Go Outside And Look At The Smallest Moon Of The Year!

Classical Mechanics Level 2

Last night (January 15th 2014), the full Moon coincided with the lunar apogee. The Moon’s apogee is the point in its orbit when it is farthest from the earth. The point at which the Moon is closest to the earth is called the perigee.

How much smaller (in diameter) did the moon appear to us last night than it did at the last perigee?

  • The distance to the Moon at the most recent perigee was about 356,900 km.
  • Last night at apogee, the moon was about 406,500 km away.
20% It is the same apparent size. Ptolemy was right, Kepler was wrong, and Heliocentrism is a hoax. 6% 12%

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Peter Taylor by Peter Taylor

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3 solutions

Discussions for this problem are now closed

Ng Donn
Jan 18, 2014

(406500-356900)/406500 x 100% = 12.2%

22 Helpful 0 Interesting 0 Brilliant 0 Confused

This is because the size of the moon appear to us do have some relationships with the distance between the moon and the earth. So, since the moon is 49600 km further than the last perigee at the apogee on the 15th January, so it is approximately 12% smaller appear to us.

敬全 钟 - 7 years, 4 months ago

can we really differentiate between the two moons?I mean based on the resolution of our eyes... :-/

Tharun Namboothiri - 7 years, 4 months ago

I think the right answer (not listed) is 14%. reason: if u read the question, "How much smaller did the moon appear to us last night than it did at the last perigee?" so the divisor should be the distance of perigee (and not the distance at apogee). (406500-356900)/356900*100%

khurram haroon - 7 years, 4 months ago

Since it is stated that the moon was being observed last night, therefore we use the distance from Moon to Earth instead, which is 406500. So the denominator of the ratio should be 406500 as well.

Bryan Edden Dexter Roy - 7 years, 2 months ago

Can u give reason for it ?

Rohitas Bansal - 7 years, 4 months ago

Using Thales theorem in geometry

Võ Trọng - 7 years, 4 months ago
Nick De Ruyck
Jan 20, 2014

356900 / 406500 = 0,8779 82779 82779 ... So it is +/- 88% and that is 12% smaller.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

it is 12.20172202, I found the difference ( 406500-356900)=49600,

then i divided this difference with large value (406500) and multiply it with 100 to get percentage

Muhammad Mushtaq Mangat - 7 years, 4 months ago
Ammar Aziz
Jan 26, 2014

Actually i calculated the difference between the two distances and then i divided this difference by the larger distance to calculate the relative reduction in distance. According to physic this reduction in distance is directly proportional to increase in visibility and hence the deteced size of moon. And at last i multiplied the unit distance with 100 to calculate the percentage reduction in size

0 Helpful 0 Interesting 0 Brilliant 0 Confused

i dont get it why is the larger distance used?

Chiya Anand - 7 years, 3 months ago

Because we're using the last perigee as the frame point.

Pi Han Goh - 6 years, 1 month ago

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