5. Planets outside our solar system are called exoplanets - Scottish Highers Physics - Question 5 - 2017

Using Newton's law of gravitation:

$F = G \frac{m_1 m_2}{r^2}$

where G is the gravitational constant, $G \approx 6.67 \times 10^{-11} \text{ N m}^2/\text{kg}^2$

Letting:

• $m_1 = 3.83 \times 10^{30} \text{ kg}$ (mass of the star)
• $m_2 = 5.69 \times 10^{27} \text{ kg}$ (mass of the exoplanet)
• $r = 3.14 \times 10^{11} \text{ m}$ (distance between them)

Then:

$F = 6.67 \times 10^{-11} \frac{(3.83 \times 10^{30})(5.69 \times 10^{27})}{(3.14 \times 10^{11})^2}$

Calculating this yields:

$F \approx 1.47 \times 10^{19} \text{ N}$

To calculate the redshift ($z$), we can use the formula:

$z = \frac{v}{c}$

where:

• $v$ is the speed of the star (let's take $v = 6 \times 10^{-13} \text{ m s}^{-1}$ for the calculation)
• $c \approx 3 \times 10^8 \text{ m s}^{-1}$ (speed of light)

Thus:

$z = \frac{6 \times 10^{-13}}{3 \times 10^8} \approx 2 \times 10^{-21}$

For an exoplanet of greater mass, the gravitational force would be stronger, affecting the circular motion of the star. The redshift would also depend on the velocity of the star due to gravitational influence. Therefore, under these conditions, the redshift should be greater than that of an exoplanet with smaller mass.