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You understand equation (3) by grasping that 'a' is a value that itself depends on "r". a varies in inverse proportion to r^2, and thus a^2 varies in inverse proportion to r^4. Thus if r doubles, r^2 increases by a factor of 4, but a^2 reduces to 1/16 its value. 4*1/16 = 1/4 and the net value of F has decreased by a factor of 1/4 or 1/r^2. The equation is misleading because it contains a variable which is not independent of another variable in the equation.

Mass in each equation, both 1 and 2, is assumed to be the same. If you don't believe me dig Newton up and ask him. (whether they should be is debatable, but our evidence to this point in time has them as equivalent. Nothing wrong with the algebra. Nothing wrong with Equation 3. Though I don't see much use in that form, it is still valid. Given the acceleration, and distance, it will in fact give you the gravitational force between the two unknown equal masses. But that does not mean the force is proportional to distance squared. Acceleration depends on the distance (and the masses). If acceleration was independent of the distance you could conclude the force is proportional to distance squared, but acceleration is not. This is the key. Let's say we are observing two equal masses orbiting each other in space, in a perfect circle. We measure their distance apart and centripetal acceleration. The greater the distance is, the much greater the masses must be, and the much greater the force must be, to maintain that constant acceleration. So in this specific set of cases of fixed acceleration you can say the force is proportional to the distance squared.

For normal people of Ukraine and Russia, it would be great news.. for politician leaders, oligarchs and businessmen around the current governments, it would be complete disaster..

Call my a cynic, but i doubt a single one of the accusing Tories genuinely believes they are championing women's views, but are rather inflaming the 'incident' to detract attention away from the daily Brexit headlines. And it has worked a treat.

While I do not necessarily disagree, the issue with intention is, of course, that folks generally do not consider their own intentions are bad. There is always some kind of justification in ones mind, otherwise one would not have engaged in the actions in the first place. In other words, behaviour in a society, since the beginning of apes gathering in one spot, actions will be judged internally as well as externally. To take a historic example, folks that were all for segregation were also often folks considering racism a bad thing. Thus, their actions and support for segregation were in their mind not driven by racism. Yet the outcome is clearly one of oppression and denied economic growth (and worse), which we see until now. So while it is well-meant that one should not preconceive someones deeper intentions, we cannot solely judge it by this measure. And just to make it clear, the call not to judge folks by their actions is the new thing. It is not that we only recently started doing so. Rather, many, if not most societies has been traditionally far more harsher in punishing non-conformism. It is really that we are exploring new degrees of freedom (plus the impact of social media) that it appears that the game has changed.

When people interpret what others say, it also says a lot about them... Isn't that the bigger issue. These types of actions or words, are 'perceived 'wrongs', not intended wrongs. In this very discussion we have no idea as to the intent of the speaker, yet we have widely varying opinions by others ( including forum members ) as to what he meant, or they perceived him to mean. This perception may have nothing to do with any actual wrong, or intent, on the part of the speaker, but may be due to the 'baggage' we all carry with us that colors our perspective. If its good practice ( or behavior, or manners ) not to call someone stupid in public, isn't it also good practice not to jump to conclusions and to assume the worst about a person based on your interpretation of what he said. ( or even to get a lip reader to decode what he said privately, and expose it in the news )

I suppose it depends which news channel or paper you listen to watch or read. :-). I don't trust them either, but there is/has been corruption in every country and I have to believe it will improve. A step to improving their abuses would be to include them and work and grow with them. They have been allies with the UK in many wars throughout history against other countries in Europe. Anyway - I'm off - Merry Christmas.x

If he had, would we be having the same discussion but accusing him of being elitist instead of sexist? I'm not necessarily condoning him, but it is difficult to please everyone.

So it's likely he just chose his words poorly (because he was misunderstood as saying something sexist), although one would think that when muttering under your breath you'd be given a little slack.

Is that what happened in parliament yesterday? Was he mocking her with a direct accusation of stupidity, emphasising the word 'woman' using it as if it was an insult?... or commenting to his friend in private (as sideways whisper for his ears only) that he thought the person was stupid? Her gender has no bearing on her intellect at all... as I said above I though what he said was childish... to suggest a woman who has risen through the ranks to take the most powerful political position in the country is 'stupid' is 'stupid' in it's own right... she would HAVE to be pretty good to reach the position and to be voted into that position by her peers. I think he was probably just releasing some frustration at her lack of understanding or wilful dismissal of his argument. That would be because you are a woman. So if someone called you stupid they would call you a stupid woman. If they called ME stupid they would use the phrase 'stupid man'. I regret to say that I have been on the receiving end of that statement and it was probably deserved. ... so in MY experience I don't really hear the phrase 'stupid woman'... it's always 'stupid man'. Is that sexist? It is only sexist if you consider using gender in language to distinguish between the sexes sexist. Maybe that is - but that is the language we have and used correctly. If you want that changed then you have to change the language - not attack those that use it correctly. I've said it before - you jump on people like this and you are preaching to the choir - this is why we have Brexit and Trump.... because we aren't allowed to discuss things for fear of upsetting the PC brigade - so they don't get discussed and peoples shit views come out at the polling stations. Better have the discussion in public and educate the people who hold their racist and misogynistic views to the fact that they are holding biases and prejudices or whatever - rather than jumping on them and shutting them up so they slink off and continue to keep their views private and vote accordingly in the ballot boxes. Now they have won (the brexit vote/trump pres) they are over the moon and feel justified in holding their views once again. Keep shutting them up and scolding them school teacher style and they will go underground again, never to be seen until next polling day.

No I mean EU is a economical union as well. It's not so easy to adhere to EU. Many member states have not yet even adopted the European currency. Romania, Poland etc. I agree for peace friendship and inclusion but what you guys are describing is some new meaning for the EU group. Political tension aside, the point of this is that there are certain standards needed to be able to join and to have a single market. Moldova for example (if we take these standards into consideration) cannot join EU yet. (political reasons aside) Also I think changing Moldavian currency (moldavian LEu) to Euro would have a crushing effect on their economy. But also politically speaking: https://www.rferl.org/a/european-parliament-slams-moldova-as-a-state-captured-by-oligarchic-interests-/29600720.html

I'm with you bro... not yet...

I think it would be great - they would have a 1/28th say in how the EU was run - but they would have to answer to the EU courts if they got up to any funny business. Why not? It would be a great marriage... they would just become part of Europe. I doubt the US would approve... and it would make the UK look pretty silly for leaving - but I'd be down with it 100% for building bridges and forging future world peace.

Ukraine could be admitted into the EU. But letting Russia join would be a bit like a deer inviting a lion into its home.

Since acceleration in the formula is dependant on distance...it is simply incorrect to conclude that With regard to force and distance? Force is inversely proportional to distance squared, same as it was in equation (1), but now less obvious.

I don't know about the rest of you but I think that letting a heavy door slam into someone behind you, whatever their sex, is an assault as well as showing a lack of common courtesy. Also, as iNow and Moontanman know from other sites, just because someone has a first name like mine, doesn't mean that they are female.

That’s even more wrong, then.

...the math is what you provided. You asked how we should understand the equation. What math are you asking for?

You should understand it by realizing that the force is proportional to the square of the distance only if acceleration is being held constant, which is generally an unnatural assumption. Mass being held constant is a somewhat natural idea; acceleration being held constant is not.

I guess the explanation would be more obvious if you could include some math. Thanks in advance.

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