Question

Mars is 99,300,000 kilometres from Earth and has an angular diameter of 14.1 arc seconds, what is the diameter of Mars?

Answer 1

Using the figures the diameter of Mars is 6,788km.

Explanation:

The formula for calculating the diameter `d` of Mars is:
`d=rtheta`
Where `r=99,300,000` is the distance from Earth to mars in kilometres and `theta` is the angular diameter in radians.

Converting the angular diameter form arc seconds to radians gives:

`theta=(14.1)/(60*60)*pi/180`

This gives `d=6788`km.

The actual diameter of Mars is `6779`km which is very close.