If you lived on Mars, what would Earth’s the greatest elongation appear as from Mars?

Question

If you lived on Mars, what would Earth’s the greatest elongation appear as from Mars. Use the distance of Earth from the Sun as 1 AU and Mars from the Sun 1.5 AU

So we know the two angles 1.5AU and 1AU, how would you get degrees to know the 3rd angle?

Answer 1

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You have a right-angled triangle, with the angle at the Earth's corner equal to 90º. The angle you want is therefore arcsin(1.0/1.5) = 41.81º.

Answer 2

The maximum elongation happens when the distance to the sun and to the earth are the same, 1.5 AU. So you have a triangle:

Mars to Sun: 1.5 AU

Mars to Earth: 1.5 AU

Earth to Sun: 1.0 AU

Solving the triangle, the angle is 38.942 degrees.

Note: During the decade 2000-2010, the max angle is actually 47.382 degrees. This was on 2005-Jul-13, when the Mars-Earth distance was 0.9352 AU, and the Mars-Sun distance was 1.3815 AU.

Source(s): http://ssd.jpl.nasa.gov/?horizons

Answer 3

Greatest Elongation

Source(s): https://shrinke.im/a9GpQ

Answer 4

Not the answer you want, but a quick check in Starry Night by actually going to Mars and looking at Earth shows the elongation to be around 38 degrees.

To solve the exact problem above, I'd recommend making a simple diagram showing the Sun, Earth, Mars, and their orbits. Then it's simple geometry.

Source(s): Starry Night software

Answer 5

The earth's orbit is an ellipse, but an approximation can be made by regarding the orbit as a circle. The hypotenuse of thes triangle EMS

is MS (distance from Mars to Sun, and one side is ES (distance from Earth to Sun.) Regarding the orbit as a circle ==> ME tangent to Earth's orbit ==> Angle MES is a right angle. Elongation is therefore

arc sin (SE/SM) or tan(-1)(SE/SM)

Source(s): retired math teacher

Answer 6

You don't need to. An equilateral triangle would have sixty degree corners, so an object Trojan to Mars would be that angular distance from the Sun. Earth is two-thirds of that distance, so it'd be forty degrees from the Sun.

Answer 7

The maximum angular separation of Earth and the sun, as seen from Mars, is 47.378°, which occurs when Earth is at heliocentric ecliptic longitude 291.644° (and about 8.8° of mean anomaly past aphelion) and when Mars is at heliocentric ecliptic longitude 334.373° (and about 1.58° of mean anomaly prior to perihelion).

For that configuration...

Distance from Sun to Earth = 1.01651 AU

Distance from Sun to Mars = 1.38144 AU

Distance from Mars to Earth = 0.93789 AU

Assumption: Orbital elements for Earth.

a = 1.0000 AU

e = 0.01671

i = 0.000°

Ω = 0.000°

ω = 102.970°

Assumption: Orbital elements for Mars.

a = 1.5237 AU

e = 0.0934

i = 1.8489°

Ω = 49.53°

ω = 286.571°