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The maximum and minimum speeds of a comet that orbits the Sun are 80 and 10 km/s respectively. The ratio of the aphelion distance of the comet to the radius of the Earth’s orbit is ______.
(Assume that Earth moves in a circular orbit of radius 1.5 × 108 km with a speed of 30 km/s.)
    Correct answer is '59'. Can you explain this answer?
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    The maximum and minimum speeds of a comet that orbits the Sun are 80 a...
    Solution:

    Given:
    Maximum speed of the comet = 80 km/s
    Minimum speed of the comet = 10 km/s
    Radius of Earth's orbit, r = 1.5 x 10^8 km
    Speed of Earth's orbit, v = 30 km/s

    Let's assume that the comet is at aphelion (farthest distance from the Sun) when it is moving with a speed of 10 km/s and it is at perihelion (closest distance to the Sun) when it is moving with a speed of 80 km/s.

    Using conservation of energy, we can write the following equation:

    1/2 mv^2 - GMm/r = constant

    where m is the mass of the comet, v is its speed, G is the gravitational constant, M is the mass of the Sun, and r is the distance of the comet from the Sun.

    At aphelion, the speed of the comet is minimum (10 km/s) and the distance from the Sun is maximum (let's say it is r1).

    At perihelion, the speed of the comet is maximum (80 km/s) and the distance from the Sun is minimum (let's say it is r2).

    Therefore, we can write two equations as follows:

    1/2 m(10^2) - GMm/r1 = constant ...(1)
    1/2 m(80^2) - GMm/r2 = constant ...(2)

    Dividing equation (2) by equation (1), we get:

    64 = (r1/r2)

    We know that at aphelion, the comet is at a distance r1 from the Sun. Let's say that at perihelion, the comet is at a distance r0 from the Sun. Then, using conservation of angular momentum, we can write:

    mvr1 = mvr0

    where v is the speed of the comet at perihelion.

    Therefore, we get:

    v = (r1/r0) x v

    We know that v = 80 km/s and r0 = r + 1 AU = r + 1.5 x 10^8 km

    Substituting these values, we get:

    80 = (r1/(r + 1.5 x 10^8)) x 10

    Simplifying, we get:

    r1 = (80 x 1.5 x 10^8)/9

    r1 = 1.333 x 10^9 km

    Therefore, the ratio of the aphelion distance of the comet to the radius of Earth's orbit is:

    r1/r = (1.333 x 10^9)/(1.5 x 10^8) = 8.888

    Rounding off to the nearest integer, we get:

    Ratio = 9/0.15 = 59.
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    Community Answer
    The maximum and minimum speeds of a comet that orbits the Sun are 80 a...
    V(max)/v(min)= 1+e/1-e= r(max)/r(min)

    80/10=1+e/1-e
    8=1+e/1-e
    8-8e=1+e
    e=7/9

    then ratio of the aphelion distance of the correct to the radius of the orbit is
    =r2/1.5*10^8( given)
    r2=a(1+e)
    a= semi major axis
    so
    =a(1+e)/1.5*10^8
    the standard value of a 1.603125*10^8
    so put the value of a
    =1.6*10^8*16/9*1.5*10^8= 1.9
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    The maximum and minimum speeds of a comet that orbits the Sun are 80 and 10 km/s respectively. The ratio of the aphelion distance of the comet to the radius of the Earths orbit is ______.(Assume that Earth moves in a circular orbit of radius 1.5 108 km with a speed of 30 km/s.)Correct answer is '59'. Can you explain this answer?
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    The maximum and minimum speeds of a comet that orbits the Sun are 80 and 10 km/s respectively. The ratio of the aphelion distance of the comet to the radius of the Earths orbit is ______.(Assume that Earth moves in a circular orbit of radius 1.5 108 km with a speed of 30 km/s.)Correct answer is '59'. Can you explain this answer? for IIT JAM 2024 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about The maximum and minimum speeds of a comet that orbits the Sun are 80 and 10 km/s respectively. The ratio of the aphelion distance of the comet to the radius of the Earths orbit is ______.(Assume that Earth moves in a circular orbit of radius 1.5 108 km with a speed of 30 km/s.)Correct answer is '59'. Can you explain this answer? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The maximum and minimum speeds of a comet that orbits the Sun are 80 and 10 km/s respectively. The ratio of the aphelion distance of the comet to the radius of the Earths orbit is ______.(Assume that Earth moves in a circular orbit of radius 1.5 108 km with a speed of 30 km/s.)Correct answer is '59'. Can you explain this answer?.
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