(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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

2. Relevant 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]

3. The attempt at a solution

I'm pretty much at a loss here:

The statement clearly asks for dimentional 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 dimentional 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 isnt dimentional 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)

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Dimentional Analysis problem

**Physics Forums | Science Articles, Homework Help, Discussion**