Confussed about transit and subsequent transits

[leonne]

Homework Statement

How long is it between subsequent transits of New Sol by New Earth
How long does each transit last? Assume that the transit is central, i.e. the
projected path of the planet goes right over the center of the star

Homework Equations

Rp=(vp+vs)(t2-t1)(1/2)

The Attempt at a Solution

Not sure which problem goes with the formula, i thought it would go with how long transit last but got the answer as 427s which seems way to fast also the second problem says that i=90 but formula does not have an i so does it go with the first one or neither?

 

[mark726]

Hello! I would like to clarify and provide some information regarding your questions.

Firstly, the formula you have provided is used to calculate the radius of a planet's orbit (Rp) based on the velocities of the planet (vp) and the star (vs) and the time between two observations (t2-t1). This formula is not directly applicable to the question about the duration of transits.

To calculate the time between subsequent transits of New Sol by New Earth, we need to know the orbital period of New Earth (how long it takes to complete one orbit around New Sol). This can be calculated using Kepler's third law: P^2 = (4π^2/G)(a^3), where P is the orbital period, G is the gravitational constant, and a is the semi-major axis of the orbit.

Once we have the orbital period of New Earth, we can use it to calculate the time between subsequent transits, which would be equal to the orbital period itself.

As for the duration of each transit, it depends on the relative sizes and distances of New Sol and New Earth. If we assume that the transit is central, meaning the projected path of New Earth goes right over the center of New Sol, then the duration of each transit would be equal to the time it takes for New Earth to move from one side of New Sol to the other, which can be calculated using the formula d=vt, where d is the distance between the two objects and v is the velocity of New Earth.

The velocity of New Earth can be calculated using the formula v=2πr/P, where r is the distance between New Earth and New Sol (which would be the sum of their radii) and P is the orbital period of New Earth.

I hope this helps clarify the questions and provides a starting point for solving them. Remember to always use appropriate formulas and units in your calculations. Good luck!