How can I save appointment information in real-time database using flutter and attach the uid?

I am using a calendar widget in booking an appointment and would love to save the appointment information in real-time database. Any help is highly appreciated. Below is the sample code:

      body: Column(
        children: [
          TableCalendar(
            focusedDay: selectedDay,
            firstDay: DateTime(1990),
            lastDay: DateTime(2100),
            calendarFormat: format,
            //changing the date
            onFormatChanged: (CalendarFormat _format) {
              setState(() {
                format = _format;
              });
            },
            startingDayOfWeek: StartingDayOfWeek.sunday,
            daysOfWeekVisible: true,
            onDaySelected: (DateTime selectDay, focusDay) {
              setState(() {
                selectedDay = selectDay;
                focusedDay = focusDay;
              });
              print(focusedDay);
            },
            selectedDayPredicate: (DateTime date) {
              return isSameDay(selectedDay, date);
            },
            eventLoader: _getEventsFromDay,
            //Styling the calendar
            calendarStyle: CalendarStyle(
              isTodayHighlighted: true,
              selectedDecoration: BoxDecoration(
                color: Colors.deepOrange,
                shape: BoxShape.rectangle,
                borderRadius: BorderRadius.circular(5.0),
              ),
              selectedTextStyle: const TextStyle(color: Colors.white),
              todayDecoration: BoxDecoration(
                color: Colors.blue,
                shape: BoxShape.rectangle,
                borderRadius: BorderRadius.circular(5.0),
              ),
              defaultDecoration: BoxDecoration(
                shape: BoxShape.rectangle,
                borderRadius: BorderRadius.circular(5.0),
              ),
              weekendDecoration: BoxDecoration(
                shape: BoxShape.rectangle,
                borderRadius: BorderRadius.circular(5.0),
              ),
            ),
            headerStyle: HeaderStyle(
              formatButtonVisible: true,
              titleCentered: true,
              formatButtonShowsNext: false,
              formatButtonDecoration: BoxDecoration(
                color: Colors.deepOrange,
                borderRadius: BorderRadius.circular(5.0),
              ),
              formatButtonTextStyle: const TextStyle(
                color: Colors.white,
              ),
            ),
          ),
          ..._getEventsFromDay(selectedDay).map(
            (Event event) => ListTile(
              title: Text(event.title),
            ),
          ),
        ],
      ),
      floatingActionButton: FloatingActionButton.extended(
        onPressed: () => showDialog(
          context: context,
          builder: (context) => AlertDialog(
            title: const Text('Add an appointment'),
            content: TextFormField(
              controller: _appointmentController,
              minLines: 2,
              maxLines: 5,
            ),
            actions: [
              TextButton(
                onPressed: () => Navigator.pop(context),
                child: const Text(
                  'Cancel',
                ),
              ),
              TextButton(
                onPressed: () {
                  if (_appointmentController.text.isEmpty) {
                  } else {
                    if (selectedEvents[selectedDay] != null) {
                      selectedEvents[selectedDay]?.add(
                        Event(title: _appointmentController.text),
                      );
                    } else {
                      selectedEvents[selectedDay] = [
                        Event(title: _appointmentController.text),
                      ];
                    }
                  }
                  Navigator.pop(context);
                  _appointmentController.clear();
                  setState(() {
                    
                  });
                  return;
                },
                child: const Text(
                  'Ok',
                ),
              ),
            ],
          ),
        ),
        label: const Text(
          'Add Appointment',
        ),
        icon: const Icon(Icons.add),
      ),
    );
  }

Is there a way I can be able to store the appointment date to real-time firebase and use the uid to save the different users' appointment dates in an organized manner?