Question

HD 85512 b was discovered by means of very high precision radial velocity measurements using a telescope at La Silla in Chile. Use the data in Table 1 (which tells you, among other things, the mass of the star HD 85512) and the radial velocity information in Figure 2 to calculate:

• i.the orbital semimajor axis (in km and AU)
• ii.the mass (in kg and Earth masses) of HD 85512 b as fully as you can.

Explain how you used the table and figure to calculate your answers, and show your working.

Table 1  Data for the HD 85512 system, the Sun and the Earth.

Mass of HD 85512	0.69 Mo
Orbital period of HD 85512 b	58.43 days
Mo	1.99 × 1030 kg
ME	5.97 × 1024 kg

2 2 -0.1 0.0 0. 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 fraction of orbit completed

Answer 1

a is the semi-major axis of the orbit

G is the gravitational constant = 6.67408 * 10^-11 m³ kg^-1 s^-2

P is the orbital period

M is the combined mass of the primary and secondary bodies.

M = Mo+M_E = (1.99 * 10³⁰ kg) + ( 5.97 * 10²⁴ kg) = 10²⁴(1990000+5.97) kg = 1990005.97* 10²⁴ kg

P = 58.43

a = 0.2256076401802377 m ~ 22.56 cm

Mass of HD 85512 = 0.69 M_o = 0.69* 1.99 *10³⁰ kg = 1.3731*10³⁰ kg