If by “2 km larger” you mean that the new orbit has a semi-major axis 2 km larger than the original orbit, then
a₂ = a₁ + 2 km.
Since e, i, ω, and Ω remain unchanged, the orientation of the orbit is unchanged. What needs to change is the spacecraft’s orbital energy.
The starting point is the vis-viva equation:
v² = μ(2/r − 1/a)
where a is the semi-major axis, r is the spacecraft’s distance from the central body, and μ = GM is the gravitational parameter.
If the original and final orbits are circular, then this becomes a standard Hohmann transfer. Let
r₂ = r₁ + 2 km.
The first burn moves the spacecraft from the original circular orbit onto the transfer ellipse:
Δv₁ = √(μ/r₁) [√(2r₂/(r₁ + r₂)) − 1]
At r₂, the second burn circularizes the orbit:
Δv₂ = √(μ/r₂) [1 − √(2r₁/(r₁ + r₂))]
Therefore, the total required velocity change is
Δv(total) = Δv₁ + Δv₂.
So, knowing only that the new orbit is “2 km larger” is not enough to calculate a numerical Δv. You also need the original orbital radius (or semi-major axis) and the gravitational parameter μ of the body being orbited.
If the original orbit is elliptical rather than circular, the calculation depends additionally on where the burns are performed, but the same vis-viva equation is the starting point.
