def R_hill(mp, m_st, a_r,rp):
    """
    compute the hill radius of a planet
    
    Parameters:
    ----------
    
    mp: array-like;
        mass of the planet in same unit as m_st
        
    m_st: array-like;
        mass of the star
        
    a_r: array-like;
        scaled semi-major axis
    
    rp: array_like;
        ratio of planetary radius to stellar radius
        
    Returns
    --------
    
    R-hill: array-like;
        radius of hill sphere in unit of planetary radius
    
    """
    return ( mp/(3*m_st) )**(1/3.) * a_r/rp