Please help on calculating area of space of the line between the Sun and an asteroid.?

Question

An asteroid is orbiting the Sun. The line from the Sun to the asteroid sweeps out an area of space equal to 6AU^2 in 2003.

a. How much area of space will this line seep out in 2006?

b. How much area of space will this line seep out over a three year period?

Answer 1

There are no factors to suggest it will sweep out more or less area in 2006 than 2003. That would only happen if its orbit changed, but you have no data to suggest changes in its orbit.

Without having any orbital change data, it can only be said that it would sweep out 6 x 3 = 18AU^2 in 3 years.

I think we are missing some data here.

Answer 2

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Answer 3

Kepler's 2nd law says it sweeps out an equal area in an equal time. Since it swept out 6AU^2 in one year, it will do the same in any other year. And it will sweep out three times as much is three years.

Answer 4

One of Kepler's Second Law is equal area in equal times. If you know the area for one year, you can solve for a month or three years without having to do advanced math.

Answer 5

a. 6 AU^2.
b. 18 AU^2.