Relevant Numbers1 AU = 150,000,000 km = 1.5x108 kmRadius of Earth: 6371 km1 mile = 1.6 km3600 arc sec=1 degreeEarth-Moon Distance: 384,400 kmLight-year: Distance light travels in oneyear (light travels at 3x105 km/s)Perihelion:p=a(1-e)Aphelion:q=a(1+e)Kepler's 3rd Law:P2 = Ca³above:a: semi-major axise: eccentricityp: perihelionq: aphelionP: Orbital periodC: Constant of proportionality 2.Z↓A.)Today we know that the Moon is on average, 384,400 km away from theEarth, while the average Earth-Sun distance is 1 au. The Moon's orbitabout the Earth has an eccentricity of 0.0549. Imagine Aristarchusrepeated his experiment when the Moon was at perigee (its closestpoint to the Earth), what angle should he have measured betweenthe Moon and the Sun?Assume he was capable of making precise measurements.B.) Given that Venus orbits with a semi-major axis of 0.723au, what is the greatest angular separation between it and the Sun asviewed fromEarth?C.) Comet Halley is an object that travels on a highly eccentric orbit aroundthe Sun. It has an orbital period of nearly 76 years. Using Kepler's thirdlaw (the square of the orbital period of an object in orbit around the Sunis proportional to the cube of the semi-major axis), approximately whatis Comet Halley's semi-major axis? It's periheilionis approximately 0.6 au; what is the eccentricity of its orbit?

Answered: A.)Today we know that the Moon is on…

Applications and Investigations in Earth Science (9th Edition)

9th Edition

ISBN:9780134746241

Author:Edward J. Tarbuck, Frederick K. Lutgens, Dennis G. Tasa

Publisher:Edward J. Tarbuck, Frederick K. Lutgens, Dennis G. Tasa

Chapter1: The Study Of Minerals

Section: Chapter Questions

Problem 1LR

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Relevant Numbers
1 AU = 150,000,000 km = 1.5x108 km
Radius of Earth: 6371 km
1 mile = 1.6 km
3600 arc sec=1 degree
Earth-Moon Distance: 384,400 km
Light-year: Distance light travels in one
year (light travels at 3x105 km/s)
Perihelion:
p=a(1-e)
Aphelion:
q=a(1+e)
Kepler's 3rd Law:
P2 = Ca³
above:
a: semi-major axis
e: eccentricity
p: perihelion
q: aphelion
P: Orbital period
C: Constant of proportionality

2.
Z↓
A.)Today we know that the Moon is on average, 384,400 km away from the
Earth, while the average Earth-Sun distance is 1 au. The Moon's orbit
about the Earth has an eccentricity of 0.0549. Imagine Aristarchus
repeated his experiment when the Moon was at perigee (its closest
point to the Earth), what angle should he have measured between
the Moon and the Sun?
Assume he was capable of making precise measurements.
B.) Given that Venus orbits with a semi-major axis of 0.723
au, what is the greatest angular separation between it and the Sun as
viewed from
Earth?
C.) Comet Halley is an object that travels on a highly eccentric orbit around
the Sun. It has an orbital period of nearly 76 years. Using Kepler's third
law (the square of the orbital period of an object in orbit around the Sun
is proportional to the cube of the semi-major axis), approximately what
is Comet Halley's semi-major axis? It's periheilion
is approximately 0.6 au; what is the eccentricity of its orbit?

Expert Solution

Step 1

Aristarchus' measurement of angle between the Sun and the Moon can be repeated when the Moon is at its perigee. We can use the following that to estimate the Aristarchus' measurements. Given that distance between Earth and Sun is 1AU = 1.5 X 10⁸ Km. The distance between Moon and Earth is given as 384,400 Km. It is also given that orbit of moon is about 0.0549 eccentricity from Earth.