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

Using Newton's law of gravitation, the gravitational force is given by:

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

Where:

• $G = 6.67 \times 10^{-11} \text{ N m}^2/\text{kg}^2$ (gravitational constant)
• $m_1 = 5.69 \times 10^{7} \text{ kg}$ (mass of the exoplanet)
• $m_2 = 3.83 \times 10^{9} \text{ kg}$ (mass of the star)
• $r = 3.14 \times 10^{11} \text{ m}$ (distance)

Computing yields:

$F = 6.67 \times 10^{-11} \frac{(5.69 \times 10^{7})(3.83 \times 10^{9})}{(3.14 \times 10^{11})^2} \approx 1.47 \times 10^{10} \text{ N}.$

The redshift $z$ can be calculated using the formula:

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

where:

• $v = 6.60 \times 10^{-13} \text{ m s}^{-1}$ (velocity of the star)
• $c = 3.00 \times 10^{8} \text{ m s}^{-1}$ (speed of light)

So we find:

$z = \frac{6.60 \times 10^{-13}}{3.00 \times 10^{8}} \approx 2.20 \times 10^{-21}.$

The redshift would be greater since the gravitational force increases with mass; thus, the star would have a more substantial gravitational influence and consequently a greater redshift effect.