Objects in elliptical orbits sweep out equal areas in equal times. This implies that the orbital speed of planet around sun is not uniform. It moves fastest at the point closest to the sun (known as the perihelion) and slowest at the point farthest away (known as aphelion). In this problem, we will calculate the difference in this speed using Pluto as an example. Pluto's orbit has an eccentricity e = 0.25. Its semi-major axis is 5.9 times 10^9 km. Determine the distance (D_aphelion) between Pluto and the sun at aphelion. You should be able to determine this using just the semi-major axis and the eccentricity. Determine the distance (D_perihelion) between Pluto and the sun at perihelion. Again, you should be able to determine this using just the semi-major axis and the eccentricity. We now want to determine the ratio between Pluto's velocity at aphelion and perihelion: v_aphelion/v_perihelion. To do this you need to find the area swept out by Pluto's orbit. This can be approximately described as a triangle with: Area = 1/2 D v_i where D is the distance from the Sun. v is velocity, and t is time. Remember that Kepler's Second Law essentially states that planets sweep out "equal areas in equal times". This means that the area swept out in some fixed time interval (Delta t) is the same at perihelion as it is at aphelion. Therefore we can say: 1/2 D_perihelion v_perihelion Delta l = 1/2 D_aphelion v_aphelion Delta l Using Equation (2), derive an expression for v_aphelion/v_perihelion. Given that Pluto's minimum orbital velocity is 3.7 km s^-1, determine values for v_aphelion, and v_perihelion.

elly's long hair:

a. if the salon only takes cash, then this isn't the problem. it doesn't matter how much she has in her checking account.   she can't get a haircut until she has the cash.

b. if she has overdraft protection, then there's no problem.   she can go ahead and write a check that her account can't cover, then sometime later, pay the bank some outrageous usury for loaning her a few bucks for a few days, but with beautiful hair.

c. if elly has some principles, and doesn't want to write a bad check, then now she has a problem.   her desire for the new hairstyle is in conflict with her honesty and integrity.

d.   if the bank will not process a check she writes, then even if she had a million $$ in her account, she couldn't use any of it.   the amount she has in her account is not the problem.   and if i may suggest, she might as well close her checking account, and put the money where it'll work for her.   it's not doing her a bit of good in a checking account, since she can't write any checks.

justin can't pay the full balance:

a. he can't even handle the credit limit he has now.   under no circumstances should he ask for a higher limit.

b.   he can ask for the grace period to be extended.   but that's no solution, the bank will almost certainly refuse anyway, and there are much better options.   he knew the rules of his credit card when he started using it.

c.   he definitely should pay the interest on the balance, plus as much of the balance as he can cover at the same time.

d.   he definitely should pay the minimum otherwise they could shut down his card.   he should also pay as much more as he possibly can.   he should also remember the awkward situation he's in, stop buying stuff on credit that he can't afford, and avoid adding any more debt.

i'd say that justin's best best option isn't on this list of choices.   what he has to do:   pay as much as he can at least the minimum payment plus as much more as he can and then avoid adding more debt.

option number c is the right answer.

a sonic boom is a loud boom that breaks the sound barrier

explanation: