- #1
Fanta
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Homework Statement
2. An object, initially still at a distance from the sun of [tex]1,5\times 10^{8}[/tex] km.
Suppose the body is only influenced by the sun's gravitational field:
2.2 Recurring to dimensional analysis, make a prediction on the time it takes for the body to fall in the sun (in days).
- The answer expected is aproximately 58 days
Homework Equations
I'm guessing :
1)
[tex]F = m a[/tex]
2)
[tex]F = G\frac{m1.m2}{R^{2}}[/tex]
and possibly:
[tex] x = x_{0} + v_{0} + \frac{a \times t^{2}}{2} [/tex]
The Attempt at a Solution
I'm pretty much at a loss here:
The statement clearly asks for dimensional analisys, but i cannot relate time with a length only, since I have to make a prediction:
I'm guessing the prediction means to try to find an equation that's dimentionally correct, without concern for the adimentional constant.
So, what I tried so far has pretty much nothing to do with dimensional analisys, because i really can't see what to do.
I have, indeed tried some things but don't get anywhere near the supposed solution (aproximately 58 days).
What I tried :
(note, this is not what the problem asks, since it isn't dimensional analisys)
[tex]x = \frac{a \times t^{2}}{2}[/tex]
and using 1) and 2) :
[tex]a = G\frac{m2}{R^{2}}[/tex]
so:
x = R
[tex]R = G\frac{m2 \times t^{2}}{2R^{2}}[/tex]
[tex]t = \sqrt{\frac{2R^{3}}{G.m2}}[/tex]
and, substituting R for the value given on the statement, G for the gravitational constant, and m2 for the mass of the sun, the result has nothing to do with the expected (58 days)