Question

Calculate the radius of Eris using equation 21.1, where R = radius in km, r = heliocentric distance (97.6 AU), ) = distance from the Earth (96.6 AU), p = albedo expressed as a decimal fraction (0.86), and V = visual magnitude (18.8).

Answer 1

R² = (4.53 x 10⁵r²Δ²)/(10^0.4v x p)

0.4 x 18.8 = 7.52

107.52 = 33.113 x 10⁶

R₂ = ((453 x 10⁵ x (97.6)²(96.6)²)/(33.113 x 10⁶ x 0.86)

R₂ = 14.140 x 10⁶ x 10^-1

R = (14.140 x 10⁵)^1/2 = 1189.0km

Note: The radius of Pluto is 1150 km (i.e., Eris is larger than Pluto).