If a comet was at aphelion (furthest distance from the sun) in 1944 and will be at perihelion (closest point to the sun) in 2050, at a distance of 0.5 AU, what would it's aphelion distance be
To determine the aphelion distance of the comet, we need to calculate the difference between the perihelion distance and the change in distance over the given time period.
Given information:
Perihelion distance (closest point to the sun) in 2050: 0.5 AU
To find the aphelion distance, we can use the concept of "conservation of angular momentum" for objects moving in elliptical orbits. According to this principle, the product of the object's mass, velocity, and the distance from the Sun remains constant throughout its orbit.
Using this principle, we can write the equation:
(mass × velocity × distance from the Sun) = constant
Since we are only interested in the changes in distance, we can rewrite the equation as:
(distance from the Sun) × (velocity) = constant
Now, we know the object's distance and velocity at both aphelion and perihelion. Let's represent the aphelion distance as 'A', aphelion velocity as 'V_a', perihelion distance as 'P', and perihelion velocity as 'V_p'.
So, we have two equations:
A × V_a = constant
P × V_p = constant
We can set up a ratio using these equations:
(A × V_a) / (P × V_p) = 1
Let's substitute the known values. At aphelion in 1944, the distance from the sun is the highest but is not provided. Therefore, we need to find it using the given perihelion distance and the ratio of constants.
Let's assume the perihelion distance in 1944 was 'x'. So, the equation becomes:
(A × 0.5 AU) / (P × 0.5 AU) = 1
(assuming P was 1 AU in 2050)
Now, we can find 'A' by solving for 'x':
(A × 0.5 AU) / (1 AU × 0.5 AU) = 1
A × 0.5 AU = 0.5 AU
A = 1 AU
Therefore, the aphelion distance of the comet would be 1 AU.