Expert: Philip A. Stahl - 7/28/2010

Question
QUESTION: HI-I'm helping a friend with a question. I'm not asking you to solve it-I'm asking you to please show me how to set it up so I can find the solution-I am stumped-please help:

What is the acceleration of Jupiter produced by the gravitational force ?
When 'g' between jupiter and the sun is 4.19 * 10 ^23 N, and Jupiter's orbital radius is 778.3 x 10^9 m.
If possible use the same information to calculate the acceleration of the Sun.

Thank you.
Jason


ANSWER: Hello,

This problem is extremely straightforward.

However, what you're calling 'g' is, in fact, NOT g (as in an 'acceleration of gravity') but rather **mg** (the equivalent of a 'weight' for Jupiter as referenced on the Sun- since the units are Newtons, N *not* m/s^2!)

Once that is understood, it all falls into place.

The solution then quickly follows (or should) once you recognize the centripetal acceleration of Jupiter (which is what you want) is being provided by the Sun, so:

F (force of attraction) = G (M(s) m/ r^2 = mv^2/ r  = mg

where m is Jupiter's mass and M(s) is the Sun's (~ 2 x 10^30 kg)

From here it is, as we say, a "piece of cake" - or ought to be for you!



---------- FOLLOW-UP ----------

QUESTION: Hi, and thank you. So m is 4.19 * 10 ^23 N, Jupiter's mass. What is G?
The gravitational constant, G = 6.67428 * 10^(-11) N(m/kg)? I just want to be sure.
Please let me know. Thank you.

Jason G.


Answer
Hello,

NO...m is NOT 4.19 * 10 ^23 N, (Jupiter's mass). It is the putative FORCE (mg) - by which Jupiter is attracted to the Sun. (Note the units for mass are in kg for the SI system, and *force* is given in N).


G is the gravitational constant as you have defined it (sorry, I thought I'd included it!)


Now, since we know:

G (M(s) m/ r^2 = mv^2/ r  = mg

and have G, M(s) and r, we can compute either m or g. (m would be found by dividing 4.19 * 10 ^23 N by the value obtained for g.)

But since the problem specifically wants the *acceleration* (v^2/r) we can see that is exactly g.

Then: v^2/ r = g  = G (M(s)/ r^2

Which you should be able to work out from here.