Distance to Mars: Earth-Mars Equation for Moon-Sized Mars View

[Scrythe]

Hey guys, With that rumor around the internet that Mars will look as big as the moon, i was wondering how far the Mars would be from the Earth for it to really look that big.

show an equation that shows the distance from Earth to Mars where Mars would have the same diameter as the moon, when viewed from earth. I guess some research would be involved to find the diameter of the moon when viewed from earth.

-Scrythe

 

[mgb_phys]

Moon:
Distance = 385,000km
Diameter = 3500km

Mars:
Diameter = 6800km

Distance Mars would have to be at to appear same size as moon
=(6800km/3500km) * 385,000km = 750,000km

Closest approach of Mars to Earth = 55,758,000km

 

[Scrythe]

hmm...seems easier than i thought. Thanks for the quick reply.

Is there any way to show this using a triangle?

 

[mgb_phys]

Is there any way to show this using a triangle?

Yes.

 

[russ_watters]

That's actually what he did - the mathematical concept is "similar triangles": http://www.gcseguide.co.uk/similar_triangles.htm

You are at one point of the triangle, the moon or Mars is at the far side and the two big sides are the distance. They aren't really making a right triangle, but you can assume it to make the calculation easier if you want.

 

[flatmaster]

Moon:
Distance = 385,000km
Diameter = 3500km

Mars:
Diameter = 6800km

Distance Mars would have to be at to appear same size as moon
=(6800km/3500km) * 385,000km = 750,000km

Closest approach of Mars to Earth = 55,758,000km

Moon angular size of diameter = (3.5/385) * 180deg/pi = 0.52 deg
Mars angular size of diameter = (6.8/55,758) * 180deg/pi = 0.0070 deg

To truly do it, you need a solid angle, but you get the picture.

 

[Scrythe]

cool, thanks guys

 

[robert Ihnot]

While the calculations show that Mars will never be so close as to appear the same size of the Moon, a matter--which comes to mind---and, perhaps, related to this discussion is the Moon illusion:

The Moon illusion is an optical illusion in which the Moon appears larger near the horizon than it does while higher up in the sky. This optical illusion also occurs with the sun and star constellations. It has been known since ancient times, and recorded by numerous different cultures.

Wikipedia has a long article on this.