How do you calculate speed at an object's perihelion?

Question

For example: The orbit of Halley's Comet around the sun is a long thin ellipse. At its aphelion the comet is 5.40 x 10^12m from the sun and moves with a speed of 13.0 km/s. What is the comet's speed at its perihelion where its distance from the sun is 8.60 x 10^10m.

Ivy Allen · Accepted Answer

(perihelion speed / aphelion speed ) = ( 1 + eccentricity) / ( 1 #-# eccentricity ) = (aphelion distance / perihelion distance)
So, the comet's perihelion speed = 816 km/s, nearly.

Perihelion speed = (5.40 x 10^12 / 8.60 x 10^10) X 13 km/s In the usual notation, v^2 = #mu# (2/r #-# 1/a ). The other results follow from this. Perihelion distance = a (1 #-# e ) and aphelion = a ( 1 + e )

Levi Alexander · Answer

undefined To calculate the speed of an object at its perihelion (closest point to the sun in its orbit), you can use Kepler's laws of planetary motion. Specifically, you can use the formula for orbital speed:

$$ v = \sqrt{\frac{GM(1 + e)}{a(1 - e)}} $$

Where:
- $ v $ is the orbital speed at perihelion,
- $ G $ is the gravitational constant ($6.67430 × 10^{-11} \, \text{m}^3 \, \text{kg}^{-1} \, \text{s}^{-2}$),
- $ M $ is the mass of the sun ($1.989 × 10^{30} \, \text{kg}$),
- $ e $ is the eccentricity of the orbit,
- $ a $ is the semi-major axis of the orbit.

The eccentricity of the orbit and the semi-major axis can be obtained from the object's orbital parameters.