Question

Halley's comet orbits the Sun with a period of 75.3 yr. a) Find the semimajor axis of the orbit of Halley's comet in astronomical units (1 AU is equal to the semimajor axis of the Earth's orbit). b) If Halley's comet is 0.586 AU from the Sun at perihelion, what is its maximum distance from the Sun, and what is the eccentricity of its orbit?

SHOW ALL WORK PLEASE!

Answer 1

According to above concept

Kepler’s third law says that a3 ? T

. If we measure a in AU and T in years, then the constant of

proportionality is 1, and we can write that a3 = T2

. Since we are given that T = 75.3 years for Halley’s

comet:

a = ?3

T2 =

?3

762 =

?3

5776 = 17.9 AU

• The perihelion distance is given by:

RP = a(1 ? e) = 17.9(1 ? 0.967) = 0.59 AU

• Similarly, the aphelion distance is given by:

RA = a(1 + e) = 17.9(1 + 0.967) = 35.2 AU

• The ratio of sunlight intensity is given by the inverse square of the ratio of these two distances:

IPerihelion

IAphelion

= (RA

RP

)

2 = (35.2

0.59

)

2 = 3560

• This is why comets put on such a showy display when they get close to the sun, because the intense

sunlight boils off liquids and gases that remain frozen when the comet is far from the sun. The resulting

cloud of gas and dust is what makes the comet’s tail

• At midnight we are looking out away from the sun. But Venus’ orbit is entirely inside the Earth’s orbit, so it is hidden by the body of the Earth. Venus and Mercury are only ever visible near the sun in the sky, so just after sunset in the evening or just before sunrise in the morning.

3. Mercury’s orbit has a semi-major axis of 0.387 AU, and an eccentricity of 0.206.