[Guest]

Picture this if you will

Let's say hypothetically, Mars is next to Mercury which is next to the Sun and are all aligned on the same plane. They both orbit the sun on the same plane as well. Mercury can completely orbit the sun in 100 days at a constant speed. Mars can completely orbit the sun in 350 days at a constant speed.

Given only the information above, if they are all align today like I mentioned, how many days from now will all three be aligned again?

[Pickett]

Picture this if you will

Let's say hypothetically, Mars is next to Mercury which is next to the Sun and are all aligned on the same plane. They both orbit the sun on the same plane as well. Mercury can completely orbit the sun in 100 days at a constant speed. Mars can completely orbit the sun in 350 days at a constant speed.

Given only the information above, if they are all align today like I mentioned, how many days from now will all three be aligned again?

140 days (at that point, mercury would have gone around the sun 1.4 times, and mars would have gone around the sun 0.4 times...)

Assuming they "start" at 0 degrees orbit around the sun, then they will align again at 144 degrees on day 140...

[Guest]

Assuming that the time interval of one day is the same for both planets, then I think Mercury, Mars and the Sun will be aligned again in 140 days.

[HoustonHokie]

they'll be realigned in the exact same position at 700 days, which is the least common multiple of 100 and 350. In that amount of time, Mercury will have circled the sun 7 times and Mars twice, which means that Mercury will have "lapped" Mars 5 times. So, the first time that they align in any position is 700 / 5 = 140 days.

[Guest]

while they will be aligned on the 140th day, that is not the correct answer

[Guest]

while they will be aligned on the 140th day, that is not the correct answer

they will be aligned many times in the future. I'm asking when the very next time will be.

[Guest]

they will be aligned many times in the future. I'm asking when the very next time will be.

The next time that they will be aligned is

70 days.

At this point, Mercury will have traveled .7 times around the sun and Mars will have traveled .2 times around. This creates a straight line with the sun inbetween.

[Guest]

77.77 days. If the planets are orbiting in opposite directions (hypothetically, as the problem indicates) in 77.77 days Mercury will have traveled 280 degrees and Mars 80 degrees at which point all three will be aligned.

Idonotexist has the correct answer, so I am adding this to the hypothetical situation of orbiting in opposite directions to equal 38.885 days.

Edited February 20, 2009 by raschaller

[preflop]

My guess

[Guest]

The next time that they will be aligned is

70 days.

At this point, Mercury will have traveled .7 times around the sun and Mars will have traveled .2 times around. This creates a straight line with the sun inbetween.

You got it!

[preflop]

doh

i was thinking 1/2 the value and not .5 away. boy do i feel sheepish. I need a scotch!