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The elongation a of planet is the angle formed by the planet, earth, and sun (see figure). It is known that the distance from the sun to Venus is 0.723 AU. At a certain time, the elongation of Venus is found to be 39.4o. Find the possible distances from the Earth to Venus at that time in astronomical units (AU).

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Coleen Amado
Coleen AmadoLv10
11 Mar 2021

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Related textbook solutions

Physics: Principles with Applications
7th Edition, 2013
Giancoli
ISBN: 9780321625922

Related questions

As implied earlier, according to Kepler’s laws, Earth’s orbit is an ellipse with the Sun at one focus. The perihelion for Earth’s orbit around the Sun is 147,098,290 km and the aphelion is 152,098,232 km.


a) By placing the major axis along the x-axis, find the average distance from Earth to the Sun.


b) The classic definition of an astronomical unit (AU) is the distance from Earth to the Sun, and its value was computed as the average of the perihelion and aphelion distances. Is this definition justified?

All of the following statements are true. Which one can be explained by Kepler's second law?

  1. The Sun is not in the precise center of Saturn's orbit.
  2. Earth is slightly closer to the Sun in January than in July.
  3. All the planets orbit the Sun in nearly the same plane.
  4. Mars moves faster in its orbit when it is closer to the Sun than when it is farther from the Sun.
  5. Venus orbits the Sun at a faster orbital speed than Earth.

The Mars Polar Lander spacecraft was launched on January 3, 1999.On December 3, 1999, the day that Mars Polar Lander touched down onthe Martian surface, the positions of the earth and Mars were givenby these coordinates:

x y z
Earth 0.3182 AU 0.9329 AU 0.0000 AU
Mars 1.3087 AU -0.4423 AU -0.0414 AU

In these coordinates, the sun is at the origin and the plane of theearth's orbit is the xy-plane. The earth passes through the +x-axisonce a year on the autumnal equinox, the first day of autumn in thenorthern hemisphere. One AU is equal to 1.496 * 10^8 km, theaverage distance from the earth to the sun.

a) In a diagram, show the positions of the sun, the earth, and Marson December 3, 1999.

b) Find the following distances in AU on December 3,1999 :

i) from the sun to the Earth


ii) from the sun to Mars


iii) from the earth to Mars



c) As seen from the earth, what was the angle between the directionto the sun and the direction to Mars on December 3, 1999?

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