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1. Homework Statement
Mars orbits the sun at a mean distance of 228 million km, in a period of 687 days. The Earth orbits at a mean distance of 149.6 million km in a period of 365.26 days. All answers should be in the range (0, 2pi)
a) suppose Earth and Mars are positioned such that Earth lies on a straight line between Mars and the Sun. Exactly 365.26 days later, when the Earth has completed one orbit, what is the angle between the Earth-Sun line and the Earth-Mars line?
b) The initial situation in part a) is a closest approach of Mars to the Earth. What is the time between 2 closest approaches? Assume constant orbital speeds and circular orbits. (Hint: when angles are equal)
c) Another way of expressing b) is with the angle between the Sun, Earth, and Mars in the two closest approach situations. What is that angle?
2. Homework Equations
Probably angular speed= 2pi/period
angle traveled = angular speed x time
3. The Attempt at a Solution
My homework is online, and we get three tries per problem. I attempted this one and apparently got all three parts wrong. For a) I used angular speed = 2pi/period to get the angular speeds for Earth and Mars. I then multiplied these speeds by time to get the angle traveled for each. Earth was 2pi, and for Mars I got 3.34 radians, which is wrong. :/
For part b) It says to use the relationship between angle, angular speed,and time, which is angle traveled = angular speed x time. The angle traveled by Earth would be angle traveled by Mars + 2pi according to the hint.
c) According to the hint. solve the equation used in b) for the angle instead of for time. I think once I get
I figure once I get a) I may be able to eventually work out the rest. Anyone know what I did wrong with a)? I've tried so many different ways but keep getting the same answer.
Thanks!
Mars orbits the sun at a mean distance of 228 million km, in a period of 687 days. The Earth orbits at a mean distance of 149.6 million km in a period of 365.26 days. All answers should be in the range (0, 2pi)
a) suppose Earth and Mars are positioned such that Earth lies on a straight line between Mars and the Sun. Exactly 365.26 days later, when the Earth has completed one orbit, what is the angle between the Earth-Sun line and the Earth-Mars line?
b) The initial situation in part a) is a closest approach of Mars to the Earth. What is the time between 2 closest approaches? Assume constant orbital speeds and circular orbits. (Hint: when angles are equal)
c) Another way of expressing b) is with the angle between the Sun, Earth, and Mars in the two closest approach situations. What is that angle?
2. Homework Equations
Probably angular speed= 2pi/period
angle traveled = angular speed x time
3. The Attempt at a Solution
My homework is online, and we get three tries per problem. I attempted this one and apparently got all three parts wrong. For a) I used angular speed = 2pi/period to get the angular speeds for Earth and Mars. I then multiplied these speeds by time to get the angle traveled for each. Earth was 2pi, and for Mars I got 3.34 radians, which is wrong. :/
For part b) It says to use the relationship between angle, angular speed,and time, which is angle traveled = angular speed x time. The angle traveled by Earth would be angle traveled by Mars + 2pi according to the hint.
c) According to the hint. solve the equation used in b) for the angle instead of for time. I think once I get
I figure once I get a) I may be able to eventually work out the rest. Anyone know what I did wrong with a)? I've tried so many different ways but keep getting the same answer.
Thanks!
)
… read the question!