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t1_ixun1vl wrote

Step 1 is to measure the mass of the planet. This is surprisingly easy. Just need to catch a view of some object in orbit around the planet (like a moon) or passing near the planet (like a comet). If you can a couple of good observations, preferable over several weeks, you can calculate the mass of the planet using newton's laws of motion.

Step 2 is to get a measurement of the diameter of the planet. This is surprisingly hard. I don't recall the methods used. One problem is "what's the definition of the diameter when you're looking at a gas giant? It basically goes from a solid core to a vet thick liquid transitioning to extreme pressure gas. Then the gas pressure, density drop off slowly to zero.

If you know the mass and diameter, it's a simple calculation.

But if you want the gravity of a gas giant at some point down inside the thick atmosphere, you do have to also figure out how much mass is inside your chosen depth.

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t1_ixxbrz9 wrote

Measuring the mass is almost always done by observing its gravitational influence, so we can skip the mass calculation and just use ratios of distances. We know the gravitational attraction of Earth better than 1 part in a billion, while the mass has an uncertainty of more than 1 in 100,000 because the gravitational constant isn't known that precisely.

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t1_ixy6khj wrote

> Step 1 is to measure the mass of the planet. This is surprisingly easy. Just need to catch a view of some object in orbit around the planet (like a moon) or passing near the planet (like a comet). If you can a couple of good observations, preferable over several weeks, you can calculate the mass of the planet using newton's laws of motion.

Measuring the mass of a planet is actually very hard, but observing a moon tells you the gravitational acceleration, which is what we actually want here. So we just cut out mass altogether and calculate surface gravity based on the gravity that we observe pulling on the moon.

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