Solving for Mercury's Perihelion Distance

[Kinash]

I have been struggling with this particular problem related to gravity.

Homework Statement

Mercury's orbital speed varies from 38.8 km/s at aphelion to 59.0 km/s at perihelion. If the planet is 6.99x10^10m from the sun's center at aphelion, how far is it at perihelion.

Homework Equations

Pe+Ke=constant

Pe= (-Gm₁m₂)/r²


Sun mass = 1.99x10³⁰kg
Sun Mean Radius= 696x10m
Sun surface gravity=274m/s²
Sun Mean distance from central body=2.6x10¹⁷km

Mercury mass = .330x10²⁴kg
Mercury mean Radius = 2.44x10⁶m
Mercury Surface Gravity = 3.7m/s²
Mercury Mean dist. from central body = 57.6x10⁶km

 

[rl.bhat]

According to Kepler's Law, when a planet is orbiting around the sun its areal velocity remains constant. So what is the formula for the areal velocity?