### GR0177-22 Need More Detailed Explaination

Posted:

**Sat Oct 21, 2006 7:01 am**Okay guys. I read Yosofun's solution but it seems like one has more variables than equations to solve for velocity, period, and mass of the planet.

I know (E) is automatically eliminated since semimajor axis is the same as maximum distance.

But Kepler's Third Law States

T^3 = (4 * pi^2/GM) * r^2

You you NEED M the mass of the planet to solve for T the period.

You also NEED M the mass of the planet to solve for v the minimum speed using the conversation of energy:

-k/(2a)=1/2mv^2-k/r

where k = GMm/r

It seems we have three unknown variables T, M, v and only two equations.

Am I missing something??

I know (E) is automatically eliminated since semimajor axis is the same as maximum distance.

But Kepler's Third Law States

T^3 = (4 * pi^2/GM) * r^2

You you NEED M the mass of the planet to solve for T the period.

You also NEED M the mass of the planet to solve for v the minimum speed using the conversation of energy:

-k/(2a)=1/2mv^2-k/r

where k = GMm/r

It seems we have three unknown variables T, M, v and only two equations.

Am I missing something??