Question

because you can detect the planet from a transit method, you can assume you are seeing its orbit edge-on, in which case the mass that you determined in question 8 is equal to its real mass. what is the density of the planet?

Answer 1

The density of the planet is calculated using the mass of the planet (70% of Jupiter's mass) and its volume (determined by a radius 35% larger than Jupiter's), leading to an understanding of the planet's composition.

Step-by-step explanation:

To calculate the density of the planet, we use the formula for density which is mass divided by volume. The volume of a sphere is given by (4/3)πr^3, where r is the radius of the planet. Given that the planet has about 70% the mass of Jupiter and a radius about 35% larger than Jupiter's, we calculate the density using these comparative figures. Assuming Jupiter's mass is approximately 1.90 × 10^27 kg and its mean radius is about 69,911 km, we calculate the mass of the transiting planet as 0.70 × 1.90 × 10^27 kg and use a radius 1.35 times that of Jupiter.

Therefore, the density (ρ) is calculated as:

ρ = Mass / Volume

ρ = (0.70 × 1.90 × 10^27 kg) / × [(4/3)π(1.35 × 69,911 km)^3]

This calculation will yield the average density of the planet, and based on this density, we can infer whether the planet is a gas giant or a terrestrial planet, much like HD 209458b was determined to be a gas giant due to its low density.