What is Upiter's speed when closest to the sun?

[kopinator]

A hypothetical planet Upiter orbits the sun. Upiter's semi-major axis is 5.2 AU. The mass of Upiter is .001 that of the sun. The eccentricity is 0.2. For this problem, ignore the other planets.

d. Compute Upiter's speed when it is closest to the sun.

I believe the equation I use for this is v^2=GM(2/r - 1/a), where a is the semi-major axis and r is the distance at perihelion. I know G is usually in m^3/kg/s^2 but since I'm given units in AU and solar masses, should I convert G to AU^3/Msun/s^2?

 

[rude man]

Convert everything to SI. EVERYTHING - even your age and the area of your living room! :-)

 

[gneill]

You could do most everything in the given units... note that GM is the gravitational parameter μ for the Sun, and it has a better known value than G or M individually.

With distance units of AU, the natural time unit TU is the sidereal Earth year divided by $2 \pi$. That gives you a value in seconds for TU which might be useful later, but for the initial calculations just use "TU". The natural velocity unit VU is the average speed of the Earth in its orbit, or AU/TU. The gravitational parameter is then μ = AU³/TU².

Just using AU, TU, VU in your formulas where applicable will allow a lot of things to just cancel out without dealing with a bunch of numerical values.

You still need a formula for the perihelion distance. Any ideas on that front?