John Carlos Baez on Nostr: The centrifugal force is called a 'fictitious force' for good reasons - but if you've ...
The centrifugal force is called a 'fictitious force' for good reasons - but if you've been in a car that makes a sharp turn and get yanked outward you'll see that a fictitious force can feel real.
For an orbiting planet, the centrifugal force acts like an additional repulsive force, besides the attractive force of gravity. While gravity decays like the inverse square of distance, the centrifugal force decays like the inverse cube! So it beats gravity at short distances, except for something moving straight in or out. This is why planets don't fall into the Sun.
Newton is famous for studying the inverse square force law for gravity. But he also had interesting things to say about the inverse cube law! I explain them in my blog article below.
Also, his assistant Roger Cotes figured out how planets would orbit in an *attractive* inverse cube force. Such a force can beat the centrifugal force and make a planet spiral in to its doom.
In the process of solving this problem, Cotes seems to have been the first to work out the derivative of the sine function!
https://johncarlosbaez.wordpress.com/2025/11/05/the-inverse-cube-force-law-2/Published at
2025-11-06 10:20:31 UTCEvent JSON
{
"id": "ce4237e91abea2596d7b2a29314cbead12db7de86be81e62fcb8ba5fd8286f26",
"pubkey": "9a6a1a8eefd0b53d7e0c966ab35bd904151246f03b1be98fa0d2d0eeb4940320",
"created_at": 1762424431,
"kind": 1,
"tags": [
[
"proxy",
"https://mathstodon.xyz/@johncarlosbaez/115502247546383178",
"web"
],
[
"proxy",
"https://mathstodon.xyz/users/johncarlosbaez/statuses/115502247546383178",
"activitypub"
],
[
"L",
"pink.momostr"
],
[
"l",
"pink.momostr.activitypub:https://mathstodon.xyz/users/johncarlosbaez/statuses/115502247546383178",
"pink.momostr"
],
[
"-"
]
],
"content": "The centrifugal force is called a 'fictitious force' for good reasons - but if you've been in a car that makes a sharp turn and get yanked outward you'll see that a fictitious force can feel real.\n\nFor an orbiting planet, the centrifugal force acts like an additional repulsive force, besides the attractive force of gravity. While gravity decays like the inverse square of distance, the centrifugal force decays like the inverse cube! So it beats gravity at short distances, except for something moving straight in or out. This is why planets don't fall into the Sun.\n\nNewton is famous for studying the inverse square force law for gravity. But he also had interesting things to say about the inverse cube law! I explain them in my blog article below.\n\nAlso, his assistant Roger Cotes figured out how planets would orbit in an *attractive* inverse cube force. Such a force can beat the centrifugal force and make a planet spiral in to its doom.\n\nIn the process of solving this problem, Cotes seems to have been the first to work out the derivative of the sine function!\n\nhttps://johncarlosbaez.wordpress.com/2025/11/05/the-inverse-cube-force-law-2/",
"sig": "f1ea081bdd81235cd739564aa7c9f1671d9a3c1c39732b2e171138797c6954c97a5bed06fa4034f6c12032bfc724fbc0075fb71a0e46312514c86bb359a23eca"
}
