Question
How was the mass and radius of the Moon and the Sun measured historically? What is the best method to measure it at present?
Step 1
They used observations of lunar eclipses, where the Earth casts a shadow on the Moon. By measuring the size of the Earth's shadow and knowing the relative distances, they could estimate the Moon's size. Aristarchus of Samos and later Hipparchus made significant Show more…
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Ptolemy: Sizes and Distances Please refer to Ptolemy's planetary model (geocentric) in an astronomical and historical context. Question 1: The absolute distance to the moon, at closest approach, is 33 earth radii (e.r.). The absolute distance to the sun, at closest approach, is 1100 e.r. You may need to refer to a calculator. (a) Use the formula for the circumference of a circle to work out the circumferences of the circles corresponding to the closest positions of the moon and sun, in earth radii. (b) If the moon and sun both seem to be half a degree wide when viewed from the earth, how much larger, in earth radii, is the diameter of the sun than the diameter of the moon?
5. Using the Moon's orbital data, i.e. its orbital period around the Earth and the Earth-Moon distance, calculate the mass of the Earth and compare your answer with the actual mass as you can find it in tables. Consider that the Earth-Moon distance was known since Antiquity and Newton's Law of Gravity since the late 17th Century. The universal constant of gravity, however, was not known until the 18th Century.
Cravitational Fields The Moon is $3.9 \times 10^{5} \mathrm{km}$ from Earth's center and $1.5 \times 10^{8} \mathrm{km}$ from the Sun's center. The masses of Earth and the Sun are $6.0 \times 10^{24} \mathrm{kg}$ and $2.0 \times 10^{30} \mathrm{kg},$ respectively. a. Find the ratio of the gravitational fields due to Earth and the Sun at the center of the Moon. b. When the Moon is in its third quarter phase, as shown in Figure $7-17$, its direction from Earth is at right angles to the Sun's direction. What is the net gravitational field due to the Sun and Earth at the center of the Moon? (FIGURE CAN'T COPY)
Gravitation
Using the Law of Universal Gravitation
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