halley's comet has a period of 76 years and in 1986 had a distance of closest approach to the sun equal to 8.9*10¹⁰m.the comets farthest distance from the sun is the mass of the sun is 2*10³⁰kg in MKSunits.

a)2.7*10¹²m

b(2.7*10¹³m

c)5.3*10¹²m

d)5.3*10¹³m

(C) Whenever a heavenly body revolves round another body it follows an elliptical path having a distance o closest and farthest approach.

For these orbits

T₂ = (4Π²/GM)a³ , where a and T are average distance of comet from Sun and time period of revolution respectively.

.•. a = [T²GM/4Π²]^1/3

or, a = [((76×3.15×10⁷)²× 6.67×10^-11×2×10³⁰)/4Π² ]^1/3

≈ 2.7 × 10¹² m.

But for ellpse,

2a = r_min. + r_max.

(where a is the semi major axis of the ellipse)

or, r_max. = 2a - r_min.

r_max = 2 × 2.7 × 10¹² - 8.9 × 10¹⁰

r_max ≈ 5.3 × 10¹² m. Ans.