Question

Let us say that at their closest approach, Mars is 54.6 million kilometers from the Earth. The Earth has a diameter of 12,742 km. How large (in arcseconds) will the Earth look from Mars? (rounded to the nearest hundredth)

Answer 1

The Earth will appear to be about 0.84 arcseconds in size from Mars.

Step-by-step explanation:

To calculate the size of the Earth as seen from Mars, we first need to calculate the angular diameter of the Earth. Angular diameter is the angle that an object appears to span when viewed from a specific location.

The formula to calculate the angular diameter is:

Angular diameter = diameter of the object / distance to the object

Plugging in the given values, the diameter of the Earth is 12,742 km and the distance between Earth and Mars is 54.6 million km, the calculation gives us:

Angular diameter of the Earth = 12,742 / 54,600,000

Angular diameter of the Earth ≈ 0.0002332 degrees

To convert this into arcseconds, multiply this value by 3600 (since there are 3600 arcseconds in a degree), giving us:

Arcseconds ≈ 0.0002332 * 3600 = 0.83952 arcseconds

Therefore, the Earth will appear to be about 0.84 arcseconds in size from Mars.