High School Gravity Constant: How Calculated & How to Measure Planet Weight

[Astro021]

Hey I have a question and I’m sorry if some of you might find it too easy xD... How did people calculate or discover the gravity constant, and how do they know how much do planets weigh? Thanks for answers

 

[Wrichik Basu]

Have you gone through the Wikipedia article on Universal Gravitational Constant? It has a section on its measurement.

 

[RPinPA]

Henry Cavendish performed the famous experiment measuring the value of G between two small masses in the lab. I had to repeat that experiment as an undergrad physics student. It used a delicate instrument called the torsion balance which, I was fascinated to learn fairly recently, was invented by Coulomb who is famous for his work on the electrostatic force.

The short answer to your second question is that Newton's theory of gravitation is used to calculate the masses of planets. But how?

If an object is much lighter than the thing it is orbiting (for instance planets around the sun), then the relationship between orbital radius and period tells you the mass of the thing it is orbiting because (to a good approximation) it only depends on the mass in the middle. So if we know the orbital radii of the planets and their periods, they can let us estimate the mass of the sun. And the behavior of planets' moons let's us estimate the mass of the planet.

In the exact Newton theory the mass of the planet or the moon comes into it, and you can use that to make more exact calculations.

The mass of the Earth is easy because we live here, we know the radius and we can directly measure how much gravitational force it causes to things on the surface.

Here's an article covering that: https://www.scientificamerican.com/article/how-do-scientists-measure/

 

[sophiecentaur]

In the 18th Century, an experiment was performed, using a Scottish Mountain and a Pendulum, to measure / estimate the average density of the Earth. They chose a mountain (Schiehallion) that was known to be very dense (contain lots of iron ore, iirc). and noted by how much a pendulum was deflected by its presence. That gave Scientists a starter for measuring / confirming G and obtaining information about the other astronomical objects. Newton, apparently, rejected the idea of that particular experiment but it was the first time that absolute data was obtained about the masses of those objects.
Edit: Newton was a bit of a 'not invented here' merchant and he didn't make the right choices every time!

 

[Janus]

One point of interest. For certain bodies, such as the Earth, we actually know the value of the product GM to a higher accuracy than we know the value of either G or M.
GM for the Earth is 3.986004418e14(8) while G is 6.67408(31)e-11, a fair difference in the number of significant digits.