surface gravity relative to Earth would be $$M/R^2$$.

I couldn't find a reason why you can't "build" a "rocky planet" as big as you want, but nature maxes out at about 20 Earth masses (The heaviest found so far has been Kepler 10c at about 17.2 Earth masses.) Even Kepler 10c is only estimated to be 2.3 Earth Radii so this gives a surface gravity of 3.2g.

Other examples would be Gliese 1214b (our best candidate so far for a "waterworld"/ low density). At 6.55 M(Earth) and 2.68 R(Earth), it's surface gravity would be 0.91g.

If you don't mind "floating" in an atmosphere, you could live on the "surface" of Jupiter (where atmospheric pressure is about 1 bar) and weigh 2.5g.

Another interesting prospect would be "floating" on the surface of a "cold" brown dwarf where atmospheric pressure and temperature would be Earthlike. If you take an example of a 12 M(Jupiter)/ 1 R(Jupiter) dwarf you woudl have a surface gravity of about 30g.