A3 - Earth/Moon/Sun system

Question 1

Name the astronomical discoveries of the Earth/Moon/Sun system in order, and briefly describe the way they were found:

Answer 1

-diameter of Earth (Syene)
-diameter of Moon (lunar eclipse)
-distance to Moon (coin)
-distance to Sun (half moon)
-diameter of Sun (solar eclipse)

Question 2

How was the Earth’s diameter determined?

Answer 2

-Eratosthenes (calculated circumference and derived diameter)

-noticed objects in Syene had shadows straight down at Summer Solstice (because Sun is at zenith on Tropic of Cancer)
-tested if Alexandria had it too, but it made a shadow of angle 7.2°

-measured distance between cities (800km)
-used proportions to calculate full circumference

Question 3

How was the Moon’s diameter determined?

Answer 3

-Aristarchus, using lunar eclipses

-Moon took 3 hours to cross umbral shadow, use ratios to calculate angular width of the shadow
-Moon’s angular width was 0.5°, shadow’s width was 1.7°
-1.7/0.5 = 3.4
-Earth’s shadow’s width is 3.4x the width of the Moon
-assuming the Sun’s rays hitting Earth are parallel, the Earth is also 3.4x the size of the Moon

Question 4

How was the distance to the Moon calculated?

Answer 4

-Aristarchus

-a coin held at arm’s length blocked the Moon fully
-ratio of distance of coin : width of coin = 108 : 1
-by similar triangles, the ratio of the Moon’s distance to its diameter was also 108 : 1
-Moon diameter was known (Earth diameter / 3.4)
-calculating this with ratios gives roughly 400,000km

Question 5

How did we find out the distance to the Sun?

Answer 5

-Aristarchus, during half-Moon phase

-measured angular separation of Moon-Sun (87°)
-use small angle approximation (convert to radians first) to calculate distance to Sun as a ratio of the Moon’s distance to the Sun’s distance (~20x further)

It should have been ~400x further

Question 6

Suggest 2 sources of inaccuracy in Aristarchus’s measurement of the distance to the Sun:

Answer 6

-angle was hard to measure because it was close to 90°
-compounding error by using previously inaccurate measurements

Question 7

How was the diameter of the Sun found?

Answer 7

-Aristarchus (yet again)

(used his previously inaccurate measurement of the distance to the Sun)
-during total solar eclipse, Sun and Moon subtended same angle
-if the Sun was 20x further, it must be 20x larger than the Moon

Question 8

What is the shape of the Sun?

Answer 8

oblate spheroid (but almost a perfect sphere)

Question 9

What are tides caused by?

Answer 9

-Moon’s gravity pulls the oceans up towards it
-forms 2 bulges on either side (bulge on rear side is due to the Earth being pulled away from the ocean)

Question 10

Why do we have a certain number of tides per day?

Answer 10

-Earth rotates under the ocean’s bulge caused by the tidal forces from the Moon
-every location goes underneath 2 high tide areas and 2 low tide areas each day

Neil DeGrasse Tyson explains

Question 11

What are spring tides, and how do they form?

Answer 11

-higher high tide, lower low tide
-gravity from both Sun and Moon

Question 12

What are neap tides, and how do they form?

Answer 12

-lower high tide, higher low tide
-gravity from both Sun and Moon

The text in the picture is slightly wrong, I said higher low tide twice

Question 13

What is axial precession?

Answer 13

Earth’s axis of rotation “wobbles” over time, completing one precession every 26,000 years

Question 14

What changes arise due to axial precession?

Answer 14

-NCP’s position moves to a different area in sky
-zodiacal constellations are changed
-star’s positions change, including the Sun/Moon height

Question 15

What is the difference between an eclipse and an occultation?

Answer 15

-an eclipse is when an object passes in front of another object relative to the observer

-an occultation is when the Moon or another Solar System body passes in front of another object

Question 16

Name the types of eclipses, and their respective sub-types:

Answer 16

-solar (partial, total, annular)
-lunar (partial, total)

annular means ring-shaped, annular eclipse is where the Moon is further away in its orbit than usual so it doesn’t cover the Sun completely, leaving a ring of light around it

Question 17

Why are lunar eclipses more common than solar eclipses?

Answer 17

-Earth’s shadow is much bigger than the Moon’s shadow
-higher chance of the Moon passing into the Earth’s shadow, causing a lunar eclipse

they appear red because the blue light is scattered away from the atmosphere, and only the red light remains

Question 18

Why are lunar eclipses visible from more places than solar eclipses?

Answer 18

-the Moon is much smaller than the Earth’s shadow during a lunar eclipse, so the whole of the night hemisphere can see the lunar eclipse
-the shadow cast on Earth’s surface in a solar eclipse is very small, and only covers a small area

Question 19

Name and label the 3 parts of a shadow:

Answer 19

Question 20

What happens during totality of a solar eclipse?

Answer 20

Sun’s corona is visible (outermost part of its atmosphere)

Question 21

An observer sees the Moon on 2 dates - one is near the Summer Solstice, and the other is near the Winter Solstice. Explain their differences in appearance:

The Moon is in the same phase, and the observer is at the same location.

Answer 21

-during the Summer Solstice, the Sun’s altitude below the horizon is the smallest (and its largest is during the Winter Solstice)

-this means the Moon gets illuminated from different angles