Imagine standing (somewhere) on the Moon's surface. How big would the Earth look from the Moon, compared to the image of the Moon we see from Earth? What would be the ratio between the diameters of each body? How would this ratio be calculated? Any help with answering such a calculation would be highly appreciated.
1$\begingroup$ Do you know the respective physical diameters of Earth and Moon? $\endgroup$– pelaMay 23, 2017 at 11:35
1$\begingroup$ For the moon 3.479 × 10^3 Km, and for Earth 12.75632 10^3 Km $\endgroup$– nilo de roockMay 23, 2017 at 11:45
7$\begingroup$ Since the angular diameter of an object is proportional to the ratio between its size and its distance (and since the distance from Earth to Moon is equal to the distance from Moon to Earth), the ratio you request is the same as the ratio between those numbers. $\endgroup$– pelaMay 23, 2017 at 11:59
$\begingroup$ Almost 4 times bigger. $\endgroup$– Florin AndreiMay 24, 2017 at 1:27
$\begingroup$ Besides knowing the ratio of apparent sizes, you should also know about how it is measured without comparison. There is also a unit of measuring the apparent size of planets and other bodies in space. The measurement is called 'Angular diameter' and the unit is 'arc minute' and 'arc second'. You can find the details easily by searching 'angular diameter' over the net. $\endgroup$– Diwakar MishraNov 15, 2018 at 8:51
There are a couple questions here. The ones you have asked are:
- What would be the ratio between the respective diameters?
- How would this ratio be calculated?
But I think you meant to ask:
- How much larger does the Earth appear when standing on the Moon than the Moon appears when standing on the Earth? (and the calculation)
For the answer to #1 (and #2), it is the ratio between the numbers (of the Earth's diameter of 12,742 km and the Moon's diameter of 3,474 km) which is $Earth:Moon = 3.668:1$ as @pela's comment mentions.
For the answer to #3, it is the same! The more interesting part is why. We know that the distance from the Earth to the Moon is the same as the Moon to the Earth, so it follows that when we are on one of them looking at the other we are gazing across the same distance. Next, we know that an object (approximately) appears larger in the same proportion as it is larger, so an object that is twice as wide or tall will appear twice as wide or tall. Since the Earth is 3.668 times as wide as the Moon, it will appear that much larger when viewed from the same distance, and we've already discussed why it is the same distance. So, that's it really. It is the ratio of the diameters.