Example in chapter: Gravitation

• EngMan
In summary, the conversation is discussing the motion of a comet in an elliptical orbit around a star with an eccentricity of 0.20. The distance between the perihelion and aphelion is 1.0 × 10^8. The question is asking for the distances of the nearest and farthest approaches of the comet and the speed of the comet at perihelion and aphelion. To find the distances, the sum of the perihelion and aphelion is divided by 2 to get the semi-major axis. The distance of the nearest approach is then found by subtracting 20% of the semi-major axis from the sum, and the distance of the farthest approach is found
EngMan

Homework Statement

consider the motion of a comet in an elliptical orbit around a star. the eccentricity of the orbit is given by e= 0.20 and the distance between the perhelion and the aphelion is 1.0 × 10^power8

a- find the distances of nearest and farthest approaches of the comet.
b- if the speed of the comet is 81 km/s at perihelion, what is its speed at aphelion?

there is a solution but i can't understand it
i hope someone help me step by step

The Attempt at a Solution

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Which part is unclear?

mfb said:
Which part is unclear?
how Rmax=1×10^8 × 1.20 ÷ 2
is the second picture

By definition, the eccentricity tells you how much periapsis and apoapsis deviate from the semi-major axis, here 20%=0.2. Periapsis is at (1-0.2) times the semi-major axis, and apoapsis is at (1+0.2) times the semi-major axis.

The semi-major axis is the mean of the two, and you are given the sum, so you have to divide the sum by 2 to get the the semi-major axis.

Q: What is the definition of gravitation?

Gravitation is a natural phenomenon by which all objects with mass are brought together towards one another.

Q: Who first discovered the concept of gravitation?

The concept of gravitation was first discovered by Sir Isaac Newton in the 17th century.

Q: How does gravitation affect objects in space?

Gravitation affects objects in space by causing them to orbit around larger objects, such as planets orbiting around stars.

Q: How is gravitation related to the force of gravity?

Gravitation and the force of gravity are closely related, as gravitation is the natural phenomenon that causes objects to be attracted to one another, while the force of gravity is the measurable force that results from this attraction.

Q: What role does gravitation play in the formation of our solar system?

Gravitation played a vital role in the formation of our solar system, as it caused particles and matter to come together and form larger objects, such as planets and moons.

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