  Exoplanets can evolve significantly between birth and maturity, as their
atmospheres, orbits, and structures are shaped by their environment. Young
planets ($<$1 Gyr) offer an opportunity to probe the critical early stages of
this evolution, where planets evolve the fastest. However, most of the known
young planets orbit prohibitively faint stars. We present the discovery of two
planets transiting HD 63433 (TOI 1726, TIC 130181866), a young Sun-like
($M_*=0.99\pm0.03$) star. Through kinematics, lithium abundance, and rotation,
we confirm that HD 63433 is a member of the Ursa Major moving group
($\tau=414\pm23$ Myr). Based on the TESS light curve and updated stellar
parameters, we estimate the planet radii are $2.15\pm0.10R_\oplus$ and
$2.67\pm0.12R_\oplus$, the orbital periods are 7.11 and 20.55 days, and the
orbital eccentricities are lower than about 0.2. Using HARPS-N velocities, we
measure the Rossiter-McLaughlin signal of the inner planet, demonstrating that
the orbit is prograde. Since the host star is bright (V=6.9), both planets are
amenable to transmission spectroscopy, radial velocity measurements of their
masses, and more precise determination of the stellar obliquity. This system is
therefore poised to play an important role in our understanding of planetary
system evolution in the first billion years after formation.
