Question

The force of gravity on an approaching asteroid is 200000 Newtons at a certain distance from the Earth. Calculate the force of gravity on the asteroid when it reaches a point one-ninth of this distance from the centre of the Earth.

Answer 1

is \[F= G \times \left[\begin{matrix}m _{1} \times m _{2} \div\\ r ^{2}\end{matrix}\right]\]the equation I should use?

Answer 2

Yes, except instead of \(r\) you have \(\frac{r}{9}\).

Answer 3

what is the little symbol under the r?

Answer 4

9

Answer 5

oh ok, where would I plug in the 200000N

Answer 6

Well, the force of gravity \(F\) is modified at a distance \(r_{new}=\frac{1}{9}r_{old}\), and you square \(r\)...

Answer 7

Alright, take for instance, I had a variable \(a\) that earlier was measured to be \(a=10\). If \(F=a^2=100\), then if I double \(a\) I get \(F=\left(2a\right)^2\).

Answer 8

k, I got \[F= 6.67 \times 10^{-11}\left[\begin{matrix}5.98 \times 10^{24} \div\\ (1/9 \times r )^{2}\end{matrix}\right]\]

Answer 9

is r the radius of the earth? and I don't really understand about what I should do with the 200000N

Answer 10

200000 N is the force of gravity as stated in the question

Answer 11

I don't really know where I would put it though, like in the equation

Answer 12

F is the force of Gravity
or just vist these site

http://en.wikipedia.org/wiki/Gravity_of_Earth

Answer 13

you should substitute the value in F of equation

Answer 14

oh, and like get the r and then put the 1/9 in to get the 1/9 of that distance?

Answer 15

as in\[200000N= 6.67 \times 10^{-11} \left[\begin{matrix}5.98 \times 10^{24} \div \\ r ^{2}\end{matrix}\right]\]and then find the r that way, and use it to plug into the r times the 1/9?

Answer 16

wait ... @badreferences can you please explain what is 1/9

Answer 17

I'm pretty sure it's the one ninth distance away from the Earth, but I might be wrong

Answer 18

sorry i did not read the question as whole
i got it

Answer 19

now calculate the radius and then find out the force of gravity when it is just 1/9 from the radius of the earth
you can divide the radius of the earth by 9
6400/9=711
then put these value in the formula

Answer 20

ok

Answer 21

I got \[6.44 \times 10^{-33}\] would that be right? I don't know if I was supposed to square the 1/9 part too with the r, or not

Answer 22

like \[r ^{2} \div9\] or\[(r \div9)^{2}\]

Answer 23

actually ya, I see that I have it in brackets up higher so that should be it, thank you so much for helping and having patients with me :)

Answer 24

its ok dude
but you should do like these
\[r ^{2}\div9\]