An introduction to exoplanets
An introduction to exoplanets

Start this free course now. Just create an account and sign in. Enrol and complete the course for a free statement of participation or digital badge if available.

Free course

An introduction to exoplanets

5.3  Small rocky planets

You’ve seen that the smaller the planet, the smaller the dip in brightness when a transit occurs. It is perfectly easy to detect the transit of a Jupiter-sized giant planet from the ground. But it turns out that from the ground it is nearly impossible to detect the transit of an Earth-sized planet across a Sun-sized star – you just can’t measure precise enough light curves.

Activity 4  The transit depth

Timing: Allow about 10 minutes

For a star approximately the same size as the Sun and a planet approximately the same size as Jupiter, the transit depth is roughly 1%.

What would be the transit depth if the planet radius was:

  1. Half the size of Jupiter’s radius? (Hint: think about how the cross-sectional area of the planet would change – you may find Equation 1 useful.)
To use this interactive functionality a free OU account is required. Sign in or register.
Interactive feature not available in single page view (see it in standard view).

Answer

Answer: 0.25% or ¼%

The cross-sectional area of the planet depends on the square of its radius. If the radius is halved then the area will be quartered (1/2 × 1/2 = 1/4).

This means that the transit depth will also be quartered. The transit depth for Jupiter is roughly 1%, so the transit depth for this smaller planet will be about 1/4%.

If you prefer, from Equation 1, if Rp is halved and Rstar stays the same then the ratio Rp/Rstar will be halved, and so (Rp/Rstar)2 will be quartered.

  1. One-third the size of Jupiter’s radius?

To use this interactive functionality a free OU account is required. Sign in or register.
Interactive feature not available in single page view (see it in standard view).

Answer

Answer: 0.111% or 1/9%

The cross-sectional area of the planet depends on the square of its radius. If the radius is multiplied by 1/3 then the area will be multiplied by 1/3 × 1/3 = 1/9.

This means that the transit depth will also be multiplied by 1/9. The transit depth for Jupiter is roughly 1%, so the transit depth for this smaller planet will be about 1/9%.

  1. One-tenth the size of Jupiter’s radius?

To use this interactive functionality a free OU account is required. Sign in or register.
Interactive feature not available in single page view (see it in standard view).

Answer

Answer: 0.01% or 1/100%

The cross-sectional area of the planet depends on the square of its radius. If the radius is multiplied by 1/10 then the area will be multiplied by 1/10 × 1/10 = 1/100.

This means that the transit depth will also be multiplied by 1/100. The transit depth for Jupiter is roughly 1%, so the transit depth for this smaller planet will be about 1/100% or 0.01%.

Remember, Earth is approximately one-tenth the radius of Jupiter, so its transit would be 100 times smaller – a transit depth of just 0.01% of the light from the star! This would be pretty tricky to measure from the ground.

EXO_1

Take your learning further

Making the decision to study can be a big step, which is why you'll want a trusted University. The Open University has 50 years’ experience delivering flexible learning and 170,000 students are studying with us right now. Take a look at all Open University courses.

If you are new to University-level study, we offer two introductory routes to our qualifications. You could either choose to start with an Access module, or a module which allows you to count your previous learning towards an Open University qualification. Read our guide on Where to take your learning next for more information.

Not ready for formal University study? Then browse over 1000 free courses on OpenLearn and sign up to our newsletter to hear about new free courses as they are released.

Every year, thousands of students decide to study with The Open University. With over 120 qualifications, we’ve got the right course for you.

Request an Open University prospectus371